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Physical Review A

(Atomic, Molecular, and Optical Physics)

August 2006

Volume 74, Number 2 , Articles (02xxxx)

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RAPID COMMUNICATIONS

Fundamental concepts
Rapid

Exact Casimir interaction between eccentric cylinders
D. A. R. Dalvit, F. C. Lombardo, F. D. Mazzitelli, and R. Onofrio
Published 1 August 2006 (4 pages)
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The Casimir force is the ultimate background in ongoing searches for extragravitational forces in the micrometer range. Eccentric cylinders offer favorable experimental conditions for such measurements as spurious gravitational and electrostatic effects can be minimized. Here we report on the evaluation of the exact Casimir interaction between perfectly conducting eccentric cylinders using a mode summation technique, and study different limiting cases of relevance for Casimir force measurements, with potential implications for the understanding of mechanical properties of nanotubes.
Rapid

Decoherence and quantum walks: Anomalous diffusion and ballistic tails
N. V. Prokof'ev and P. C. E. Stamp
Published 23 August 2006 (4 pages)
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The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasiclassical (in fact, diffusive) in the long time limit. We present here a counterexample, in which a particle makes quantum transitions between the sites of a d-dimensional hypercubic lattice while strongly coupled to a bath of two-level systems that "record" the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballistic behavior, with <n2>~t2, but simultaneously a kind of weakly localized behavior near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks.

Quantum information
Rapid

Fidelity estimation and entanglement verification for experimentally produced four-qubit cluster states
Yuuki Tokunaga, Takashi Yamamoto, Masato Koashi, and Nobuyuki Imoto
Published 23 August 2006 (4 pages)
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We propose methods of fidelity estimation and entanglement verification for experimentally produced four-qubit cluster states. We show that we can obtain a high lower bound of the fidelity using only four local projective measurement settings. The lower bound is close to the exact fidelity, which is determined only by at least nine local projective measurement settings. We also present witness operators for distinguishing entanglement around a four-qubit cluster state from specific classes of genuine four-qubit entanglement, e.g., a class including GHZ and W types of entanglement.
Rapid

Experimental implementation of high-fidelity unconventional geometric quantum gates using an NMR interferometer
Jiangfeng Du, Ping Zou, and Z. D. Wang
Published 23 August 2006 (4 pages)
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Following a key idea of unconventional geometric quantum computation developed earlier [S. L. Zhu and Z. D. Wang, Phys. Rev. Lett. 91, 187902 (2003)], here we propose a more general scheme in such an intriguing way: gammad=alphag+etagammag, where gammad and gammag are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with eta as a constant and alphag being dependent only on the geometric feature of the operation. More interestingly, we demonstrate an experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system.

Atomic and molecular structure and dynamics
Rapid

Relativistic coupled-cluster theory of quadrupole moments and hyperfine structure constants of 5d states in Ba+
Bijaya Kumar Sahoo
Published 23 August 2006 (4 pages)
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The narrow optical frequency resonances of the 6s  2S1/2-->5d  2D3/2 and 6s  2S1/2-->5d  2D5/2 forbidden transitions in Ba+ have been proposed as suitable frequencies for a new optical frequency standard. The major sources of errors in measurements of singly ionized systems are due to the quadratic Zeeman and electric quadrupole shifts. We report here the most accurate calculations to date for the hyperfine structure constants and electric-quadrupole moments of the 5d  2D3/2 and 5d  2D5/2 states in Ba+, which determine the quadratic Zeeman and electric quadrupole shifts. Relativistic coupled-cluster theory has been employed to calculate these quantities and large electron correlation effects are observed. It is also shown that for the high accuracy calculation of the 5d  2D5/2 state in Ba+, all order core polarization effects play a significant role.
Rapid

Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks
Sergey G. Porsev and Andrei Derevianko
Published 30 August 2006 (4 pages)
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Blackbody radiation (BBR) shifts of the 3P0-1S0 clock transition in the divalent atoms Mg, Ca, Sr, and Yb are evaluated. The dominant electric-dipole contributions are computed using accurate relativistic many-body techniques of atomic structure. At room temperatures, the resulting uncertainties in the E1 BBR shifts are large and substantially affect the projected 10–18 fractional accuracy of the optical-lattice-based clocks. A peculiarity of these clocks is that the characteristic BBR wavelength is comparable to the 3P fine-structure intervals. To evaluate relevant M1 and E2 contributions, a theory of multipolar BBR shifts is developed. The resulting corrections, although presently masked by the uncertainties in the E1 contribution, are required at the 10–18 accuracy goal.

Atomic and molecular collisions and interactions
Rapid

Cold Cs Rydberg-gas interactions
Arne Schwettmann, Jeff Crawford, K. Richard Overstreet, and James P. Shaffer
Published 25 August 2006 (4 pages)
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We present calculations of potential curves for very high-n (89D) Cs Rydberg-atom pairs, including a background electric field. From these potentials, we show that energy transfer occurs at rates of ~30–70  MHz, background electric fields play an important role and dipole-dipole- and quadrupole-quadrupole-induced avoided curve crossings should lead to conversion of electronic to kinetic energy, n-changing collisions, and observable ultracold long-range Rydberg molecules.

Matter waves
Rapid

Beaming matter waves from a subwavelength aperture
A. I. Fernández-Domínguez, Esteban Moreno, L. Martín-Moreno, and F. J. García-Vidal
Published 17 August 2006 (4 pages)
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We show theoretically that the shape of a beam of matter waves (cold atoms) emerging from one subwavelength aperture pierced in a film can be collimated within a few degrees. By means of an external laser field, a potential well for the atoms in the direction perpendicular to the surface is created. In this way, a running surface matter wave can be excited when atoms diffract from the aperture. If the aperture is surrounded with a finite array of indentations, coherent scattering of the surface matter wave with these indentations molds the angular distribution of the matter wave in the far field.
Rapid

Finite temperature effects in trapped Fermi gases with population imbalance
Chih-Chun Chien, Qijin Chen, Yan He, and K. Levin
Published 24 August 2006 (4 pages)
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We study the finite temperature T behavior of trapped Fermi gases as they undergo BCS–Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at T[not-equal]0 and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the "pseudogap phase."

