Research Interests:

The following research directions were explored in my group during thepast year

Qubit coherent control with squeezed light fields

Quantum control fields that operate on a qubit in a single quantum gatemay become entangled with the qubit and thus contribute to the gate error.We have investigated the possible advantage of the use of squeezed light forqubit coherent control and compared it with the more standard coherent lightcontrol field. We have calculated the entanglement between a short pulse ofresonant squeezed light and a two-level atom in free space during the ¼ pulseoperation on a qubit and the resulting operational error. We found thatfor squeezed light, the interplay of three phases – the squeezing-phase, thephase of the light field and the atomic phase related to the superpositionof qubit levels, determine the error and the entanglement magnitude. Incomparison with the coherent control using coherent light, the error and theentanglement can be either enhanced or suppressed depending on the abovephase relations. We have discussed the possibility to measure the increasedgate error as a signature of this entanglement.

Coherent optical control of correlation waves of spins in semiconductors

We have calculated the dynamical fluctuation spectrum of electronic spinsin a semiconductor under a steady-state illumination of light containing po-larization squeezing correlations. In this externally driven system we foundthat the contribution which is fourth order in the optical field is sensitive tothe squeezing phase of the light. We have demonstrated the possibility tocontrol the spin fluctuations by optically modulating this phase as a func-tion of frequency in a pulse shaper. We found that the spin-spin correlationfunctions in time domain can be non-trivial in the case when the oppositepolarizations are used in combination with linear and quadratic phase func-tions.

New methods of analyzing photonic crystals

We have applied the Lippman Schwinger techniques to analyze phenom-ena in photonic crystals which have analogies of narrow resonance scatteringof a discrete state in Quantum Mechanics. We have extended and adoptedthe appropriate quantum mechanical modeling in order to describe such phe-nomena and predict classes of similar ones. This has important consequencesin applications of photonic crystals in optical communications.Path integration for photons in dielectric media.This work has just began. The goal is to write solutions of the fullvectorial Maxwell equations in an arbitrary dielectric media via a suitablepath integral.

Edge states and excitations in the Quantum Hall Effect

Quantum Hall Effect is a striking new phenomenondiscovered some 15 years ago. It occursin artificially prepared conductors in which electrons canmove only in a plane. When put in a strong magnetic field the electroncurrent flows perpedicular to applied voltage and the voltage tocurrent ratio is to an incredible accuracy equal to an integer number of units of quantum resistance. In verypure samples this ratio can also be equal to a fraction with odddenominator, like 1/3, 1/5, 2/7 etc. Such an effect is called a FractionalQuantum Hall Effect (FQHE). It turns out that edges of a sample playa special role in such effect. There existsa peculiar type of waves which can propagateonly along the edges. These waves move in opposite directions onoppositely lying edges. With my students I have investigated the processin which such waves can interact and "drag" each each other in theirown direction. Because of this interaction onecan excite such waves by sending an alternatingcurrent through the sample.

Quantum Chaos and Interactions in Disordered Quantum Dots

One of the most exciting aspectsof the quantum condensed matter physics is theinterplay between interactions and disorder.Electrons placed in very small disordered cavities (called quantum dots) exhibit unusual phenomenon called Quantum Chaos. Their energy levels are expected to be distributed not completely randomly but according to special rules called Wigner-Dyson Statistics. As itturns out interactions among the electrons modifythese rules and open a gap in the energy spectrumcalled the Coulomb gap. The quantum levels aquire awidth and become quasiparticle levels. I am presently interestedin the statistics of the quasiparticle levels, the fluctuatons of the Coulombgap and the dependence of the statistics on the spin properties andthe temperature of the electrons. Among thetechnical tools I am working with the Random Matrix Theory, Supersymmetryand the Replica methods.

Controlled Decoherence of Mesoscopic Systems

In recent experiments performed in our SubmicronCenter one began to fabricate coupledpairs of mesoscopic systems which can act as a controlleddephasor-dephasee device. I am investigating how in such pairsone can achieve a controlled decoherence of various quantumphenomena such as tunneling, shapes of the so-called Fano resonances, Berry phases, quantum pumps, Anderson localization, etc.

Other Interests

Other interests include non-perturbative methods in Quantum Chromodynamics; random colormagnetic fields; matrix models with free random variables; variational methods with free random variables - Fock space formulation.