The major areas of current research in our group are quantum computing, transport in 2D electron systems, classical and quantum activation in nonequilibrium
systems.
In the theory of transport phenomena, we are
currently working on many-electron transport in strongly
correlated 2D electron systems. For nondegenerate electron fluids
and Wigner crystals, we have developed a theory which is
nonperturbative in the electron-electron interaction. The results have
been fully confirmed by experiments on electrons on helium surface
performed at several laboratories. We also explained giant
nonlinearity of the conductivity for electrons forming a Wigner
crystal. Recently we found how to relate the behavior of nondegenerate
2D many-electron systems in quantizing magnetic fields to the
phenomenology of the integer quantum Hall effect, and predicted
non-monotonic dependence of the microwave conductivity on frequency
and magnetic field. We have also analyzed tunneling from a
strongly correlated electron system and revealed the many-electron
recoil mechanism that exponentially increases the rate of tunneling
transverse to a magnetic field. Current work is centered at
nonlinear resonant effects , including saturation of interband
absorption and absorption hysteresis.
In physics of systems away from thermal
equilibrium, we are interested primarily in understanding large
quantum and classical fluctuations, in particular tunneling and
activated processes. Large fluctuations play a key role in a broad
range of physical phenomena, from diffusion in solids to nucleation at
phase transitions, mode switching in lasers, and protein
folding. Among important applications are bifurcation amplifiers used
in quantum measurements. No generally accepted principles have been
found that describe probabilities of large fluctuations in
nonequilibrium systems. A key to the theoretical analysis is that, in
a large fluctuation to a given state, a classical system is most likely to
move along a certain optimal path. Optimal paths for activated
processes are physically observable. We revealed generic
features of the distribution of fluctuational paths and showed that it
may display critical behavior.
Many predictions of the theory of activated processes, including
the onset of several types of the scaling behavior of the
escape rates, have been recently confirmed by experiments on
well-characterized systems. This includes observation of a sharply
peaked distribution of fluctuational paths in lasers and the
characteristic parameter dependence of the switching rates between
different types of coexisting periodic states of electrons in Penning
traps, atoms in modulated traps, micro- and nano-mechanical
resonators, Josephson junction based systems, and particles in
modulated optical traps. Understanding dynamics of activated processes
paves the way to controlling them. We developed a general
nonadiabatic theory of the response of fluctuation probabilities to
external fields. This response can be exponentially strong. In a broad
parameter range the activation energy is linear in the field
amplitude. The response is then described in terms of the
logarithmic susceptibility.
Decay of a metastable state is usually considered as resulting
from tunneling or thermal activation. We have predicted that
periodically modulated systems display a different decay mechanism,
quantum activation. As tunneling, quantum activation is due to
quantum fluctuations, but as thermal activation, it involves diffusion
over an effective barrier separating the metastable state. It is
often more probable than tunneling even for low temperatures.
Quantum computing has attracted much
attention recently. In 1999 we proposed electrons floating on helium
surface as a candidate for a quantum computer. This system has
the highest electron mobility known in condensed matter. The electrons
can be conveniently controlled using dc and microwave fields, and
their final state can be read out directly, because different states
of an electron qubit have different electric dipole moments. We have
identified the mechanisms of electron scattering, and our realistic
estimates show that the electron qubits have extremely long relaxation
times. We are closely collaborating with several labs which have
started experimental work on making a quantum computer with electrons
on helium.