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Dissipative quantum coherent dynamics probed in phase-space: Electronically resonant 5-color 4-wave mixing on I2(B) in solid Kr
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View: Figures


Image of FIG. 1.

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FIG. 1.

The measurement: (a) (top panel) time circuit diagrams overlaid on the molecular potentials show the preparation of two packets on the B-state, and interrogation via coherent Raman scattering between the two packets; (b) (bottom panel) phase-space representation of the electronically resonant process highlights that the time-ordered correlation leads to selective scattering. For ɛ 1 > ɛ 2, AS- and S-scattering occur at p and p + momentum branches, respectively.

Image of FIG. 2.

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FIG. 2.

Experimental scheme: three non-collinear pulses, in three different colors are used. The directional AS-/S-polarizations are simultaneously collected with fibers. They are dispersed in a monochromator and the spectra are simultaneously recorded on a 2-D CCD array. The phase matching is accomplished on glass, by optimizing for high order scattering, as in the photographed image shown.

Image of FIG. 3.

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FIG. 3.

The spectra of the three input pulses used in narrow-band four-color measurements (solid lines) and the non-resonant S- and AS-spectral windows (dashed red and blue, respectively) that arise by their triple convolution. The pulses are centered at λ 1 = 550 nm, λ 2 = 560 nm, and λ 3 = 500 nm, with fwhm Δλ 1 = 8 nm, Δλ 2 = 7 nm,, and Δλ 3 = 12 nm and pulse widths of Δτ 1 = 95 fs, Δτ 2 = 105 fs,, and Δτ 3 = 60 fs.

Image of FIG. 4.

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FIG. 4.

Simultaneously recorded S-and AS-scattered spectra in the five-colors shown in Fig. 3, as a function of probe delay t 31, for fixed t 21 = –30 fs. The two vertical lines in the fifth period correspond to p + and p intersections.

Image of FIG. 5.

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FIG. 5.

Semilogarithmic spectral cuts taken at 495 nm and 505 nm from the AS- and S-signals (bottom panel) of Fig. 4, along with the pump-probe induced fluorescence signal (top panel). The markers show the slippage of phase between the two scattering channels, and the appearance of period doubling in the AS-signal.

Image of FIG. 6.

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FIG. 6.

A representative trajectory from molecular dynamics simulations of I2/Kr (Ref. 10). The damping of the amplitude of the oscillator is modulated by the cage motion, with cage-molecule collisions identifiable at the step jumps marked by the stars. These steps are perfectly correlated with the drop in the AS-scattering intensity seen in Fig. 4.

Image of FIG. 7.

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FIG. 7.

Recursion periods, t n+ 1 –t n as a function of cycle number n, obtained from: AS-signal (green) at 500 nm (squares) and at 495 nm (circles) including the recursions after period doubling; S-signal (red) circles at 500 nm (squares) and at 505 nm (circles); LIF data for individually prepared packets at 550 nm (blue) and at 560 nm (black). The right ordinate relates period to vibrational energy assuming a Morse potential.

Image of FIG. 8.

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FIG. 8.

Reconstruction of the time-dependent coherence in energy representation for the data in Fig. 3. The initially prepared coherence (0) dictated by the laser pulses; and three subsequent distributions obtained from the first, third, and fifth recursions at 0.2, 1, and 1.6 ps of the AS-scattering in Fig. 4. The diagonal energies and spreads are obtained from the period analysis in Fig. 6, while the off-diagonal widths are from the spectral shift and width of the recursions in Fig. 4. The provided vibrational grid is artificial, the system does not sustain vibrational eigenstates – the spectrum of the oscillator is continuous.

Image of FIG. 9.

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FIG. 9.