Quantum optics, physics of lasers, nonlinear optics
Rapid

Sagnac effect in resonant microcavities
Satoshi Sunada and Takahisa Harayama
Published 10 August 2006 (4 pages)
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The Sagnac effect in two-dimensional resonant microcavities is studied theoretically and numerically. The frequency shift due to the Sagnac effect occurs as a threshold phenomenon for the angular velocity in a rotating microcavity. Above the threshold, the eigenfunctions of a rotating microcavity become rotating waves while they are standing waves below the threshold.
Rapid

Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity
Thomas Corbitt, David Ottaway, Edith Innerhofer, Jason Pelc, and Nergis Mavalvala
Published 15 August 2006 (4 pages)
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We report on experimental observation of radiation-pressure induced effects in a high-power optical cavity. These effects play an important role in next-generation gravitational wave detectors, as well as in quantum nondemolition interferometers. We measure the properties of an optical spring, created by coupling of an intense laser field to the pendulum mode of a suspended mirror, and also the parametric instability (PI) that arises from the coupling between acoustic modes of the cavity mirrors and the cavity optical mode. We measure an unprecedented optical rigidity of K=(3.08±0.09)×104  N/m, corresponding to an optical rigidity that is 6000 times stiffer than the mechanical stiffness, and PI strength R[approximate]3. We measure the unstable nature of the optical spring resonance, and demonstrate that the PI can be stabilized by feedback to the frequency of the laser source.

ARTICLES

Fundamental concepts

Greenberger-Horne-Zeilinger argument of nonlocality without inequalities for mixed states
GianCarlo Ghirardi and Luca Marinatto
Published 3 August 2006 (6 pages)
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We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball (in the trace distance topology) surrounding the pure GHZ state and containing arbitrary mixed statistical operators which cannot be described by any local and realistic hidden variable model and which are, as a consequence, noncompletely separable. As a practical application, we focus on certain one-parameter classes of mixed states which are commonly considered in the experimental realization of the original GHZ argument and which result from imperfect preparations of the pure GHZ state. In these cases we determine for which values of the parameter measuring the noise a nonlocality argument can still be exhibited, despite the mixedness of the considered states. Moreover, the effect of the imperfect nature of measurement processes is discussed.

Quantum dynamics in fluctuating traps: Master equation, decoherence, and heating
Thimo Grotz, Libby Heaney, and Walter T. Strunz
Published 8 August 2006 (16 pages)
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We present a remarkably simple derivation of an exact time-local master equation describing the dynamics of quantum states in harmonic traps subject to arbitrary fluctuating forces. The relation between our master equation and known master equations of irreversible harmonic oscillator dynamics are established. Motivated by recent experiments, we focus on decoherence and in particular on the precise decoherence dynamics of a superposition of wave packets. We determine the decaying purity resulting from the time evolution based on our master equation and study its connection to experimentally accessible observables. Finally, we discuss the heating of the system subjected to arbitrary Gaussian noise.

Experimental test for the conductivity properties from the Casimir force between metal and semiconductor
F. Chen, U. Mohideen, G. L. Klimchitskaya, and V. M. Mostepanenko
Published 11 August 2006 (14 pages)
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The experimental investigation of the Casimir force between a large metallized sphere and semiconductor plate is performed using an atomic force microscope. Improved calibration and measurement procedures permitted a reduction in the role of different uncertainties. Rigorous statistical procedures are applied for the analysis of random, systematic, and total experimental errors at 95% confidence. The theoretical Casimir force is computed for semiconductor plates with different conductivity properties, taking into account all theoretical uncertainties discussed in the literature. The comparison between experiment and theory is done at both 95% and 70% confidence. It is demonstrated that the theoretical results computed for the semiconductor plate used in experiment are consistent with the data. At the same time, the theory describing a dielectric plate is excluded by experiment at 70% confidence. Thus, the Casimir force is proved to be sensitive to the conductivity properties of semiconductors.

Greenberger-Horne-Zeilinger–type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting
Hyunseok Jeong and Nguyen Ba An
Published 17 August 2006 (8 pages)
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We study Greenberger-Horne-Zeilinger–type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

Role of the electromagnetic field in the formation of domains in the process of symmetry-breaking phase transitions
Emilio Del Guidice and Giuseppe Vitiello
Published 22 August 2006 (9 pages)
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In the framework of quantum field theory we discuss the emergence of a phase locking among the electromagnetic modes and the matter components on an extended space-time region. We discuss the formation of extended domains exhibiting in their fundamental states nonvanishing order parameters, whose existence is not included in the Lagrangian. Our discussion is motivated by the interest in the study of the general problem of the stability of mesoscopic and macroscopic complex systems arising from fluctuating quantum components in connection with the problem of defect formation during the process of non-equilibrium symmetry breaking phase transitions characterized by an order parameter.

Noncyclic geometric changes of quantum states
David Kult, Johan Åberg, and Erik Sjöqvist
Published 25 August 2006 (5 pages)
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Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.

Quantum information

Spin decoherence from Hamiltonian dynamics in quantum dots
D. D. Bhaktavatsala Rao, V. Ravishankar, and V. Subrahmanyam
Published 1 August 2006 (11 pages)
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The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a Gaussian decay, and at later times it is revived displaying nonmonotonic time dependence. The decoherence time scale depends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be described by a master equation with non-Markovian features.

Relation between two measures of entanglement in spin-1/2 and spinless fermion quantum chain systems
Xiao-Feng Qian and Z. Song
Published 2 August 2006 (6 pages)
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The concepts of concurrence and mode concurrence are the measures of entanglement for spin-1/2 and spinless fermion systems, respectively. Based on the Jordan-Wigner transformation, any spin-1/2 system is always associated with a fermion system (called the counterpart system). A comparison of concurrence and mode concurrence can be made with the aid of Marshall's sign rule for the ground states of spin-1/2 XXZ and spinless fermion chain systems. We observe that there exists an inequality between concurrence and mode concurrence for the ground states of the two corresponding systems. The spin-1/2 XY chain system and its spinless fermion counterpart as a realistic example are discussed to demonstrate the analytical results.

Experimental quantum teleportation with a three-Bell-state analyzer
J. A. W. van Houwelingen, A. Beveratos, N. Brunner, N. Gisin, and H. Zbinden
Published 3 August 2006 (12 pages)
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We present a Bell-state analyzer for time-bin qubits allowing the detection of three out of four Bell states with linear optics, two detectors, and no auxiliary photons. The theoretical success rate of this scheme is 50%. A teleportation experiment was performed to demonstrate its functionality. We also present a teleportation experiment with a fidelity larger than the cloning limit of F=(5/6).

Experimentally realizable quantum comparison of coherent states and its applications
Erika Andersson, Marcos Curty, and Igor Jex
Published 3 August 2006 (11 pages)
022304  Full Text: PDF (207 kB)  | Buy Article
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When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent states, which is the simplest example of quantum state comparison for continuous variables. The method we present has a high success probability, and is experimentally feasible to realize as the only required components are beam splitters and photon detectors. An easily realizable method for quantum state comparison could be important for real applications. As examples of such applications we present a "lock and key" scheme and a simple scheme for quantum public key distribution.

