*Corresponding author. Fax: #7-096-576-4111.E-mail address: misochko@issp.ac.ru (O.V. Misochko).

Physica B 293 (2000) 33}37

Coherent phonons in InSb and their propertiesfrom femtosecond pump}probe experiments

O.V. Misochko!,",*, P. Gu", K. Sakai"

!Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka 142432, Moscow region, Russia"Kansai Advanced Research Center, Communications Research Laboratory, Iwaoka, Kobe, Hyogo 651-2401, Japan

Received 26 November 1999; received in revised form 6 March 2000; accepted 2 May 2000

Abstract

We report the ultrafast impulsive excitation of coherent LO phonons with the frequency of 5.57THz in InSb. Thesephonons, when generated by femtosecond laser pulses, exhibit phase-dependent #uctuation properties, that is, thevariance of coherent amplitude is a function of time delay. The variance oscillations occur, for short time delays, at twicethe frequency of the coherent amplitude. ( 2000 Elsevier Science B.V. All rights reserved.

PACS: 71.55.Eq; 74.25.Kc; 78.47.#p; 72.70.#m

Keywords: Coherent phonons; Ultrafast pump}probe experiment; Squeezed phonons

InSb is a well-established material for many ap-plications in today electronics. With the lowestband gap of any binary III}V semiconductors, itexhibits very low electron e!ective mass and highmobility. These interrelated features make the ma-terial one of the promising candidates for ultrafastelectronics. Optical, magnetic and transport prop-erties of the material have been extensively studied;however fast optical response remains essentiallyunknown. As far as optical phonons are concerned,their study traditionally is carried out in the fre-quency domain using such techniques as Ramanscattering and infrared spectroscopy. With the de-velopment of ultrafast lasers, it was demonstratedthat lattice dynamics can also be studied in the time

domain since the solids subjected to femtosecondlaser pulses exhibit lattice vibrations with a highdegree of coherence, which are usually called coher-ent phonons [1,2]. Moreover, following the obser-vation of squeezing for molecular vibrations [3], ina few ultrafast experiments the lattice squeezinghave been reported [4}7]. Production of thesqueezed states has attracted a great attentionamong the physical community over the last twodecades [8,9], and the achievement of squeezing formassive bosons in atomic systems [3] as well as incondensed matter [4}7] provides the opportunityto get a deeper insight into the issue. In this paperwe explore the possibilities and consequences ofimpulsively excited coherent phonons in InSb usinglight pulses which are short in duration comparedto the phonon oscillation period. We show thatcoherent phonons can be excited in InSb and re-port the results that aim at the investigation of

0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 5 3 7 - 8

Fig. 1. Transient fractional re#ectivity change in InSb versustime delay. The inset shows Fourier transform of the oscillatorytrace.

Fig. 2. The mean (circles, left-hand scale) and the variance (solidline, right-hand scale) of the oscillatory trace as a function oftime delay.

#uctuation properties of the phonons created byultrafast laser pulses.

The experiments were performed at room tem-perature using the standard pump}probe setup de-scribed in detail elsewhere [7,10]. Thetitanium}sapphire laser operating at 800 nm pro-vided 78MHz train of the pulses whose durationdid not exceed 50 fs. The pulses were divided intoa pump and a probe pulse and focused by a singlelens into a spot diameter of 50lm. The averagepower of the pump and probe pulses was in theratio 30 : 1 with the probe power less than 1mW.The transient re#ectivity was obtained with thephase-sensitive detection scheme in which thepump beam was modulated at 550Hz with a shakerand the time delay between the pump and probewas controllably varied. The InSb "lms used forour measurements were optically thick, homogene-ous, crystalline "lms deposited by MOCVD onGaAs (0 0 1) substrate, with a typical thickness of1.4lm. From infrared measurements, we derivedfor the "lms the e!ective mass and carrier mobilityto be 0.0152m

%and 2]104 cm2V~1 s~1, respective-

ly, and the carrier density to be 6.7]1016 cm~3.Fig. 1 shows a typical pump}probe result for

