Observation of an Amplitude Collapse and Revival of Chirped Coherent Phonons in Bismuth O.V. Misochko, 1 Muneaki Hase, 2 K. Ishioka, 2 and M. Kitajima 2 1 Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow Region, Russia 2 Materials Engineering Laboratory, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan (Received 29 September 2003; published 10 May 2004) We have studied the A 1g coherent phonons in bismuth generated by high fluence ultrashort laser pulses. We observed that the nonlinear regime, where the phonons’ oscillation parameters depend on fluence, consists of subregimes with distinct dynamics. Just after entering the nonlinear regime, the phonons become chirped. Increasing the fluence further leads to the emergence of a collapse and revival, which next turns into multiple collapses and revivals. This is explained by the dynamics of a wave packet in an anharmonic potential, where the packet periodically breaks up and reconstitutes in its original form, giving convincing evidence that the phonons are in a quantum state, with no classical analog. DOI: 10.1103/PhysRevLett.92.197401 PACS numbers: 78.47.+p, 03.75.Kk, 63.20.–e, 67.90.+z Coherent excitation of optical phonons is a general phenomenon occurring whenever an ultrashort laser pulse interacts with crystalline solids [1]. The necessary con- dition to realize the coherent excitation is the availability of Raman active phonons with frequencies smaller than the inverse of a laser pulse duration. For semimetals, the generation mechanism of coherent phonons was initially identified as a displacive one. However, it was later shown that the displacive mechanism is not a distinct process, but a particular case of stimulated Raman scattering [2]. Although many studies have dealt with time-resolved lattice dynamics, experiments performed with the use of high-energy laser pulses are still rare [3–7]. These high fluence studies revealed a specific feature of coherent oscillations: Above a well-defined threshold, the coherent oscillations are not linear with optical excitation, so that their parameters (including frequency) are a function of fluence. Even though in most situations involving pho- nons a classical description is adequate, at low enough temperatures or at sufficiently short time scales, quantum fluctuations become dominant [8]. This quantum behavior has been successfully demonstrated by the observation of squeezed coherent phonons [9,10]. Motivated by these recent developments, we have made a thorough study of coherent oscillations in a wide temperature and laser fluence range. Note that until now there were not any high fluence experiments performed at low temperatures. We report in this Letter that in the nonlinear regime the coherent A 1g phonons in Bi are chirped and, moreover, above a critical fluence they exhibit a collapse and revival phenomenon, testifying to nonclassical dynamics. In this study, we used a single crystal of bismuth (10 10 1 mm 3 ) with the cleaved surface perpendicular to the trigonal axis. The crystal was mounted into a closed- cycle cryostat and our experiment was performed in a conventional degenerate pump-probe scheme. The ex- perimental setup is similar to previous experiments [6,7] except the detection: We employed a phase-sensitive scheme modulating the pump beam at 2 kHz with a chopper and recording the signal by a lock-in amplifier. A Ti:sapphire mode-locked laser oscillator at 800 nm was amplified using a regenerative 100 kHz amplifier. The final amplified and compressed laser pulse had the dura- tion of 130 or 140 fs (at the sample position). The ampli- fied output was divided into pump and probe beams polarized perpendicular to each other. Both the pump and probe beams were kept close to normal incidence, and focused to a spot diameter of 300 m by a single 10 cm lens. From the linear absorption coefficient 6 10 5 cm 1 at 800 nm [6], we estimated that the absorp- tion depth was around 17 nm, whereas the photoexcited carrier density at the maximum pump fluence of 15 mJ=cm 2 was ’ 6 10 21 cm 3 , which comprised ’ 4% of all the valence electrons. We observed permanent damage of the crystal only above a threshold F ’ 22 mJ=cm 2 . Consequently, all of our experiments were performed at fluences lower than the damage threshold. The high intensity laser pulses can excite coherent acous- tic phonons and also transient temperature changes; how- ever, none of them were detected in our experiments. Figure 1(a) shows the transient reflectivity data dem- onstrating the high-amplitude coherent oscillations gen- erated by a high fluence laser pulse at room temperature. The signal consists of nonoscillatory and oscillatory parts. Attempts to model the transient signal as R R 0 A e exp t e A p exp t p sin2t ’; (1) where A e and e are the amplitude and the decay time for nonoscillatory component, A p , , and p are the coherent phonon amplitude, the frequency, and the oscillation de- cay time, ’ is the initial phase with respect to time zero, were unsatisfactory. It was impossible to obtain a good fit for all time intervals where the oscillations exist, since the frequency providing a good fit for short time delays does not match that at longer time delays (see the inset of PHYSICAL REVIEW LETTERS week ending 14 MAY 2004 VOLUME 92, NUMBER 19 197401-1 0031-9007= 04=92(19)=197401(4)$22.50 2004 The American Physical Society 197401-1