Detecting a set of entanglement measures in an unknown tripartite quantum state by local operations and classical communication
Yan-Kui Bai, Shu-Shen Li, Hou-Zhi Zheng, and Z. D. Wang
Published 4 August 2006 (8 pages)
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We propose a more general method for detecting a set of entanglement measures, i.e., negativities, in an arbitrary tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers do not need to perform partial transposition maps by the structural physical approximation; instead, they only need to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state.

Quantum optimal control theory and dynamic coupling in the spin-boson model
H. Jirari and W. Pötz
Published 7 August 2006 (18 pages)
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A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum Z gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.

Practical evaluation of security for quantum key distribution
Masahito Hayashi
Published 7 August 2006 (19 pages)
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Many papers have proven the security of quantum key distribution (QKD) systems in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system required, it is needed to evaluate a protocol with a finite coding length. For this purpose, we derive a tight upper bound of the eavesdropper's information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper's information. Further, we approximate our bound by using the normal distribution.

Class of positive partial transposition states
Dariusz Chruscinski and Andrzej Kossakowski
Published 7 August 2006 (4 pages)
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We construct a class of quantum bipartite d[direct-product]d states which are positive under partial transposition (PPT states). This class is invariant under the maximal commutative subgroup of U(d) and contains as special cases many well-known examples of PPT states. States from our class provide criteria for testing the indecomposability of positive maps. Such maps are crucial for constructing entanglement witnesses.

Experimental polarization state tomography using optimal polarimeters
Alexander Ling, Kee Pang Soh, Antía Lamas-Linares, and Christian Kurtsiefer
Published 8 August 2006 (7 pages)
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We report on the experimental implementation of a polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-(1/2) quantum systems and the alignment procedure for this polarimeter. We also show how to use this polarimeter to estimate the polarization state for identically prepared ensembles of single photons and photon pairs and extend the method to obtain the density matrix for generic multiphoton states. State reconstruction and performance of the polarimeter is illustrated by actual measurements on identically prepared ensembles of single photons and polarization entangled photon pairs.

Quantum walks with random phase shifts
Jozef Kosík, Vladimír Buzek, and Mark Hillery
Published 9 August 2006 (9 pages)
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We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail the role of decoherence in quantum walks and to investigate the quantum-to-classical transition. We also provide classical analog of the quantum random walks studied. Interestingly enough, it turns out that the classical counterparts of some quantum random walks are classical random walks with a memory and biased coin. In addition random phase shifts "simplify" the dynamics (the cross-interference terms of different paths vanish on average) and enable us to give a compact formula for the dispersion of such walks.

Quantum memory scheme based on optical fibers and cavities
Patrick M. Leung and Timothy C. Ralph
Published 10 August 2006 (6 pages)
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An optical quantum memory scheme using two narrow-linewidth cavities and some optical fibers is proposed. The cavities are connected via an optical fiber, and the gap of each cavity can be adjusted to allow photons with a certain bandwidth to transmit through or reflect back. Hence, each cavity acts as a shutter and the photons can be stored in the optical fiber between the cavities at will. We investigate the feasibility of using this device in storing a single photon. We estimate that with current technology storage of a photon qubit for up to 50 clock cycles (round trips) could be achieved with a probability of success of 85%. We discuss how this figure could be improved.

Microwave potentials and optimal control for robust quantum gates on an atom chip
Philipp Treutlein, Theodor W. Hänsch, Jakob Reichel, Antonio Negretti, Markus A. Cirone, and Tommaso Calarco
Published 15 August 2006 (13 pages)
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We propose a two-qubit collisional phase gate that can be implemented with available atom chip technology and present a detailed theoretical analysis of its performance. The gate is based on earlier phase gate schemes, but uses a qubit state pair with an experimentally demonstrated, very long coherence lifetime. Microwave near fields play a key role in our implementation as a means to realize the state-dependent potentials required for conditional dynamics. Quantum control algorithms are used to optimize gate performance. We employ circuit configurations that can be built with current fabrication processes and extensively discuss the impact of technical noise and imperfections that characterize an actual atom chip. We find an overall infidelity compatible with requirements for fault-tolerant quantum computation.

Effects of detector efficiency mismatch on security of quantum cryptosystems
Vadim Makarov, Andrey Anisimov, and Johannes Skaar
Published 17 August 2006 (11 pages)
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We suggest a type of attack on quantum cryptosystems that exploits variations in detector efficiency as a function of a control parameter accessible to an eavesdropper. With gated single-photon detectors, this control parameter can be the timing of the incoming pulse. When the eavesdropper sends short pulses using the appropriate timing so that the two gated detectors in Bob's setup have different efficiencies, the security of quantum key distribution can be compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84) protocol that if the efficiency mismatch between 0 and 1 detectors for some value of the control parameter gets large enough (roughly 15:1 or larger), Eve can construct a successful faked-states attack causing a quantum bit error rate lower than 11%. We also derive a general security bound as a function of the detector sensitivity mismatch for the BB84 protocol. Experimental data for two different detectors are presented, and protection measures against this attack are discussed.

Operational classification and quantification of multipartite entangled states
Gustavo Rigolin, Thiago R. de Oliveira, and Marcos C. de Oliveira
Published 18 August 2006 (13 pages)
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We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.

Deterministic secure communications using two-mode squeezed states
Alberto M. Marino and C. R. Stroud, Jr.
Published 18 August 2006 (5 pages)
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We propose a scheme for quantum cryptography that uses the squeezing phase of a two-mode squeezed state to transmit information securely between two parties. The basic principle behind this scheme is the fact that each mode of the squeezed field by itself does not contain any information regarding the squeezing phase. The squeezing phase can only be obtained through a joint measurement of the two modes. This, combined with the fact that it is possible to perform remote squeezing measurements, makes it possible to implement a secure quantum communication scheme in which a deterministic signal can be transmitted directly between two parties while the encryption is done automatically by the quantum correlations present in the two-mode squeezed state.

Optimal partial estimation of quantum states from several copies
Ladislav Mista, Jr. and Jaromír Fiurásek
Published 22 August 2006 (5 pages)
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We derive an analytical formula for the optimal trade-off between the mean estimation fidelity and the mean fidelity of the qubit state after a partial measurement on N identically prepared qubits. We also conjecture an analytical expression for the optimal fidelity trade-off in case of a partial measurement on N identical copies of a d-level system.