InSb. The transient re#ectivity signal consists ofa decaying electronic response and an oscillatorypart. The oscillations decay relatively fast and arenot detectable, within the sensitivity of the experi-ment, after 4 ps. These oscillations in the transientre#ectivity follow cosine dependence with initialphase close to p, as deduced from zero-time ampli-tude. Further, the frequency and the lifetime ofcoherent oscillations, both determined froma Lorentzian "t to the Fourier transform shown inthe inset of Fig. 1, are 5.57THz and 2.9 ps, respec-tively. This frequency of 5.57 is characteristic of thematerial and corresponds to LO phonon mode. Wewould like to emphasize that no feature at thefrequency of the LO overtone appears in the transi-ent re#ectivity. InSb has been thoroughly studiedby Raman scattering, and its Raman spectrumdominated by LO-mode at 188 cm~1 (5.64THz)and TO-mode appearing as a shoulder at 180 cm~1

(5.4THz) is well known [11}13]. The LO phononin the polarized spectra is dipole-forbidden for in-elastic light scattering and its Raman activity inInSb is primarily derived from additional scattering

mechanism involving impurities [12]. There is alsoa contribution from the FroK hlich interaction, whichis weaker [13]. The two scattering mechanisms arediagonal, thus making time-domain observation ofthe phonon possible. Second-order Raman scatter-ing is usually substantially weaker appearing asa peak at 380 cm~1 (11.4THz) [11]. For our "lmsthe LO and TO frequencies, when measured byRaman, were 5.72 and 5.4THz, respectively. The

34 O.V. Misochko et al. / Physica B 293 (2000) 33}37

Fig. 3. Schematic diagrams of the uncertainty areas for thermaland squeezed coherent states and of the measuring scheme.

Fig. 4. The mean (circles, left-hand scale) and the variance (solidline, right-hand scale) in an extended scale as a function of phaseangle.

lower frequency detected in our pump}probe ex-periment for LO-mode (5.57 THz in the time do-main against 5.72THz measured by Raman) maybe due to our inability to resolve the LO}TO doub-let. The same reason can account for a largerlinewidth detected in the time domain. The inten-sity of the second-order phonon feature located inour Raman spectrum at 11.43THz was 4}5 timesweaker than that of LO phonon. Summarizing, wehave experimentally shown that coherent phononscan be excited and detected by ultrafast pulses inInSb. The mode that contribute mostly to the oscil-lations in transient re#ectivity has been identi"edwith LO phonon.

We concentrate henceforth on the #uctuation(noise) properties of the state created in InSb byultrafast pulses. To study the properties as a func-tion of time delay we made 80 repeated measure-ments of the oscillatory waveform shown in Fig. 1.Keeping the record of all the waveforms allows usto obtain not only the "rst moment (the mean) butalso the higher-order moments of phonon distribu-tion function. From these 80 waveforms *R(t

*) we

calculated the mean, *R."S*R(t

*)T, and the vari-

ance, p2"S(*R(t*)!*R

.)2T, at each delay time

(phase angle), the brackets denote ensemble aver-age. The obtained mean and variance are shown inFig. 2. To get insight into noise properties, we splitthe sampled time interval into three distinct parts:negative time delays, a few hundreds femtosecondsafter the pump pulse strikes, and the region domin-ated by the oscillatory part. In this study we will beinterested only in the "rst and last regions. Atnegative time delays the variance is independent oftime, which represents the situation with time inde-pendent noise. More exactly, for the thermal state,which exists before the pump pulse strikes thesample, there is no preferred phase and the time-independent variance re#ects the circular shape ofuncertainty contour; see a pictorial representationof thermal and squeezed states given in Fig. 3. Theappearance of coherent phonons makes the situ-ation di!erent and the variance becomes time de-pendent. However, the variance time dependencedoes not follow that of coherent phonon. The vari-ance is peaked at the nodes of coherent amplitudeand is minimal for the antinodes, which can be seenin Fig. 2 and is shown in an extended scale in Fig. 4.

Note that when the laser was unstable in the experi-ments or the coherent amplitude was too small, westill observed the phase-dependent noise; however,the variance frequency coincides with that of coher-ent phonon and the similar behavior was observedfor larger time delays even when the laser wasstable. Such behavior most probably stems fromthe fact that we could not resolve in time the minorpeak in variance, which was clearly seen at shorttime delays, since the phase for the small coherentamplitude was not well de"ned.

