Three-Pulse Photon Echo in a Dense PotassiumV~or

Virginia O. Lorenzl,2, Steven T. Cundiff, Wei Zhuang3 and Shaul Mukamee

1 .Tll-A, University of Colorado and National Institute of Standards and Technology,Boulder, Colorado 80309-0440E-mail: cundiffs@jiIa.colorado.edu

2 Department of Physics, University of Colorado, Boulder, Colorado 80309-03903 Department of Chemistry, University of Cali fomi a, Irvine, California 92697-2025

Abstract. Time-integrated tbree-pulse photon echo (3PE) and tiJ:ne..resolved 3PEmeasurements in a dense potassium vapor reveal clear signatures of non-Markoviandynamics. We pursue a molecular dynamics simulation to study the resonance effectscontributing to the response.

Relaxation phenomena in condensed phase systems often occur in time scaleson the order of a picosecond or less. In these short time regimes, the dynamicsdepart from Markovian behavior, meaning phase memory during interactions mustbe taken into account. Nonlinear time--domain optical techniques have been usedin molecular systems to study non-Markovian changes in molecular structure [1],but the time scales of the local structural transitions is often close to that of thesolvent interactions and the pulse-width limit can be an issue. In a time-integratedthree-pu1se photon echo (3PE) and time-resolved 3PE experiment, we haveobserved the non-Markovian dynamics of a simple atomic system whosedephasing time is large compared to the collision duration, allowing clearseparation of time scales. While the measured echo peak shift qualitativelysupports the use of an exponential correlation function in the current theory {2], atthe densities studied (>1017cm-3) collisions are no longer merely binary. Thecurrent theory describes foreign atom broadening and does not include resonanceeffects. Thus we are currently pursuin.g a molecular dynamics simulation toinclude resonance effects through an eXc1ton picture. Potassium vapor is an idealsystem in which to study disordered excitons due to its electronic simplicity andits easily adjusted density and temperature.

In the three-pulse photon echo (3PE) technique, three optical pulses interactnonlinearly in a sample, resulting in a background-ftee signal that is time­integrated by a slow detector (Fig. 1). The fitst pulse excites a coherence betweenthe ground and excited states. During the ensuing delay 't, dephasing occurs due tocollisions. Then the second pulse arrives and converts the remaining coherence toexcited-state or ground-state population. During the second delay T, loss ofpopulation and spectral redistribution occurs due to natural decay and collisions,and the system's ability to rephase and form a photon echo decreases. The thirdand final pulse forms a third-order coherence that radiates 8$ the signal. The time­integrated 3PE is measured by scanning the first delay 't for various fixed valuesof the second delay T, with negative delay corresponding to the conjugate pulsecoming second In the time-resolved version of3PE (time-gated 3PE), a reference

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pulse is correlated with the emitted 3PE signal at a particular 't and T in a BBOcrystal for up-conversion, resulting in a time-resolved scan of the nonlinearresponse versus the delay between the signal and the reference, t.

. Ti:sapph k_----:--,14 42P312...•... --F25MHz Detectors{ ."•...) J 42P100fs Oetay '\. .• / D1 mn2

768nm ,f-4... ~~ ~ ~ 'Ii:' 7l0nm 767nmk =..It +1<.+kc I I- '"8 -0 428

J. 112

, IPotassiumvapor:f

above input beams " ,~=-ktJ+ka+kcFig. t. The time-integrated 3PE experiment setup. The signals are detected in reflection dueto the small absorption length (••..A/21t) of the potassium vapor.

As exhibited by the data shown in Fig. 2(a), and considering only the k..signal forsimplicity, for 't > 0 the overall signal versus 't (ignoring the quantum beating dueto simultaneous excitation of both excited states) rises, peaks, and thenexponentially decays. Across the peak, the real-time signal changes from a photonecho to ~ee polarization decay, corresponding to the crossover from non­Markovian to Markovian dynamics. As. T is increased, the system's ability to forma photon echo decreases, and thus the crossover approaches 't = 0 (Fig. 2(b». Thepresence of the photon echo is clearly seen in the time-resolved signal (Fig. 3).

__ (a) T= 0.59ps (b) T=36ps (eto PeakShift

~ A1t ~

- Uil ' a..

