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Physical Review A

Learning about non-Markovian effects by degenerate four-wave-mixing processes

Boris D. Fainberg

Published Jul 1, 1993• 23 citations
Publisher

Abstract

I analyze the conditions for the correctness of the formula proposed by Lavoine and Villaeys [Phys. Rev. Lett. 67, 2780 (1991)] for learning about the non-Markovian effects by degenerate four-wave-mixing processes. I show that this dependence does not provide information about non-Markovian relaxation dynamics for the case of the inhomogeneously broadened transition. Such information can be obtained by the modification of a three-pulse four-wave-mixing experiment.

DOI
10.1103/physreva.48.849

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I analyze the conditions for the correctness of the formula proposed by Lavoine and Villaeys [Phys. Rev. Lett. 67, 2780 (1991)] for learning about the non-Markovian effects by degenerate four-wave-mixing processes. I show that this dependence does not provide information about non-Markovian relaxation dynamics for the case of the inhomogeneously broadened transition. Such information can be obtained by the modification of a three-pulse four-wave-mixing experiment.
The transient four-wave mixing signal from a three-level system coupled to a bath of harmonic oscillators is calculated in the short-pulse limit. This allows an examination of the non-Markovian effects on the relaxation processes in the excited levels between which beating occurs. In particular, it is possible to distinguish between oscillations which are due to oscillatory dephasing, a consequence of the memory effects, and oscillations due to the quantum beats. This also allows one to analyze how these two kinds of oscillations are mixed together. We show that we not only have an amplitude modulation of the beats as in the Markovian case but also deformations of the beats for short delays between the exciting light pulses. These deformations are a consequence of the nonequilibrium motion of the surroundings of the system under optical excitation. \textcopyright{} 1996 The American Physical Society.
Oscillatory dephasing is a characteristic signature of non-Markovian relaxation phenomena. From its analysis one can obtain valuable information about the dynamics of the surroundings of a given system. In this paper we calculate the transient four-wave mixing signal in the short pulse limit from two-level systems coupled to a bath of harmonic oscillators for arbitrary coupling strengths and in the presence of inhomogeneous broadening. The strong and weak coupling cases having already been analyzed, we focus on the study of the intermediate case where oscillatory dephasing is observed. We specifically show that even in the presence of inhomogeneous broadening, information about the surroundings can still be extracted in the intermediate coupling regime. The formation and the evolution of the photon echo in such experiments are also analyzed. \textcopyright{} 1996 The American Physical Society.
Oscillatory dephasing is a characteristic of non-Markovian relaxation phenomena when the coherence losses are essentially due to pure dephasing processes. In this paper, we wish to consider the case where the phase relaxation is essentially due to population decay. To this end, we calculate the transient four-wave mixing signal in the short pulse limit from a three-level sytem nondiagonally coupled to a bath of harmonic oscillators. We will show that no oscillatory dephasing is observed in the non-Markovian regime, only a nonexponential decay. Therefore, oscillatory dephasing appears to be a signature of pure dephasing processes.
Using transient four-wave mixing, wehaveobserved therelaxation dynamics ofadense potassium vapor whosedephasing timeislarge compared tothecollision duration, revealing a clear transition from non-Markovian toMarkovian dynamics. 02005 Optical Society ofAmerica OCIScodes: (320.7150) Ultrafast spectroscopy; (300.6240) Coherent transient spectrosopy Relaxation phenomena incondensed matter often occur intime scales ontheorder ofapicosecond orless. Inthese short timeregions, thedynamics depart from Markovian behavior, meaning thedynamics arealtered duetothe phase memoryofcollisions. Nonlinear optical time-domain techniques using two- andthree-pulse excitation are powerful tools that canreveal characteristics ofthedynamics. Suchexperiments have beenperforned inmolecular systems (1). Inthose experiments, theform oftheinteractions isoften difficult tocalculate theoretically because the time scale ofthelocal structural transitions isclose tothat ofthesolvent interactions andbeing pulse-width limited canbeanissue. Wehaveobserved inatwo-pulse transient four-wave mixing experiment thenon-Markovian dynamics inasimple atomic system whose dephasing time islarge compared tothecollision duration, allowing clear separation oftime scales, making accurate theoretical description possible. Inmolecular systems, thetime scales corresponding toelectronic andvibrational dynamics areoften difficult to separate. Asimple atomic system hasinteractions well-separated into short- andlong-time regimes, making it possible tocalculate theformoftheinteractions andconfirm itexperimentally. Westudy thephase relaxation dynamics ofadense potassium vapor using thetime-domain technique oftransient four-wave mixing (TFWM). Inself-diffracted TFWM,twopulses with wavevectors k,andk2interact nonlinearly inasample, resulting ina background-free signal indirection 2k,-k1 which istime-integrated byaslowdetector. Theloss ofcoherence ofthe system isprobed byvarying thedelay between thepulses. Intheshort timelimit, thesystem canbeconsidered inhomogeneously broadened duetothetemporally static butspatially varying distances between atoms. Atan intermediate time, which isfinite butless than thecollision duration between atoms, therelaxation dynamics are dominated bytheperturbations ofthetransifion frequency oftheatoms asthey collide. Thecollision canbethought ofasthetransient formation ofapotassium dimer(KA2) Interns ofthepotential energy surfaces ofthepotassium dimer, showninFig. 1,this timescale reveals dynamics modified bypotential energy fluctuations atsmall intermolecular spacings, r.Attimes muchgreater than thecollision duration, wecanestimate theperturbations as delta functions intime andpositions cannolonger beconsidered fixed duetothemofions oftheatoms, making the system homogeneously broadened. This limit inthedimer picture corresponds totheatoms traversing therange of theintermolecular potential intimes that canbeconsidered infinitely fast. ~~~~K2' 4