Generalized decoding, effective channels, and simplified security proofs in quantum key distribution
Joseph M. Renes and Markus Grassl
Published 23 August 2006 (9 pages)
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Prepare and measure quantum key distribution protocols can be decomposed into two basic steps: delivery of the signals over a quantum channel and distillation of a secret key from the signal and measurement records by classical processing and public communication. Here we formalize the distillation process for a general protocol in a purely quantum-mechanical framework and demonstrate that it can be viewed as creating an "effective" quantum channel between the legitimate users Alice and Bob. The process of secret key generation can then be viewed as entanglement distribution using this channel, which enables application of entanglement-based security proofs to essentially any prepare and measure protocol. To ensure secrecy of the key, Alice and Bob must be able to estimate the channel noise from errors in the key, and we further show how symmetries of the distillation process simplify this task. Applying this method, we prove the security of several key distribution protocols based on equiangular spherical codes.

Group-theoretical approach to entanglement
J. K. Korbicz and M. Lewenstein
Published 23 August 2006 (8 pages)
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We present a universal description of quantum entanglement using group theory and noncommutative characteristic functions. It leads to reformulations of the separability problem, which allows us to generalize the latter, thus connecting the theory of entanglement and harmonic analysis. As an example, we translate and analyze the positivity of partial transpose criterion and a simple criterion for pure states into the group-theoretical language. We also show that when applied to finite groups, our formalism embeds the separability problem in a given dimension into a higher dimensional but highly symmetric one. Finally, our formalism reveals a connection between the very existence of entanglement and group noncommutativity.

Optimal control of a single qubit by direct inversion
M. Wenin and W. Pötz
Published 23 August 2006 (13 pages)
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Optimal control of a driven single dissipative qubit is formulated as an inverse problem. We show that direct inversion is possible which allows an analytic construction of optimal control fields. Exact inversion is shown to be possible for dissipative qubits which can be described by a Lindblad equation. It is shown that optimal solutions are not unique. For a qubit with weak coupling to phonons we choose, among the set of exact solutions for the dissipationless qubit, one which minimizes the dissipative contribution in the kinetic equations. Examples are given for state trapping and Z-gate operation. Using analytic expressions for optimal control fields, favorable domains for dynamic stabilization in the Bloch sphere are identified. In the case of approximate inversion, the identified approximate solution may be used as a starting point for further optimization following standard methods.

Classical simulation of quantum many-body systems with a tree tensor network
Y.-Y. Shi, L.-M. Duan, and G. Vidal
Published 23 August 2006 (4 pages)
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We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Single atom as a macroscopic entanglement source
Ling Zhou, Han Xiong, and M. Suhail Zubairy
Published 24 August 2006 (5 pages)
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We discuss the generation of a macroscopic entangled state in a single atom cavity-QED system. The three-level atom in a cascade configuration interacts dispersively with two classical coherent fields inside a doubly resonant cavity. We show that a macroscopic entangled state between these two cavity modes can be generated under large detuning conditions. The entanglement persists even under the presence of cavity losses.

Divergence of the entanglement range in low-dimensional quantum systems
L. Amico, F. Baroni, A. Fubini, D. Patanè, V. Tognetti, and Paola Verrucchi
Published 25 August 2006 (5 pages)
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We study the pairwise entanglement close to separable ground states of a class of one-dimensional quantum spin models. At T=0 we find that such ground states separate regions, in the space of the Hamiltonian parameters, which are characterized by qualitatively different types of entanglement, namely parallel and antiparallel entanglement; we further demonstrate that the range of the concurrence diverges while approaching separable ground states, therefore evidencing that such states, with uncorrelated fluctuations, are reached by a long range reshuffling of the entanglement. We generalize our results to the analysis of quantum phase transitions occurring in bosonic and fermionic systems. Finally, the effects of finite temperature are considered: At T>0 we evidence the existence of a region where no pairwise entanglement survives, so that entanglement, if present, is genuinely multipartite.

Engineering of arbitrary U(N) transformations by quantum Householder reflections
P. A. Ivanov, E. S. Kyoseva, and N. V. Vitanov
Published 25 August 2006 (8 pages)
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We propose a simple physical implementation of the quantum Householder reflection (QHR) M(v)=I–2|v><v| in a quantum system of N degenerate states (forming a qunit) coupled simultaneously to an ancillary (excited) state by N resonant or nearly resonant pulsed external fields. We also introduce the generalized QHR M(v;phi)=I+(eiphi–1)|v><v|, which can be produced in the same N-pod system when the fields are appropriately detuned from resonance with the excited state. We use these two operators as building blocks in constructing arbitrary preselected unitary transformations. We show that the most general U(N) transformation can be factorized (and thereby produced) by either N–1 standard QHRs and an N-dimensional phase gate, or N–1 generalized QHRs and a one-dimensional phase gate. Viewed mathematically, these QHR factorizations provide parametrizations of the U(N) group. As an example, we propose a recipe for constructing the quantum Fourier transform (QFT) by at most N interaction steps. For example, the QFT requires a single QHR for N=2, and only two QHRs for N=3 and 4.

Scaling behavior of the adiabatic Dicke model
Giuseppe Liberti, Francesco Plastina, and Franco Piperno
Published 28 August 2006 (4 pages)
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We analyze the quantum phase transition for a set of N two-level systems interacting with a bosonic mode in the adiabatic regime. Through the Born-Oppenheimer approximation, we obtain the finite-size scaling expansion for many physical observables and, in particular, for the entanglement content of the system.

Optical implementation of the encoding of two qubits to a single qutrit
Lucie Bartusková, Antonín Cernoch, Radim Filip, Jaromír Fiurásek, Jan Soubusta, and Miloslav Dusek
Published 28 August 2006 (6 pages)
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We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore either of the two encoded qubit states error-free but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables us to retrieve both qubits simultaneously with average fidelity above 90% and we have proposed an extension of the original encoding transformation to encode N qubits into one (N+1)-dimensional system.

Entanglement and the lower bounds on the speed of quantum evolution
A. Borrás, M. Casas, A. R. Plastino, and A. Plastino
Published 28 August 2006 (8 pages)
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The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state psiI may need so as to evolve into a state orthogonal to itself. Recently [V. Giovanetti, S. Lloyd, and L. Maccone, Phys. Rev. A 67, 052109 (2003)] this bound has been generalized to the case where psiI does not necessarily evolve into an orthogonal state, but into any other psiF. It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution "speed" of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with psiF a not necessarily orthogonal state to psiI. We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.

