1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation
Rent:
Rent this article for
USD
10.1063/1.2386159
/content/aip/journal/jcp/125/19/10.1063/1.2386159
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/19/10.1063/1.2386159

Figures

Image of FIG. 1.
FIG. 1.

Energy level diagram for the line transitions (described in text and Table I). For the purposes of our experiments, the system behaves as a three-level atom with ground state , first excited state , and second excited state .

Image of FIG. 2.
FIG. 2.

Illustration of a train of phase-modulated pulse pairs. Each pulse pair is labeled by the superscript ; the individual pulses are labeled by the subscripts 1 (target pulse) and 2 (reference pulse). A pulse pair is characterized by the interpulse delay , and the relative temporal phase . (A) Both target and reference pulses are spectrally identical and Fourier transform limited. (B) The target pulse is spectrally chirped, while the reference pulse is transform limited.

Image of FIG. 3.
FIG. 3.

Schematic diagram of the experimental setup for phase modulation (PM-) WPI (described in text). Abbreviations have the following meanings. APD: amplified photodiode; PD: pin photodiode; AO: acousto-optic Bragg cell; BS: beam splitter.

Image of FIG. 4.
FIG. 4.

(A) Typical noncollinear pulse autocorrelation measurements (open circles) used to minimize the optical pulse length by predispersion compensation (described in text). The solid curve is the best-fit Gaussian function with . Assuming a Gaussian temporal pulse envelope, the corresponding FWHM pulse width is . (B) Power spectrum measurement of the same pulses measured in (A). The dashed gray curve is the best-fit Gaussian with center wavelength (indicated by the vertical dashed line) and FWHM spectral width . Also shown are the narrow line transitions of the Rb system, with magnitude ratio proportional to the square of the transition dipole moments (see Table I).

Image of FIG. 5.
FIG. 5.

(A) Spectral density measurement (black) and spectral phase (gray) of a chirped laser pulse resulting from BK7 glass [calculated using Eq. (2.9) and the Sellmeier equation] (Refs. 56 and 57). The best-fit Gaussian (not shown) has a center wavelength and . Also indicated are the monochromator setting , and the Rb line transitions. (B and C) Expected PM-WPI signal [see Eqs. (3.15) and (3.16)] corresponding to the spectral conditions summarized in (A) (see also Table II). The signal is plotted in the complex plane with and axes defined as and , respectively. The signal (, shown in black) is a vector superposition of two counterprecessing components ( and , shown in gray). (B) The initial condition is determined by the spectral overlap of the target pulse with the Rb line transitions. (C) During the evolution period , the resultant traces a quasielliptical trajectory (shown in black), with magnitude and phase function .

Image of FIG. 6.
FIG. 6.

Monochromator setting dependence of the PM-WPI undersampled interferograms for spectrally identical pulses, with and . In-phase data [, gray filled circles], and in-quadrature data [, solid black circles], are superimposed with theoretical curves (gray and black, respectively) given by Eqs. (4.1a) and (4.1b). (A) . The fully sampled interferogram is also shown (light gray). (B) . (C) .

Image of FIG. 7.
FIG. 7.

Complex linear susceptibility determined [according to Eqs. (3.28) and (3.29)] from the same undersampled interferograms shown in Fig. 6. The real and imaginary parts of are shown as black and white curves, respectively. Superimposed onto each plot is the Gaussian fit to the laser spectral density with and . (A) . (B) . (C) .

Image of FIG. 8.
FIG. 8.

[(A)–(C)] Laser center wavelength dependence of PM-WPI signal for spectrally identical pulses, with and (see Table II). The signal magnitude (gray filled circles) and the signal phase function (solid black circles) are superimposed with the “expected” signal [shown as solid black curves, Eq. (4.6)] and the “reconstructed” signal [shown as dashed gray curves, Eq. (4.5)]. Also shown are the pulse-pulse autocorrelation envelopes (open black circles) and Gaussian fits (solid black curves) used to determine time origins for each data set. (A) . (B) . (C) . [(D)–(F)] Phasor diagram representation of the expected signals [Eq. (4.6)] corresponding to (A)–(C)). The coordinate system axes and component phasor labels are the same as in Figs. 5(b) and 5(c).

Image of FIG. 9.
FIG. 9.

[(A)–(C)] Laser center wavelength dependence of PM-WPI signal for spectrally distinct pulses, with (see Table II). The signal magnitude (gray filled circles) and the signal phase function (solid black circles) are superimposed with the “expected” signal [shown as solid black curves, Eq. (4.6)] and the “reconstructed” signal [shown as dashed gray curves, Eq. (4.5)]. Also shown are the pulse-pulse autocorrelation envelopes (open black circles) and Gaussian fits (solid black curves) used to determine time origins for each data set. (A) and . (B) and . (C) and . [(D)–(F)] Phasor diagram representation of the expected signals [Eq. (4.6)] corresponding to (A)–(C). The coordinate system axes and component phasor labels are the same as in Figs. 5(b) and 5(c).

Image of FIG. 10.
FIG. 10.

(Color) Comparison between PM-WPI signals obtained from excitation using a chirped target pulse and transform-limited pulse . [(A) and (B)] Phase function and magnitude data for the chirped and transform-limited experiments (shown as open circles and squares) are superimposed with the “expected” signals (solid curves) and “reconstructed” signals (dashed gray curves) described by Eqs. (4.6) and (4.5), respectively.

Tables

Generic image for table
Table I.

Physical constants associated with optical line transitions. is the transition index, is the transition frequency, is the transition wavelength, is the transition dipole moment (in units of D), is the lifetime, and is the natural linewidth (Ref. 45).

Generic image for table
Table II.

State reconstruction parameters and results. For these data, . is the laser center wavelength, is the magnitude ratio of the expected target state amplitudes, is the relative phase of the expected target state amplitudes, is the magnitude ratio of the reconstructed target state amplitudes, is the relative phase of the reconstructed target state amplitudes, and is the fidelity of the reconstructed state [Eq. (4.4)].

Loading

Article metrics loading...

/content/aip/journal/jcp/125/19/10.1063/1.2386159
2006-11-16
2014-04-23
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/19/10.1063/1.2386159
10.1063/1.2386159
SEARCH_EXPAND_ITEM