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