ISSN 0021-3640, JETP Letters, 2009, Vol. 90, No. 4, pp. 284–288. © Pleiades Publishing, Ltd., 2009. Original Russian Text © O.V. Misochko, M.V. Lebedev, 2009, published in Pis’ma v Zhurnal Éksperimental’noі i Teoreticheskoі Fiziki, 2009, Vol. 90, No. 4, pp. 309–314. 284 Coherence is inherent in many physical phenom- ena that are manifestations of quantum properties at the macroscopic scale. Among them are superfluidity, superconductivity, Bose–Einstein condensation, the Bernar effect, and laser effect [1]. In the last two phe- nomena, coherence appears under the conditions of nonequilibrium formed and maintained by external pumping, i.e., in the situation that is in many respects similar to the conditions of the appearance of coher- ence in the system of lattice excitations (phonons) in a crystal irradiated by an ultrashort laser pulse. After the interaction with such a pulse, the system of phonons is in the superposition state whose properties depend on the phase relations of lattice modes forming a phonon ensemble [2]. This superposition state is manifested in the time modulation of the reflection/transmission signal of a weak (probe) pulse, which follows after a pump pulse with a controlled delay time. The stable phase of the phonon ensemble (oscillations) appearing when the duration of the pump pulse is smaller than the inverse phonon frequency provides the possibility of the coherent control of lattice displacements, which was implemented for a number of materials [3]. The coherent dynamics of a lattice in nontransparent crys- tals becomes very nontrivial with an increase in the excitation level and exhibits a time-dependent (chirped) frequency [4, 5], nonexponential relaxation [6], and other interesting effects such as collapse and revival [4, 7]. For this reason, the optical control of high-amplitude coherent phonons is expected to clar- ify the details of this complex dynamics. In view of this circumstance, the aim of this work is to compare the results of the optical control of small- and large- amplitude coherent phonons in a bismuth single crys- tal at liquid-helium temperature. Bismuth, which is a semimetal that is crystallized in a rhombohedral A7 lattice [8] and has optically active phonon modes of the A 1g and E g symmetries, is a model system for analyzing the coherent dynamics of nontransparent crystals [2, 6, 7]. The fully symmet- ric A 1g mode investigated in this work coincides with the order parameter of a hypothetical first-order phase transition, which transforms bismuth into a semimetal [6], and is formed as a result of the out-of-phase dis- placements of two atoms of a unit cell along the trigo- nal axis. The investigation of these two coherent A 1g phonons was performed at a temperature of T = 4.5 K close to liquid-helium temperature using a femtosec- ond laser facility consisting of a sapphire titanate gen- erator of femtosecond pulses and a regenerative ampli- fier. The measurements were carried out with ultrashort pulses (wavelength λ = 805 nm, pulse dura- tion τ = 45 fs) of low and high energies in the degener- ate pump–probe scheme [6]. The normalized differ- ence reflection ΔR/R 0 was measured in the experi- ments as a function of time t between the pump and probe pulses in the two-pulse excitation scheme. In this case, the first pulse prepares the coherent state of the lattice and the second pulse modifies coherent oscillations. The optical (coherent) control of lattice displacements is similar to the interference of two light waves with a constant phase difference at which the total light intensity increases at some places and decreases at other points with the only difference that Optical Control of the Coherent Dynamics of a Bismuth Lattice at Liquid-Helium Temperature at Low and High Excitation Levels O. V. Misochko and M. V. Lebedev Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia e-mail: misochko@issp.ac.ru Received July 6, 2009 The fully symmetric A 1g phonons of bismuth have been investigated at liquid-helium temperature by the coherent control method for various crystal excitation levels. It has been found that large-amplitude coherent phonons exhibit the “rigidity” of the phase, which is absent at a small amplitude. The impossibility of chang- ing the phase of phonon oscillations appears at the excitation levels at which their amplitude relaxation law changes from exponential to power. The modification of the phase properties and relaxation law of the exci- tations of the crystal lattice can be understood in terms of the concept of the condensation of phonons, which occurs with an increase in the crystal excitation level. PACS numbers: 78.47.J-, 78.47.-p DOI: 10.1134/S0021364009160127