E 1~'1" ~! d ~ -8 0.5m I xc m9 --It CDo - a..111 --It -_ok ",-0. . + + p 0.0(")-4 -2 0 2 -2 0 4 0 5 10 152~5 303540

~, delay between first and second pulse (ps) T,delay between 2 & 3'" pulse (ps)

Fig. 2. Experimental signals at 600°C (1.3xlOI8 em-3). (a) 3PE for T = 0.58 ps. The non­exPonential behavior at small 't is due to non-Markovian dynamics. (b) 3PE for T= 36 ps.The echo peaks ~ve shi&d to 'r = 0 ps due to the loss ofrephasing capability. (e) 3PEPSand bi-exponential fit (solid line).

For some molecular systems the three-pulse echo peak shift (3PEPS) reveals thetwo-time correlation function offtequency fluctuations directly [3]. H9wever, thisis only possible due to a theoretical simplification arising from the presence ofboth fast and slow modulation in the system. For a dense atomic vapor, suchsimplifications do not necessarily occur, but a qualitative form for the correlationfunction can be found from the 3PEPS. The experimental peak location versus T isexponential at lower temperatures and thus qualitatively supports the use of anexponential correlation function in modeling two-pulse experiments, as was donein [4]. The peak shift is bi-exponential above 500°C (Fig. 2(c». It is not yet clear

Tim~ved 3PESig~ (~M3f~)Photon et:ho decay$.tvIth T I

Photon echoT = O~~ T =2.32OODs T = 6.9600

shjifts with 1: r .s.A "--- -,

; f~ir~ iT Co O.psi-· ~ ""''''''-----1

L.l~~\IJ...~_--1T=O.Bps! ",,+ IT = 1.76ps~1J:'\AA"'---i1" = 2.9 U'lf\JV\tLj

2ps 0123456 0123456 0123456t,delay between $I.gnat and reference (ps)Fig. 3 (a) Experimentaltime-resolved 3PE signals at 6000C (1.3xl0Is em-J).smaU arrowspoint to t = 't, the photon echo loCationfor perfect rephasing. Photon echo strength clearlydecreases with increasing T.

whether this represents the presence of two coUision mechanisms~ such as bothbinary (hard) and many-body (soft) collisions, or contributions Rom higher orderpowers of the correlation function {5]. The current. theory does not account forresonance broadening, which dominates at these high densities [6]. To takeresonance effects into account and gain a mOre complete description of the systemresponse, we are currently J>f;rlonning molecular dynamics simulations in anexciton picture, with the signals calculated via the SPECTRONcomputationalpackage [7,8]. This win provide insight into. the non-Markovian dynamics ofdisordered excitonic systems in general and a resol131lte-broadened vapor inparticular.

In sunnnary, we have explored the non-Markovian dynamics of a dense pot$siumvapor with time ...integrated and time-resolved 3PE. Studying SUCha sUnple systemwith unusually well-separated dephasing time and collision duration lends insightinto the signatures of non-Markovian effects. II1 addition, future moleculardynamics simulations will shed light on the effects of many-body interactions indisordered excitons. Understanding the nonlinear response of this simple systemshould provide insight into other disordered excitonic systems such as molecularaggregates, semiconductors and biological systems. VOL and STC acknowledgethe support of the NSF JILA Physics Frontier Center. 8M acknowledges thesupport of the Chemical Sciences, Geosciences and BiO$ciences Division Officeof Basic Energy Sciences. U.S. Department~fEnergy.

References

1 see, for exmnple, T. 100 etal.,J. Chern. Phys. 104, 6089-61()8 (1996).2 S. Mukamel,Principles of Nonlinear Optical Spectroscopy, (Oxfuro, NY. 1995).3 B..T. J. NibberingetaL. Phys. Rev. Len. 66, 2464~2467(1991).4 V. O. Lorenz and S. T. Cunditt Phys. Rev. Len. 9S, 163601 (2005).5 D. A. Farrow et aL, J. Chern. Phys. US, 9348~9356(2003).6 J. A Leegwaterand S. MuIaunel,Pbys. Rev. A 49, 1:146-155 (1994).7 S. Mukamel,Annu. Rev. Phys. Chern.51:691-729 (2000).8 W. Zhuang et aI .• J. Pbys. Chern. B 108, 180:34-18045 (2006).

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