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Physical Review Letters

Non-Markovian Strong-Field Excitation of Optical Coherent Transients

P. Tchénio, Anne Débarre, J. Keller, J.-L. Le Gouët

Published Jan 23, 1989• 29 citations
Publisher

Abstract

A transient, time-delayed, four-wave mixing experiment is performed in strontium vapor under stochastic excitation conditions. The first two broad-bandwidth laser pulses are correlated and their delay is adjustable. Thus they combine into a non-Markovian excitation process with adjustable memory time. One of the correlated pulses is allowed to be strong. In contrast with previous investigations, it is shown both theoretically and experimentally that under strong-field conditions the atoms are not able to keep the excitation memory over time intervals longer than the inverse laser bandwidth.

DOI
10.1103/physrevlett.62.415

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Physical Review A•Oct 1, 1993•7 citations
A transient, time-delayed, four-wave mixing experiment is performed in strontium vapor under stochastic excitation conditions. The first two broad-bandwidth laser pulses are correlated and their delay is adjustable. Thus they combine into a non-Markovian excitation process with adjustable memory time. One of the correlated pulses is allowed to be strong. In contrast with previous investigations, it is shown both theoretically and experimentally that under strong-field conditions the atoms are not able to keep the excitation memory over time intervals longer than the inverse laser bandwidth.
Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.
Abstract : In this research program, the investigators have explored the role of fluctuations of a laser field on coherent interactions between the laser field and simple atomic systems. A key feature of these experiments is their ability to provide measurements of complex nonlinear optical interactions which are sufficient for direct, quantitative comparison with theory. The main thrust of the present work has been the study of non-Markovian field statistics, present in experiments that use multiple, time-delayed input beams to drive the nonlinear system. The specific interaction studied was Phase-Conjugate Four-Wave Mixing in an optically-pumped beam of atomic sodium, which the researchers measured as a function of laser bandwidth, Rabi frequency, and delay time between the pump and probe beams. The investigators have also calculated the expected signal strength through numerical integration of the Optical Bloch Equations. Experimental and numerical results are in very good agreement. The investigators also studied theoretically two-photon absorption with correlated, time-delayed input fields, and provided the first experimental confirmation of the fundamental theory of Phase-Conjugate Four-Wave Mixing with monochromatic fields in a simple atomic system.
We explore theoretically the signal generated by a fluctuating radiation field via a four-wave mixing process in an atomic vapor undergoing Markovian dephasing collisions. We consider specifically a broadband laser field well detuned from the atomic resonance and calculate the signal generated using counterpropagating pump fields as a function of the time delay of the incident probe field. We assume that the pulse duration is long compared to the correlation time of the incident fields. By considering the various time-ordered pathways and treating the incident-field amplitudes as random Gaussian variables, we find that the signal generated is dominated by two specific pathways that depend only on the incident-field bandwidth and the decay rate of the ground to excited state coherence. An interesting aspect of the far-impact-detuning case is that the signal is dominated by resonances involving spatially separated atoms. Our formalism provides a basis for describing the effects of mode correlations on four-wave-mixing signals generated by stochastic fields.
A theory is developed to describe the optical transient signals that arise when a sample of two-level atoms is irradiated by a sequence of two or three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations. These pulses whose temporal width is much greater than the delay time are fully correlated with one another and can be strong enough to saturate the two-level atomic transition. In the case of three-pulse transients the third pulse is weak non-correlated with the first two and is delayed in time so that it does not overlap them. Taking into account the effects ofinhomogeneous and homogeneous broadening we calculate the intensity of the transient signals as a function of delay time. The signals are found to depend dramatically on the intensities of the excitation pulses. It is shown that for strong excitation pulses a direct dependence of the signal on the cross-correlation time of the pulses r occurs that does not exist when the pulses are weak. In particular for saturating pulses the signals exhibit a peak of width of order r . In the case of the two-pulse transient the peak is found to disappear when the Doppler width of the atomic ensemble becomes sufficiently large. This peak can have a very narrow dip near its maximum whose width is much
Four-wave mixing in homogeneously broadened, two-level atoms, driven by time-delayed, correlated phase-diffusing optical fields is investigated. The spectrum of the driving field has an arbitrary bandwidth, i.e., it can have a Lorentzian or a Gaussian profile or an intermediate profile (Voigt). A time delay between the strong pump and weak probe field provides a partial correlation between the fields, and this time delay makes the composite field seen by the atoms non-Markovian. It is shown that the calculation of the four-wave-mixing signal reduces to the solution of six coupled Langevin equations with multiplicative noise; Monte Carlo techniques are utilized to study the response of the atoms to non-Markovian fields. A technique for numerically simulating phase-diffusing fields with colored frequency fluctuations is shown. The four-wave-mixing profiles are found to be significantly different from those for which the driving field is chaotic. The profiles show oscillatory behavior as evidence of the Rabi frequency, a feature not seen in previous works. For some parameter values, a revival of the signal is seen for an increasing time delay, analogous to the revivals seen in chaotic field signals [Phys. Rev. A 44, 6009 (1991)].