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Journal of the Optical Society of America B

Optical-pumping model of synchronized quantum-beat echoes

M. Tanigawa, Yukio Fukuda, T. Hashi, Tomobumi Mishina, Masakazu Kunitomo

Published Mar 1, 1992• 5 citations
Publisher

Abstract

We develop a new theoretical treatment that can explain, for the first time to our knowledge, unexpectedly strong synchronized-quantum-beat-echo (SQBE) signals that we previously observed in the ground state of sodium atoms. The SQBE is obtained by successive application of two light-pulse trains tuned to an optical transition under the condition that the pulse repetition frequency or that of one of its harmonics is equal to the separation of a ground-state sublevel pair. The theory is developed for weak optical pumping for which the duration of the light-pulse trains is much longer than the spontaneous decay time of the excited state. We show that the echo is formed effectively as a result of nonuniform depopulation from the sublevel pair to the other levels because of frequency-selective optical pumping during the rapid spontaneous decay of the excited state. Details of the experiment with sodium atoms are described also.

DOI
10.1364/josab.9.000313

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 26, 1997•0 citations
We develop a new theoretical treatment that can explain, for the first time to our knowledge, unexpectedly strong synchronized-quantum-beat-echo (SQBE) signals that we previously observed in the ground state of sodium atoms. The SQBE is obtained by successive application of two light-pulse trains tuned to an optical transition under the condition that the pulse repetition frequency or that of one of its harmonics is equal to the separation of a ground-state sublevel pair. The theory is developed for weak optical pumping for which the duration of the light-pulse trains is much longer than the spontaneous decay time of the excited state. We show that the echo is formed effectively as a result of nonuniform depopulation from the sublevel pair to the other levels because of frequency-selective optical pumping during the rapid spontaneous decay of the excited state. Details of the experiment with sodium atoms are described also.
We report on a new type of sublevel echoes, synchronized-quantum-beat (SQB) echoes, generated by a successive application of two resonant light-pulse trains. The echoes are selectively generated for a sublevel pair whose frequency splitting is equal to an integral multiple of the repetition frequency of the light pulses. By using mode locked laser pulses tuned to the D(1) transition, we observed SQB echoes (and free induction decay) for all Zeeman and hyperfine transitions in the ground state of sodium atoms in low magnetic fields.
Recent femtosecond transmission-correlation measurements1 of large organic dye molecules revealed surprising details concerning the ultrafast relaxation dynamics of such dyes. Superposed on simple exponential decays, the observation of damped sinusoidal oscillations with a period of ~ 150 fs has been puzzling. We theoretically and numerically demonstrate that such oscillatory behavior could be due to quantum beats of closely spaced two levels, whose coherent superposition state is optically prepared and monitored by a pair of femtosecond pulses. Although studies of quantum beats have been developed in both fluorescence-type2 and nonfluorescence-type measurements, such as those based on photon echoes3 or polarization spectroscopy,4 this simple method gives a new approach to femtosecond time domain spectroscopy. The generalized perturbation theory5 of optical coherent transients is extended to the case of optical transmission-correlation or pump-probe-type experiments. The model used is a three-level system which has split levels in either the ground or optically excited states. Especially, if the ground state has sublevels, the system becomes quite similar to the case of coherent Raman beats. Both cases are shown to give quantum beats when the excitation pulses are short compared with the inverse sublevel splitting. The period and decay time of the damped sinusoid represent the separation energy and the dephasing time between the sublevels, respectively. Using third-order perturbation theory, the transmission-correlation signal STC(τ) as a function of the first-to-second pulse delay time Is derived for arbitrary-shaped excitation pulses and is given in the form of fourfold integrals with many terms.
A photon echo in a multilevel quantum medium excited by two extremely short pulses with durations of less than one period of oscillation of the light is investigated theoretically. It is shown thatQ echo signals (Q is the number of allowed transitions) can form at each frequency of the allowed transitions, and the number of echo responses for all the allowed transitions equalsQ 2. Of these,Q(Q−1) signals are separated in both time and space. The otherQ echo signals of all the allowed frequencies all arise at the time 2τ 21 (τ 21 is the time interval between application of the first and second pulses to the medium) and are collinear with one another.
The dynamics of coherences between sublevels of an electronic ground state is investigated under conditions of modulated optical pumping. It is shown that the modulation corresponds to an effective reduction of the apparent sublevel splitting, thereby allowing the excitation of coherences between atomic sublevels whose energy splitting would require very high laser intensities for dc excitation. In addition, the frequency and phase of the modulation introduce additional degrees of freedom that can be utilized for the design of new experiments. The theoretical evaluations are compared with experiments on the ground state of atomic sodium.
A full density-matrix theory for quantum beats in optical transmission-correlation or pump-probe type of experiments is developed. The model used is a three-level system with split excited-state levels. It is demonstrated on the basis of perturbation theory that quantum beats should be observable in such experiments. Theoretical and numerical results are compared with the complex details, including damped sinusoidal decays, observed in recent femtosecond relaxation studies of large organic dye molecules. It is also shown that there is no separately identifiable decay component corresponding to any homogeneous or inhomogeneous optical dephasing time in such experiments. Similar beating should also be observable in ultrafast spectroscopy using incoherent light and in Raman-type energy-level configurations where the ground state contains split levels.
It is shown theoretically that, when two-level atoms are nonresonantly excited by a double light pulse that is a superposition of two rectangular pulses of identical frequency but different amplitude, it is possible to form multiple nutational echo signals whose amplitude is determined by the relationships between the Rabi frequencies of the double pulse, the inhomogeneous line width, and the detuning from resonance. It is established that these signals result from null beats between polarization vibrations at variable frequencies and at the generalized Rabi frequency. The optimum conditions for observing multiple echo signals in different experimental situations are considered.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.