Entanglement properties of quantum spin chains
Stein Olav Skrøvseth
Published 29 August 2006 (5 pages)
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We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.

Decoherence effects on the quantum spin channels
Jian-Ming Cai, Zheng-Wei Zhou, and Guang-Can Guo
Published 29 August 2006 (6 pages)
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An open ended spin chain can serve as a quantum data bus for the coherent transfer of quantum state information. In this paper, we investigate the efficiency of such quantum spin channels which work in a decoherence environment. Our results show that the decoherence will significantly reduce the fidelity of quantum communication through the spin channels. Generally speaking, as the distance increases, the decoherence effects become more serious, which will put some constraints on the spin chains for long distance quantum state transfer.

Entanglement scaling in critical two-dimensional fermionic and bosonic systems
T. Barthel, M.-C. Chung, and U. Schollwöck
Published 29 August 2006 (5 pages)
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We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way and calculate the scaling of the entanglement entropy of finite systems in an infinite universe exactly. For critical fermionic two-dimensional (2D) systems at T=0, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, then we find an area law with a sublogarithmic correction. For a critical bosonic 2D array of coupled oscillators at T=0, our results show that the entanglement entropy follows the area law without corrections.

Quantum computing with magnetic atoms in optical lattices of reduced periodicity
Boris Ravaine, Andrei Derevianko, and P. R. Berman
Published 29 August 2006 (6 pages)
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We investigate the feasibility of combining Raman optical lattices with a quantum computing architecture based on lattice-confined magnetically interacting neutral atoms. A particular advantage of the standing Raman field lattices comes from reduced interatomic separations leading to increased interatomic interactions and improved multiqubit gate performance. Specifically, we analyze a J=3/2 Zeeman system placed in sigma+-sigma– Raman fields which exhibit lambda/4 periodicity. We find that the resulting controlled-NOT (CNOT) gate operations times are in the order of millisecond. We also investigate motional and magnetic-field induced decoherences specific to the proposed architecture.

Quantum entanglement via nilpotent polynomials
Aikaterini Mandilara, Vladimir M. Akulin, Andrei V. Smilga, and Lorenza Viola
Published 30 August 2006 (34 pages)
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We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.

Secure quantum bit commitment against empty promises
Guang Ping He
Published 31 August 2006 (6 pages)
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The existence of unconditionally secure quantum bit commitment (QBC) is excluded by the Mayers-Lo-Chau no-go theorem. Here we look for the second-best: a QBC protocol that can defeat certain quantum attacks. By breaking the knowledge symmetry between the participants with quantum algorithm, a QBC protocol is proposed and is proven to be secure against a major kind of coherent attacks—the dummy attack, in which the participant makes an empty promise instead of committing to a specific bit. Therefore it surpasses previous QBC protocols which are secure against individual attacks only.

Atomic and molecular structure and dynamics

Laser-assisted antihydrogen formation
A. Chattopadhyay and C. Sinha
Published 1 August 2006 (11 pages)
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Laser-assisted antihydrogen ([overline H]) formation cross sections (differential and total) for collisions of antiprotons with positronium (Ps) are studied in the framework of the eikonal approximation for two geometries, when the field polarization is parallel (||L) or perpendicular ([perpendicular]r) to the incident Ps momentum. The variations of the [overline H] formation cross sections with respect to the field strength and the laser photon energy are studied for the multiphoton (absorption and emission) processes. The contribution of the atomic (both Ps and [overline H]) dressing terms to the enhancement of the [overline H] formation cross section is studied for both the geometries (||L and [perpendicular]r). The most important prediction from the present work is the enhancement of the field-free (FF) [overline H] formation cross sections particularly at lower incident energies when the system (Ps+[overline p]) is irradiated by a single mode, linearly polarized laser, the enhancement being more pronounced for a wider range of incident energy in the [perpendicular]r geometry than in the ||L one.

Ionic dipole and quadrupole matrix elements from nonadiabatic core polarization
E. S. Shuman and T. F. Gallagher
Published 2 August 2006 (9 pages)
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The radial matrix elements connecting the ionic Ba+6s ground state to low-lying excited 6p and 5d states can be extracted from the K splittings of the bound 6sn[script-l] states in much the same way that ionic polarizabilities are extracted from the separations between [script-l] states. We develop an expression for the K splitting by a pair of expansions which allows us to compare the contributions of different ionic states. This comparison confirms that all but the lowest two may be safely ignored. Finally, we extract the radial Ba+ matrix elements <6s|r|6p>=4.03(12) and <6s|r2|5d>=9.76(29) from the experimentally obtained K splittings.

Measurement of the 6d  2DJ hyperfine structure of cesium using resonant two-photon sub-Doppler spectroscopy
A. Kortyna, N. A. Masluk, and T. Bragdon
Published 3 August 2006 (6 pages)
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We report the hyperfine coupling constants for the 6d  2DJ states of 133Cs using two-color absorption spectroscopy with sub-Doppler resolution. Two single-mode diode lasers resonantly excite cesium in a low-pressure vapor cell. The frequency scale is directly referenced to the ground hyperfine interval of 87Rb using a radio-frequency modulation technique. The 6d  2D5/2 coupling constants are measured as A=–4.66±0.04  MHz and B=0.9±0.8  MHz, agreeing with the literature. The 6d  2D3/2 coupling constants are measured as A=16.34±0.03  MHz and B=–0.1±0.2  MHz, which significantly improve the precision of previous measurements.

Relativistic many-body calculations of the Stark-induced amplitude of the 6P1/2-7P1/2 transition in thallium
M. S. Safronova, W. R. Johnson, U. I. Safronova, and T. E. Cowan
Published 8 August 2006 (5 pages)
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Stark-induced amplitudes for the 6P1/2-7P1/2 transition in Tl  I are calculated using the relativistic singles-doubles (SD) approximation in which single and double excitations of Dirac-Hartree-Fock levels are summed to all orders in perturbation theory. Our SD values alphaS=368a0<sup>3</sup> and |betaS|=298a0<sup>3</sup> are in good agreement with the measurements alphaS=377(8)a0<sup>3</sup> and betaS=313(8)a0<sup>3</sup> by D. DeMille, D. Budker, and E. D. Commins [Phys. Rev. A 50, 4657 (1994)]. Calculations of the Stark shifts in the 6P1/2-7P1/2 and 6P1/2-7S1/2 transitions are also carried out. The Stark shifts predicted by our calculations agree with the most accurate measured values within the experimental uncertainties for both transitions.