O.V. Misochko et al. / Physica B 293 (2000) 33}37 35

Fig. 5. Fourier transforms of the mean (upper panel) and thevariance (lower panel).

The variance (noise) is not phase dependent forany of the classical or quantum states except thesqueezed state [7}9]. Given the coherent state ofthe lattice after the pump pulse strikes the sample,the phase-dependent noise is suggestive of squeez-ing of the LO phonons created in the pump}probeexperiment. The phonon squeezing has been dem-onstrated for semimetals Bi and Sb where coherentamplitude is signi"cantly larger [6,7]. The inter-pretation of phase-dependent noise as a signatureof the squeezing was based on the assumption thatthe coherent state detected in ultrafast experimentis a minimum uncertainty state and its #uctuationproperties are similar to those of vacuum stategoverned by zero-point #uctuations. This assump-tion is a crucial point since we note that our tech-nique lacks a readily de"ned benchmark levelcorresponding to the shot-noise. Even though thesignal in InSb is substantially lower than in thesemimetals like Bi and Sb, the qualitative behaviorof noise is similar to that observed in thesemimetals. First of all, the angular frequency of the#uctuations is twice the frequency of the coherent

amplitude as can easily be seen from Fig. 4. Thesame frequency ratio can also be deduced from theFourier transforms of the variance and of the mean,the two made for the time window not exceeding2 ps. Fig. 5 where the Fourier transforms are depic-ted shows that there is a substantial increase of thespectral weight around 11THz for the varianceonly. Second, the `squeezeda and `stretcheda quad-rature components relax to an unsqueezed value,the former increases and the latter decreases in thecourse of time. This relaxation seems to occur attwo di!erent rates. The squeezed state can bethought as the state with two excitations, that is,the phonons are created in pairs. The pairwisecorrelations are common for the description of thesqueezed state in optics [14] and were demon-strated for insulators [4,5] where the phonons werecorrelated in k-vector (the pairs from di!erentedges of the Brillouin zone) and detected in thetransient optical response measured in transmis-sion. However, this second-order Raman mecha-nism responsible for the squeezing in the latterexperiments cannot be applied to our case since wedetected no second-order feature in the transientre#ectivity for InSb.

Finally, we would like to draw attention to thefeature that seemingly cannot be explained with thesqueezing hypothesis. For every cycle of the coher-ent amplitude there are two peaks with distinctheights in the variance, see Fig. 4. For the squeezedstate it is natural to expect that the noise in thegiven quadrature is constant for a stationary stateor a smooth function of time for a transient state. Inany case the reading for *R(u) and *R(u#n)should be almost of the same value, whereas inexperiment this requirement is apparently violated.However, the additional modulation can be causedby other squeezed modes, which have zero coherentamplitude and therefore contribute to the varianceonly. For instance, for InSb, if TO phonon issqueezed and its initial (or squeezing) phase is dif-ferent from that of LO phonon, then the cumulativee!ect of the two phonon modes will lead to addi-tional modulation. We noticed that this additionalmodulation was more pronounced for lower pumppower and, for the Fourier-transformed variance,the stronger modulation was accompanied bya higher ratio between the intensities of the peaks at

36 O.V. Misochko et al. / Physica B 293 (2000) 33}37

X and 2X. It should also be noted that the similaradditional modulation with resembling pump de-pendence has been observed in GaAs, Sb, and Bi[6,7].

At the end, we would like to mention that whenthe laser pulse excites coherent phonons, the result-ing polarization could be used to generate coherentTHz radiation. The THz emission of the phononscreated by ultrafast laser has been suggested theor-etically and realized experimentally [15,16]. LOphonons in InSb can also be a source for such THzemission. If the phonons can be squeezed in ultra-fast experiments, it will be interesting to address thestatistical properties of radiation "eld generated bythe phonons. Note that InSb is a better candidatefor such experiments than GaAs, where the squeez-ing for LO phonon has been recently reported [7],since the frequency of coherent phonons in InSb islower and well within the range accessible to con-ventional dipole antenna.

To conclude, in the femtosecond pump}probeexperiments on InSb we have detected oscillationsascribed to the excitation of coherent LOphonons. These oscillations demonstrate phase-dependent noise similar to that observed earlier insemimetals.

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O.V. Misochko et al. / Physica B 293 (2000) 33}37 37