Transient three-pulse four-wave mixing spectra of magnetoexcitons coupled with an incompressible
quantum liquid
M. E. Karadimitriou, E. G. Kavousanaki,* and I. E. Perakis
Department of Physics, University of Crete, Heraklion, Crete 71003, Greece and Institute of Electronic Structure & Laser, Foundation
for Research and Technology-Hellas, Heraklion, Crete 71110, Greece
Keshav M. Dani
Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Received 1 April 2010; revised manuscript received 14 August 2010; published 8 October 2010
We present a nonequilibrium many-body formulation of the coherent ultrafast nonlinear optical response of
doped semiconductors and systems with a strongly correlated ground state, such as the quantum Hall system
QHS. Our theory is based on a truncation of the density-matrix equations of motion in the absence of a small
interaction parameter, obtained by expanding in terms of the optical field and by using Hubbard operator
density matrices to describe the exact dynamics within a subspace of many-body states. We identify signatures
of noninstantaneous interactions between magnetoexcitons X and the incompressible two-dimensional elec-
tron gas 2DEG during femtosecond and picosecond time scales by describing X coupling to inter-Landau-
level magnetoroton MR and magnetoplasmon excitations. We show that strong X coupling to X +MR con-
figurations changes the temporal evolution of the nonlinear optical spectra as compared to the random-phase
approximation RPA. We calculate the three-pulse four-wave mixing signal, whose dependence on frequency
and two time delays reflects the dephasing and relaxation of the strongly coupled X-2DEG system, and
demonstrate that the dynamics of the X-2DEG interaction process can be resolved with femtosecond optical
pulses. Our results shed light into unexplored subpicosecond and coherent dynamics of the QHS and may be
used to interpret and guide two-dimensional correlation spectroscopy experiments.
DOI: 10.1103/PhysRevB.82.165313 PACS numbers: 42.50.Md, 73.43.Lp, 82.53.Mj, 78.20.Bh
I. INTRODUCTION
While the thermodynamic, linear response, and transport
properties of many condensed-matter systems do not depend
critically on the residual interactions among their elementary
excitations, these interactions dominate the nonlinear re-
sponse to external stimuli. The interactions among quasipar-
ticles lead to decoherence and dephasing but also create new
quantum coherences between many-body states.
1–4
Under-
standing and manipulating coherent dynamics is essential for
building a new generation of controllable devices, whose
speed limits are governed by the time scales of fundamental
many-body processes. At the same time, a detailed under-
standing of the interaction processes leading to coherence
and decoherence is of primary importance in the fields of
macroscopic quantum phenomena, coherent control of mo-
lecular phenomena and femtochemistry, and for under-
standing the concepts underlying quantum information
technology.
5
In undoped semiconductors, the interactions among exci-
ton quasiparticles determine the transient nonlinear optical
response during the femtosecond temporal regime following
photoexcitation,
1,3,6
where well-established quasiequilibrium
concepts such as the free energy break down. To extract in-
formation from the experiments, nonequilibrium many-body
theories such as the semiconductor Bloch equations,
4,7
dy-
namics controlled truncation scheme DCTS,
2,8,9
correlation
expansion,
3
Keldysh Green’s functions,
4,7
and the canonical
transformation “dressed semiconductor” approach
10
have
been used. The exciton-exciton X-X interactions dominate
the one-dimensional two-pulse four-wave mixing FWM
spectra for negative time delays, where the phase-space fill-
ing Pauli blocking, PSF nonlinearities do not contribute.
1,6
The time-dependent Hartree-Fock treatment of the X-X
interactions
4,7
predicts a negative time delay signal that de-
cays twice as fast as the positive time delay signal.
1,6
In
undoped semiconductors, deviations from such an asymmet-
ric temporal profile were interpreted as a signature of corre-
lations and scattering among exciton quasiparticles.
1,11
To interpret the nonlinear optical spectra of undoped
semiconductors, one need not take into account correlations
involving ground-state electrons. A rigid Hartree-Fock
ground state, with full valence band and empty conduction
band, suffices when Auger processes are negligible.
12
The
lowest electronic excitations are then high-energy interband
transitions, which react instantaneously to the photoexcited
carriers. In doped semiconductors and metals, however, the
situation is different because low-energy electronic excita-
tions interact with the photoexcited carriers. The fundamen-
tal reaction time, the period of one oscillation of the lowest
excited state, can be long, in which case the system responds
unadiabatically to photoexcitation. The nonlinear response is
then strongly influenced by the quantum dynamics of the
entire system, including the ground-state electrons. The theo-
ries describing the nonlinear response of undoped semicon-
ductors must be extended when considering doped semicon-
ductors with strong e-h correlations
10,13,14
or the quantum
Hall system QHS.
15–19
For example, the DCTS truncates
the hierarchy of density matrices generated by the interac-
tions based on the assumption that all Coulomb interactions
occur between photoexcited e-h pairs and are thus dynami-
cally generated by the optical excitation. In the QHS how-
PHYSICAL REVIEW B 82, 165313 2010
1098-0121/2010/8216/16531324 ©2010 The American Physical Society 165313-1