High-resolution microwave-optical double-resonance spectroscopy of hyperfine splitting of trapped 113Cd+ ions
B. M. Jelenkovic, S. Chung, J. D. Prestage, and L. Maleki
Published 8 August 2006 (5 pages)
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We performed double resonance spectroscopy on the ground-state hyperfine splitting of 113Cd+ ions trapped in a rf linear trap. The ions were optically pumped by UV light from the 106Cd lamp and cooled by He buffer gas. The ground-state hyperfine splitting was measured to be 15  199  862  855  Hz with the precision of 1.3×10–11. The uncertainty stems from the error in extrapolation to zero magnetic field and from the resonance linewidth. This value is 3  Hz lower than the previous high-precision measurements by [Tanaka et al., Phys. Rev. A 53, 3982 (1996)], in which the laser light was used for optical excitation. The potential for a new microwave frequency standard based on the 15.2-GHz ground-state hyperfine splitting of 113Cd+ ions is also discussed. Stability of the hyperfine frequency of 113Cd+ ion, with microwaves locked to the hydrogen maser, is ~2×10–13tau–1/2.

Noncrossing theorem for the ground ensembles of systems with noninteger particle numbers
Espen Sagvolden
Published 16 August 2006 (6 pages)
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That the external potential vext(r-vector   ) of a system of electrons is determined uniquely by the ground-state density is one of the central statements of the first Hohenberg-Kohn theorem. It is known that the validity of this statement extends to densities n(r-vector   ) with noninteger particle number [i.e., n(r-vector   ) integrates to a number that is not an integer] if the functional derivative of Ts[n(r-vector   )]+U[n(r-vector   )]+Exc[n(r-vector   )] exists or (without relying on the existence of functional derivatives) if the ground-state energy is a strictly convex function of the particle number. In the present article, a proof that relies neither on the existence of the above functional derivative nor on the strict convexity of the ground-state energy is presented. The fact that the density determines the external potential leads to a noncrossing theorem for ground-state densities. The noncrossing theorem produces knowledge as to what the integer-particle-number ground-state densities of a system cannot be. The noncrossing theorem produces inequalities that the functional derivatives of the exchange-correlation energy functional Exc[n(r-vector   )] and the noninteracting kinetic energy functional Ts[n(r-vector   )] must fulfill.

Expectation value constraints for the N-representability problem
Neil Shenvi and K. Birgitta Whaley
Published 18 August 2006 (12 pages)
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It has long been known that reduced density matrices (RDM) can be used to obtain the exact ground state energy of many-particle Hamiltonians by performing a constrained minimization over the set of all N-representable reduced density matrices. In this paper, we present a set of N-representability constraints for both bosons and fermions based on expectation values. These expectation value constraints are derived from a simple yet nontrivial recursive formula, and can easily be included in RDM-based variational schemes. The expectation value constraints are shown to provide additional N-representability information when compared to existing N-representability constraints.

Hyperfine-structure splitting in beryllium-muonic ions and atoms
Alexei M. Frolov
Published 21 August 2006 (5 pages)
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The bound-state properties and hyperfine-structure splitting in the ground S(L=0) states in the 9Be4+µ–e– and 10Be4+µ–e– beryllium-muonic ions are determined numerically with the use of highly accurate variational-wave three-body functions. Analogous hyperfine splittings are computed for the triplet (electronic) 2  3S(L=0) states in the four-body beryllium-muonic ions 9Be4+µ–e2<sup>-</sup> and 10Be4+µ–e2<sup>-</sup> and for the ground states in the five-body beryllium-muonic atoms 9Be4+µ–e3<sup>-</sup> and 10Be4+µ–e3<sup>-</sup>.

Calculation of the fourth-rank nuclear magnetic hypershielding of some small molecules
G. I. Pagola, M. C. Caputo, M. B. Ferraro, and P. Lazzeretti
Published 22 August 2006 (7 pages)
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A computational scheme has been implemented to evaluate magnetic hypershielding at the nuclei of a molecule in the presence of an external spatially uniform, time-independent magnetic field, accounting for cubic response contributions via Rayleigh-Schrödinger perturbation theory. Numerical estimates have been obtained for hydrogen and heavier atoms in H2, HF, H2O, NH3, and CH4 molecules at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach. Gaugeless basis sets of increasing size and flexibility have been employed in a numerical test, to estimate the degree of convergence of theoretical tensor components. A further test for convergence has been carried out by evaluating properties for two different coordinate systems.

Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences
H. C. Ho, W. R. Johnson, S. A. Blundell, and M. S. Safronova
Published 24 August 2006 (9 pages)
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Third-order relativistic many-body perturbation theory (MBPT) is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented in this paper, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is the Dirac-Hartree-Fock potential VN–2, and B-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through the second order of perturbation theory, and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z=4–7, and for the magnesiumlike ion P  IV. The third-order excitation energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with second-order MBPT results, and with other calculations. The third-order energy correction is shown to be significant, improving the previous second-order calculations by an order of magnitude.

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory
Michael Mundt and Stephan Kümmel
Published 24 August 2006 (7 pages)
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The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential is analyzed.

alpha4[script R] corrections to singlet states of helium
Krzysztof Pachucki
Published 31 August 2006 (17 pages)
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Corrections of order alpha4[script R] are calculated for the singlet states 1  1S0 and 2  1S0 of the helium atom. The result for the 1  1S0 state is in slight disagreement with that of Korobov and Yelkhovsky [Phys. Rev. Lett. 87, 193003 (2001)]. The results obtained lead to a significant improvement of the transition frequencies between low-lying levels of the helium atom. In particular theoretical predictions for the 2  1S0-1  1S0 transition are found to be in disagreement with experimental values.

Atomic and molecular collisions and interactions

Multiple ionization of Ar by F– impact: Projectile-electron-loss and direct-ionization collision channels
M. M. Sant'Anna, F. Zappa, A. C. F. Santos, L. F. S. Coelho, W. Wolff, A. L. F. de Barros, and N. V. de Castro Faria
Published 1 August 2006 (8 pages)
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We have measured single- and multiple-target ionization cross sections for the F–+Ar collision system. Measurements of the final target and projectile charge states were performed in coincidence, separating the collision channels for single-, double-, and triple-projectile-electron loss and for direct ionization. The studied velocity region extends from v=0.46 to v=1.45 atomic units. Results are compared with existing H–+Ar data as well as with Ar multiple ionization by protons, electrons, and antiprotons. For the direct-ionization channel, ratios for multiple-to-single target ionization are similar to those found for H++Ar collisions. For this channel multiple ionization is well described by independent single-ionization events by a frozen projectile. For the projectile-electron-loss collision channels, on the other hand, the correlation between projectile electrons and target electrons plays an important role. Our data show that the average final charge state of the target, <q>, increases steeply with the final charge state of the projectile, while an independent-particle model (neglecting two-center electron-electron correlation) only accounts for small variations of <q>.

