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Non-Markovian Dynamics inaDensePotassium Vapor

T. Cundiff

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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

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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
Until the advent of laser, optical spectroscopy was limited to absorption and emission. These linear techniques often provided incomplete information because of the presence of inhomogeneous broadening, which arises in gases from Doppler shifts and in solids from random crystal elds or structural disorder (Figure 10.1). Lasers provided the high intensity needed to implement nonlinear spectroscopic techniques, which can make measurements “below” the CONTENTS 10.1 Introduction 371 10.1.1 Physical Description of TFWM for a Two-Level System 373 10.1.2 Overview of Variants and Extensions of TFWM 375 10.1.3 Use of TFWM Spectroscopy in Solids, Semiconductors, and Complex Systems 376 10.2 Theory 377 10.2.1 TFWM Signal from an Inhomogeneously Broadened Ensemble of Two-Level Systems 378 10.2.2 Phenomenological Inclusion of Many-Body Effects 381 10.3 Experimental Details of TFWM 382 10.3.1 Basics of Excitation Pulse Generation, Alignment, and Signal Detection 382 10.3.2 Time-Integrated Two-Pulse TFWM 385 10.3.3 Time and Spectrally Resolved Two-Pulse TFWM 386 10.3.4 Three-Pulse TFWM 386 10.3.5 Co-Linear TFWM 387 10.4 Case Study: TFWM from Excitons in GaAs Quantum Wells 387 10.4.1 Dephasing 388 10.4.2 Many-Body Effects 389 10.4.3 Disorder 391 10.4.4 Quantum Beats 391 10.4.5 Polarization Dependence 392 10.5 Multidimensional Fourier Transform Spectroscopy 392 10.6 Summary 393 References 393 inhomogeneous line width and determine the underlying homogeneous line widths. Often the homogeneous width is more interesting because it reects dynamics such as scattering and/ or radiative decay.
Phase relaxation of optical excitations in condensed matter can be studied by coherent four—wave—mixing experiments in the time domain without requiring assumptions on the spectral properties of the material. For inhomogeneously broadened transitions, three laser pulses at times t = 0, t = t21 and t = T with wave vectors k1, k2 and k3, respectively, generate a stimulated photon echo pulse, emitted time—delayed at t = T+t21 in the momentum—matching direction according to k3+k2−k1. As a function of t21 the echo amplitude decays due to scattering events, described by the dephasing time constant T2 [1].