(a) A schematic diagram illustrating the pulse arrangement of the pump (Pu) and probe (Pr) beams in the forward boxcar configuration. (b) depicts the temporal arrangement of these beams. The two pump beams are overlapped temporally to form a transient grating. This defines time zero for all experiments. The probe pulse is scanned in incremental steps (typically ) up to a maximum delay of . (c) and (d) are similar to (a) and (b) but with the inclusion of the control pulse (Pco). (c) The control pulse occupies the center of the box while (d) illustrates the relative timings of all four pulses.
Time-resolved rotational recurrence data [(a), (b), and (c)] and the corresponding FFTs [(d), (e), and (f)] for three different laser intensities, , , and respectively. (a), (b), and (c), each show two plots that correspond to experiment (bottom) and theory (top). The theoretical plots are modeled using Eq. (2) with their base line indicated by a dashed horizontal line. These plots were obtained using 0, 0.35, and 1 for the values of for (a), (b) and (c), respectively. (d), (e), and (f) are the FFTs of the experimental recurrence plots. Two progressions are observed in (d) indicated by the dotted lines. The two progressions arise from squaring Eq. (1) and are labeled and , , , respectively (see text for details). The star in (d) denotes the rotational recurrence time appearing at . The dashed vertical lines are the wave number values of the beat frequencies between the pairs of rotational states the wave packet is composed of ( or ). (f) shows essentially a single series that matches perfectly with these beat frequencies (labeled and in the text). The transformation from a homodyne-detected to a heterodyne-detected signal [from (d) to (f)] is the main focus of the paper.
Theoretical plot of the alignment parameter as a function of time for . The plot is calculated using Eq. (4) and assuming a laser field intensity of . Alignment corresponds to values of while antialignment corresponds to values of . Also indicated on this plot are the delay times where the control pulse (Pco) is sent in for the data presented in Figs. 4 and 5.
(a) Rotational recurrence plots for three different delays of the control pulse, 5.7, 5.8, and (long dashes, solid line, and short dashes, respectively). The pump/probe and control pulses were kept at and , respectively. (b), (c), and (d) correspond to FFTs of recurrence signals at these delays. Notice in (c) the emergence of an additional sequence of peaks, indicated by a comb of arrows. This points towards a switching from homodyne to heterodyne detection. The step in the base line (a) is indicative of additional scatter of the probe which is hypothesized as being caused by an additional, time-independent grating. This results from permanent alignment of the molecules through enhanced Rabi cycling after the interaction with the intense control field. This can serve as a local oscillator to heterodyne the signal.
Variation in the base line intensity as the control pulse is scanned through two successive recurrences (2.9 and ). (a) corresponds to the probe pulse fixed at while the control pulse is scanned from while (b) corresponds to the probe pulse fixed at and the control pulse scanned from 5.7 through . Note that no spectral averaging is employed and the lines through the points serve to guide the eye. The base line is seen to rise to a maximum around the recurrence time.
Rotational recurrence plot in which the control pulse is sent into the sample prior to the grating pair pulses. Peaks appear at twice the recurrence period (see text for details). The alternating intensities result from the twofold difference in intensity of the control and grating pulses, respectively.
Histogram plot depicting the change in the peak ratios of the calculated (solid blocks) and measured (open blocks) FFTs for the most intense rotational state superposition peak and the rotational recurrence peak ( at ). The data are for two field strengths of the pump pulses corresponding to and .
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