Comparative study for elastic electron collisions on C2N2 isomers
S. E. Michelin, A. S. Falck, K. T. Mazon, J. J. Piacentini, M. A. Scopel, L. S. S. da Silva, H. L. Oliveira, M. M. Fujimoto, I. Iga, and M.-T. Lee
Published 1 August 2006 (8 pages)
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In this work, we present a theoretical study on elastic electron collisions with the four C2N2 isomers. More specifically, calculated differential, integral, and momentum transfer cross sections are reported in the 1–100  eV energy range. Calculations are performed at both the static-exchange-absorption and the static-exchange-polarization-absorption levels. The iterative Schwinger variational method combined with the distorted wave approximation is used to solve the scattering equations. Our study reveals an interesting trend of the calculated cross sections for the four isomers. In particular, strong isomer effect is seen at low incident energies. Also, we have identified a shape resonance which leads to a depression in the calculated partial integral cross section.

Quantum state-to-state cross sections for atom-diatom reactions: A Chebyshev real wave-packet approach
Shi Ying Lin and Hua Guo
Published 1 August 2006 (8 pages)
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We describe the implementation of a quantum mechanical method to calculate state-to-state differential cross sections for atom-diatom reactive scattering processes. The key ingredient of this approach is the efficient and accurate propagation of a real scattering wave packet in the Chebyshev order domain, from which the S-matrix elements can be extracted. This approach is implemented with Open MP and applied to compute differential and integral cross sections for the direct H+H2 abstraction reaction and the more challenging N(2D)+H2 insertion reaction.

Resonant photoionization of singly charged sulfur
S. S. Tayal
Published 2 August 2006 (11 pages)
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Resonance structures in the photoionization of S+ for the removal of a 3p or 3s electron from the ground 3s23p3 4So and excited metastable 2Do and 2Po states have been studied in the B-spline R-matrix approach. The nonorthogonal orbitals have been used for an accurate representation of the initial S+ bound states, the final S2+ ion plus photoelectron states and S2+ thresholds. Calculations have been carried out in 17- and 27-state close-coupling approximations. The relativistic effects have been incorporated in the Breit-Pauli Hamiltonian. Photoionization cross sections are dominated by 3s23p2(1D)ns 2D, 3s23p2(1D)nd 2F, 2D, 2P, and 3s3p3(5So, 3So, 3Do, 3Po)np 4P Rydberg series of autoionizing resonances. The resonance states are identified and analyzed to obtain resonance positions Er, effective quantum numbers n*, and widths Gammar using a procedure of eigenphase gradients. The resonance line shape and correlation parameters have also been determined. Photoionization cross sections have been calculated in both length and velocity formulations that exhibit very good agreement (within 5%) with each other for most photon energies. Our results are compared with a recent merged ion-photon beam experiment. Significant discrepancies between the theoretically predicted and experimentally measured resonance structures and continuum cross sections are noted.

Ab initio study of Tm-He interactions and dynamics in a magnetic trap
A. A. Buchachenko, G. Chalasinski, M. M. Szczesniak, and R. V. Krems
Published 2 August 2006 (6 pages)
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The dynamics of magnetic relaxation of Tm atoms in cold helium gas is investigated using ab initio interaction potentials between Tm(2F) and He atoms. The interaction of Tm(2F) with He gives rise to four adiabatic potentials of Sigma+, Pi, Delta, and Phi symmetries, which are found to be degenerate to within 0.1  cm–1 at all interatomic distances larger than R=5.4  Å. The small splitting between the interaction potentials leads to suppression of Zeeman transitions in Tm-He collisions. Our quantum scattering calculations yield a small rate constant of 1.5×10–15  cm3  s–1 for Zeeman relaxation of the Tm(2F7/2) atoms in the maximally stretched M=7/2 sublevel at the temperature 0.8  K, in reasonable agreement with the measured value (5.0±2.1)×10–15  cm3  s–1. The sensitivity of Zeeman-relaxation cross sections to details of the interaction potentials is examined. To our knowledge, this is one of only two comparisons of ab initio quantum scattering calculations with experimental measurements of inelastic collisions at subkelvin temperatures near one Kelvin. Our work thus demonstrates the feasibility of describing cold collisions from first principles.

R-matrix calculation of differential cross sections for low-energy electron collisions with ground-state and electronically excited-state O2 molecules
Motomichi Tashiro, Keiji Morokuma, and Jonathan Tennyson
Published 2 August 2006 (8 pages)
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Differential cross sections for electron collisions with the O2 molecule in its ground X  3Sigmag<sup>-</sup> state, as well as excited a  1Deltag and b  1Sigmag<sup>+</sup> states are calculated. As previously, the fixed-bond R-matrix method based on state-averaged complete active space self-consistent-field orbitals is employed. In addition to elastic scattering of electron with the O2 X  3Sigmag<sup>-</sup>, a  1Deltag, and b  1Sigmag<sup>+</sup> states, electron impact excitation from the X  3Sigmag<sup>-</sup> state to the a  1Deltag and b  1Sigmag<sup>+</sup> states as well as 6  eV states of c  1Sigmau<sup>-</sup>, A[prime]  3Deltau, and A  3Sigmag<sup>+</sup> states is studied. Differential cross sections for excitation to the 6  eV states have not been calculated previously. Electron impact excitation to the b  1Sigmag<sup>+</sup> state from the metastable a  1Deltag state is also studied. For electron impact excitation from the O2 X  3Sigmag<sup>-</sup> state to the b  1Sigmag<sup>+</sup> state, our results agree better with the experimental measurements than previous theoretical calculations. Our cross sections show angular behavior similar to the experimental ones for transitions from the X  3Sigmag<sup>-</sup> state to the 6  eV states, although the calculated cross sections are up to a factor of 2 larger at large scattering angles. For the excitation from the a  1Deltag state to the b  1Sigmag<sup>+</sup> state, our results marginally agree with the experimental data except for the forward scattering direction.

