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European Quantum Electronics Conference (EQEC)

Time-Delayed Four-Wave Mixing: The Interplay Between Iaser Field Fluctuations and the Atomic Memory Time

J.V. Gomes, Michael Scott Belsley, M. Kaczmarck, P. Ewart

Published Jan 1, 1996• 0 citations

Abstract

Coherent signals induced by fundamentally incoherent phenomena through a four-wave mixing process are among the most intriguing and subtle effects in nonlinear spectroscopy. These effects were initially observed by Bloembergen and his co-workers in the form of pressure-induced extra resonances in four-wave mixing. Using standard perturbance techniques based on the optical Bloch equations, they suggested that these collision induced resonances were the result of a destruction of the destructive interference existent between two alternate time-ordered pathways. Subsequently, Prior et al realised that fluctuations in the incident radiation fields could play essentially the same role as the collisionally induced dephasing. In practice, of course, both collisional dephasing and field fluctuations are present in a typical atomic vapor pulsed four-wave mixing experiment. If the timescales governing these two effects approach one another, one can expect to gain valuable new insight into this fascinating process of incoherently inducing a coherent signal

DOI: 10.1109/eqec.1996.561882

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Coherent signals induced by fundamentally incoherent phenomena through a four-wave mixing process are among the most intriguing and subtle effects in nonlinear spectroscopy. These effects were initially observed by Bloembergen and his co-workers in the form of pressure-induced extra resonances in four-wave mixing. Using standard perturbance techniques based on the optical Bloch equations, they suggested that these collision induced resonances were the result of a destruction of the destructive interference existent between two alternate time-ordered pathways. Subsequently, Prior et al realised that fluctuations in the incident radiation fields could play essentially the same role as the collisionally induced dephasing. In practice, of course, both collisional dephasing and field fluctuations are present in a typical atomic vapor pulsed four-wave mixing experiment. If the timescales governing these two effects approach one another, one can expect to gain valuable new insight into this fascinating process of incoherently inducing a coherent signal

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.

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...

Collision enhanced resonances represent an interesting class of nonlinear-optical processes. They occur because collisional dephasing can rephase quantum mechanical amplitudes that ordinarily cancel out exactly, thereby allowing otherwise unobservable wave-mixing resonances to be seen. This is an especially interesting phenomenon because these resonances are coherent effects that are induced by an incoherent process (collisional dephasing). First predicted1 in the late 1970s and eventually observed2 in 1981, these novel effects have now been seen in a wide variety of four-wave-mixing experiments, ranging from self-focusing to coherent anti-Stokes Raman spectroscopy.

Four wave mixing experiments are normally performed near atomic (molecular) resonances, when some of the input frequencies or their combinations are at resonance with the atomic transitions. If dephasing process are present, several new resonances appear, that may be traced directly to the influence of the dephasing processes. The origin of the ‘‘dephasing’’ may vary from collisions and other material relaxation processes, to field fluctuations, to higher order interactions in the wave mixing process. The source of these extra resonances is discussed, and specific results are shown for the various cases.

The effect of pump fluctuations on various coherent processes that arise in three-level systems interacting with two external fields is examined. Such coherent processes include the forward Hanle effect and various four-wave mixing effects such as the generation of phase-conjugate signals. A general formulation that enables one to calculate the influence of laser linewidth on the coherent signals produced in various directions is presented. Ensemble averages, over laser temporal fluctuations, of various physical quantities, such as atomic polarization, are calculated. The spectrum of polarization fluctuations is shown to consist of several new features which lead to coherent radiation in different directions depending on the resonant frequencies in the polarization fluctuations. The influence of pump linewidth on pressure-induced extra resonance (PIER) is treated in detail. The possibility of producing a laser-fluctuation-induced coherent signal at one of the atomic frequencies is examined. This new signal, which is produced in a direction different from that of the PIER signal, but has the same type of resonant character as PIER, is found to have significantly different pressure dependence than the PIER signal. The results of our numerical computations are qualitatively explained in terms of the convolutions of products of third-order susceptibilities and pump field-correlation functions.