The same experiment as in Fig. 3 (S, top; AS, bottom), but with φ 2 launched ahead of φ 1: with t 21 = 70 fs (100 fs time difference in t 21). The S-signal tracks φ 2 as it turns the corner (1–3), while the AS-signal captures φ 1 at large phase angles (2, 4). The outer contour profiles can be compared with the intensity plots in Fig. 5, they show the same cage modulation. The stars mark the abrupt decoherence, when the signal drops to the energy diagonal of Fig. 8.

Image of FIG. 10.

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FIG. 10.

The synchronization required to form the signal in Fig. 6 can be understood using classical trajectory ensembles to represent packets. We show the two circulating packets (red, green) captured at the identified t 31 times, which correspond to the four marked events in Fig. 9, along with the E-state packet (blue) formed by the interception of φ 2/φ 1 by the FC window carved in time by the probe pulse to generate the S-/AS-scattering cases, respectively. The trajectories are propagated on a Morse potential, and the effect of the environment is only taken into account as an energy dependent dissipation.

Image of FIG. 11.

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FIG. 11.

Spectral cuts from Fig. 9, at the indicated wavelengths. The AS-signal in the degenerate window is on a constant background due to the permanent volume grating burned in the sample. The negative dips arise from the heterodyned signal.

Image of FIG. 12.

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FIG. 12.

AS-scattering obtained with pulse parameters λ 1 = 540 nm, λ 2 = 560 nm, and λ 3 = 500 nm, with bandwidths 20 nm, 25 nm, and 13 nm, respectively. The delay between packets is adjusted to obtain maximum signal at first blue recursion, and assigned t 12 = 0. The red shift in the spectrum indicates energy overlap, while the decay of the blue-shifted peaks indicates non-linear dissipation and collapse of the anti-diagonal spread in energy. The cuts at λ = 505 nm and λ = 495 nm show the cage motion in their amplitude modulation. While the blue wing decays rapidly, the red wing decay is close to that of the population. The insets identify the phase space overlaps and projections that lead to the observed timing and color of the blue and red wings.

Image of FIG. 13.

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FIG. 13.

Arrested dissipation. The periods collected from different t 21 sets, extracted at 505 nm, show a perfectly correlated modulation that tracks the breathing of the cage. The vibrational energy of the molecule (right ordinate) remains within a narrow band of ∼500 cm−1, in stark contrast with that seen in Fig. 6.

Image of FIG. 14.

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FIG. 14.

Contour plot of the two-time correlation, at two selected wavelengths: AS at 485 nm (green), and S at 504 nm (red). The ordinate, t 21, is the delay between packets, while the abscissa, t 31 is the probe time. Overlaid on the last AS-recursion is the simulated signal, using Eq. (15) of text, assuming two Morse trajectories.

Image of FIG. 15.

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FIG. 15.

Quantum versus classical coherence as a function of energy separation between preparation pulses. The FWM signal (green) and the simultaneously recorded pu-pr signal (black), detected through leaked LIF at 423 nm, are shown for two different pairs of preparation colors (purple): λ 1/λ 2 = 540/560 and 545/560 (λ 3 = 500 nm, not shown). The signal amplitudes are normalized on the first recursion. The FWM signal, which measures the cross-coherence, decays rapidly as the spectral overlap between the preparation pulses diminishes. The pu-pr signal, which measures the classical coherence (diagonal bath), is not affected.


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Spectrally resolved, 4-wave mixingmeasurements in five resonant colors are used to interrogate vibronic quantum coherences in phase-space. We highlight the principles through measurements on the B-state of I2 in solid Kr – a prototype of a system strongly coupled to its environment. The measurements consist of preparing a superposition of wavepackets on the B-state and interrogating their cross-coherence as they get entangled with the environment. The study provides direct realizations of fundamental quantum principles in the mechanics of molecular matter, among them: the distinction between quantum and classical coherent dynamics of a system entangled with the environment, coherent dissipation, event-driven decoherence, environment selected coherent states, and non-local mechanics.


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Scitation: Dissipative quantum coherent dynamics probed in phase-space: Electronically resonant 5-color 4-wave mixing on I2(B) in solid Kr