Angular and high-frequency analysis of electron interference structures in ~60  MeV/u Kr34++H2 collisions
J. A. Tanis, J.-Y. Chesnel, B. Sulik, B. Skogvall, P. Sobocinski, A. Cassimi, J.-P. Grandin, L. Adoui, D. Hennecart, and N. Stolterfoht
Published 2 August 2006 (6 pages)
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Detailed analyses of previous measurements, combined with additional measurements reported here, have been made of electron interference structures observed in 60  MeV/u Kr34++H2 collisions. Results are used to characterize the angular dependence of the primary interference structures over a wide range of electron ejection angles, particularly backward angles, and, additionally, to search for high-frequency structures as reported recently for 1–5  MeV/u H++H2 collisions [Hossain et al., Phys. Rev. A 72, 010701(R) (2005)]. The data for backward ejection angles, in combination with earlier data, permit a detailed comparison with theory over the range 30°–150°, showing that none of the existing theories predict accurately the observed oscillation frequencies for backward angles. Electron spectra for 90° and 150° taken in small energy steps and with improved statistics compared to earlier measurements were examined by means of a Fourier analysis but no evidence of the high-frequency structures reported for H++H2 collisions was found.

Triply charged carbon dioxide molecular ion: Formation and fragmentation
R. K. Singh, G. S. Lodha, Vandana Sharma, I. A. Prajapati, K. P. Subramanian, and B. Bapat
Published 4 August 2006 (4 pages)
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In an experiment involving detection of a photoelectron and up to three photoions from CO2 in coincidence, we observe the triple ion coincidence C+:O+:O+. Moreover, we observe double coincidences between doubly charged cations and singly charged cation pairs C2+:O+, O2+:C+, O2+:O+. These ion triplets and pairs arise from fragmentation of the triply charged molecular ion CO23+. Other ion pairs—viz., C+:O+, O+:O+, O+:CO+—arising from the doubly charged molecular ion CO22+, are also observed. From an analysis of the coincidence pattern we postulate four decay modes of the CO23+ ion. Kinetic energy release in the channel leading to C+:O+:O+ is measured, and its distribution is postulated to have four contributing precursor states.

Low-energy capture of antiprotons by helium ions
Kazuhiro Sakimoto
Published 4 August 2006 (10 pages)
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Low-energy antiproton capture, [overline p]+He+-->[overline p]He2++e, is investigated using a wave-packet-propagation full-quantum-mechanical method or a quantum-classical hybrid (i.e., semiclassical) approximation. If the adiabatic picture (i.e., Born-Oppenheinmer separation) is a good approximation, the antiproton capture, which is a typical nonadiabatic process, can rarely occur. It is found that the probability of the nonadiabatic transition is small (at most ~0.1). However, even in the zero energy limit (E-->0), the antiproton capture always occurs for the total angular momenta J<~40. Correspondingly, the cross section for the antiproton capture diverges as E-->0. This happens due to the peculiarity that the Coulomb force range is longer than the centrifugal one. The importance of a Rydberg series of resonances in the capture process is emphasized. On the low-energy dynamical feature, some interesting similarities to the e+ion system are also found.

Stationary phase approximation for the strength of optical Feshbach resonances
R. Ciurylo, E. Tiesinga, and P. S. Julienne
Published 7 August 2006 (9 pages)
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Analytic expressions for the width and shift of a photoassociative resonance or an optically induced Feshbach resonance in ultracold collisions are derived using the quasi-classical stationary phase approximation. This approach for the width is applicable over a wider range of cases than the reflection approximation. Possible applications for optical Feshbach resonances between ultracold alkaline-earth-metal atoms, such as Ca and Sr, are discussed. Our approach also applies to photoassociation in gases of heteronuclear alkali-metal atoms.

Low-energy electron scattering by N2O
M. H. F. Bettega, C. Winstead, and V. McKoy
Published 8 August 2006 (6 pages)
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We present elastic integral, differential, and momentum-transfer cross sections for electron collisions with N2O. We show that, with a slight modification of a method of incorporating polarization effects proposed recently by us [Winstead, McKoy, and Bettega, Phys. Rev. A 72, 042721 (2005)] along with a flexible one-particle basis set, we can reproduce features in the experimental data that were not reproduced by earlier calculations. We also find evidence of a Ramsauer-Townsend minimum, which our calculation places at about 0.2  eV.

Analytical solutions for the dynamics of two trapped interacting ultracold atoms
Zbigniew Idziaszek and Tommaso Calarco
Published 8 August 2006 (14 pages)
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We discuss exact solutions of the Schrödinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering length we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.

Polarization measurements of the Lyman-alpha1 x-ray emission lines of hydrogenlike Ar17+ and Fe25+ at high electron-impact energies
D. L. Robbins, P. Beiersdorfer, A. Ya. Faenov, T. A. Pikuz, D. B. Thorn, H. Chen, K. J. Reed, A. J. Smith, K. R. Boyce, G. V. Brown, R. L. Kelley, C. A. Kilbourne, and F. S. Porter
Published 9 August 2006 (5 pages)
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We have measured the polarization of the 2p3/2-->1s1/2 Lyman-alpha1 x-ray line of hydrogenlike Ar17+ and Fe25+ at electron-impact energies ranging from 7 to 25 threshold units. The highly charged argon and iron ions were produced using the Lawrence Livermore National Laboratory SuperEBIT electron beam ion trap. A combination of two crystal spectrometers and a microcalorimeter were used to record the Lyman-alpha x-ray emission of Ar17+ and Fe25+ and to infer the polarization of the Lyman-alpha1 line. Our results show a systematic discrepancy with the predictions of distorted-wave calculations.

Differential and integrated cross sections for excitation to the 3s, 3p, and 3d states of atomic hydrogen by electron impact below the n=4 threshold
Philip L. Bartlett, J. F. Williams, Igor Bray, A. G. Mikosza, and Andris T. Stelbovics
Published 10 August 2006 (7 pages)
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Integrated cross sections for the electron-impact excitation of ground-state hydrogen to the 3s, 3p, and 3d final states have been calculated using propagating exterior complex scaling and convergent close-coupling methods at energies between the n=3 and 4 excitation thresholds. The calculations are in excellent agreement and demonstrate that exterior complex scaling methods can accurately reproduce the resonance structure and magnitude of the excitation cross sections below the ionization threshold. Measurements of the separate 3s, 3p, and 3d differential cross sections were made at 12.24  eV, and are consistent with both calculations within a total experimental uncertainty of about 35%.

Photoionization cross section measurements of the 3p  1,3P excited states of helium in the near-threshold region
Shahid Hussain, M. Saleem, M. Rafiq, and M. A. Baig
Published 15 August 2006 (5 pages)
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We present measurements of photoionization cross sections of the 3p  1P and 3p  3P excited states of helium, at threshold and near-threshold region (0–0.2  Ry). The experiments have been performed using a dc glow discharge and employed the saturation technique to determine the photoionization cross sections. A smooth frequency dependence of the cross section has been observed for both the excited states in accordance to the