Chern-Simons Theory and Quantum Fields in the Lowest Landau Level

By considering the area preserving geometric transformations in the configuration space of electrons moving in the lowest Landau level (LLL) we arrive at the Chern-Simons type Lagrangian. Imposing the LLL condition, we get a scheme with the complex gauge fields and transformations. Quantum theory for the matter field in LLL is considered and formal expressions for Read's operator and Laughlin wave function are presented in the second quantized form.Comment: 8 pages, RevTe

Geometric Transformations and NCCS Theory in the Lowest Landau Level

Chern-Simons type gauge field is generated by the means of the singular area preserving transformations in the lowest Landau level of electrons forming fractional quantum Hall state. Dynamics is governed by the system of constraints which correspond to the Gauss law in the non-commutative Chern-Simons gauge theory and to the lowest Landau level condition in the picture of composite fermions. Physically reasonable solution to this constraints corresponds to the Laughlin state. It is argued that the model leads to the non-commutative Chern-Simons theory of the QHE and composite fermions.Comment: Latex, 13 page

Rashba coupling in quantum dots: exact solution

We present an analytic solution to the problem of the Rashba spin-orbit coupling in semiconductor quantum dots. We calculate the exact energy spectrum, wave-functions, and spin--flip relaxation times. We discuss various effects inaccessible via perturbation theory. In particular, we find that the effective gyromagnetic ratio is strongly suppressed by the spin-orbit coupling. The spin-flip relaxation rate has a maximum as a function of the spin-orbit coupling and is therefore suppressed in both the weak- and strong coupling limits.Comment: 5 pages, 4 figs, reference adde

The Study of Goldstone Modes in ν\nu=2 Bilayer Quantum Hall Systems

At the filling factor $\nu$=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase.Comment: 13 pages, no figures. One reference is added. Typos correcte

Radiation induced oscillations of the Hall resistivity in two-dimensional electron systems

We consider the effect of microwave radiation on the Hall resistivity in two-dimension electron systems. It is shown that the photon-assisted impurity scattering of electrons can result in oscillatory dependences of both dissipative and Hall components of the conductivity and resistivity tensors on the ratio of radiation frequency to cyclotron frequency. The Hall resistivity can include a component induced by microwave radiation which is an even function of the magnetic field. The phase of the dissipative resistivity oscillations and the polarization dependence of their amplitude are compared with those of the Hall resistivity oscillations. The developed model can clarify the results of recent experimental observations of the radiation induced Hall effect.Comment: 4 pages, 1 figur

Temperature dependence of polarization relaxation in semiconductor quantum dots

The decay time of the linear polarization degree of the luminescence in strongly confined semiconductor quantum dots with asymmetrical shape is calculated in the frame of second-order quasielastic interaction between quantum dot charge carriers and LO phonons. The phonon bottleneck does not prevent significantly the relaxation processes and the calculated decay times can be of the order of a few tens picoseconds at temperature $T \simeq 100$K, consistent with recent experiments by Paillard et al. [Phys. Rev. Lett. {\bf86}, 1634 (2001)].Comment: 4 pages, 4 figure

Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems

Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of $N$-component electrons at the integer filling factor $\nu=k\leq N$. The basic algebra is the SU(N)-extended W$_{\infty}$. A specific feature is that noncommutative geometry leads to a spontaneous development of SU(N) quantum coherence by generating the exchange Coulomb interaction. The effective Hamiltonian is the Grassmannian $G_{N,k}$ sigma model, and the dynamical field is the Grassmannian $G_{N,k}$ field, describing $k(N-k)$ complex Goldstone modes and one kind of topological solitons (Grassmannian solitons).Comment: 15 pages (no figures

Ultrafast Coulomb-induced dynamics of 2D magnetoexcitons

We study theoretically the ultrafast nonlinear optical response of quantum well excitons in a perpendicular magnetic field. We show that for magnetoexcitons confined to the lowest Landau levels, the third-order four-wave-mixing (FWM) polarization is dominated by the exciton-exciton interaction effects. For repulsive interactions, we identify two regimes in the time-evolution of the optical polarization characterized by exponential and {\em power law} decay of the FWM signal. We describe these regimes by deriving an analytical solution for the memory kernel of the two-exciton wave-function in strong magnetic field. For strong exciton-exciton interactions, the decay of the FWM signal is governed by an antibound resonance with an interaction-dependent decay rate. For weak interactions, the continuum of exciton-exciton scattering states leads to a long tail of the time-integrated FWM signal for negative time delays, which is described by the product of a power law and a logarithmic factor. By combining this analytic solution with numerical calculations, we study the crossover between the exponential and non-exponential regimes as a function of magnetic field. For attractive exciton-exciton interaction, we show that the time-evolution of the FWM signal is dominated by the biexcitonic effects.Comment: 41 pages with 11 fig

Nonlinear optics and saturation behavior of quantum dot samples under continuous wave driving

The nonlinear optical response of self-assembled quantum dots is relevant to the application of quantum dot based devices in nonlinear optics, all-optical switching, slow light and self-organization. Theoretical investigations are based on numerical simulations of a spatially and spectrally resolved rate equation model, which takes into account the strong coupling of the quantum dots to the carrier reservoir created by the wetting layer states. The complex dielectric susceptibility of the ground state is obtained. The saturation is shown to follow a behavior in between the one for a dominantly homogeneously and inhomogeneously broadened medium. Approaches to extract the nonlinear refractive index change by fringe shifts in a cavity or self-lensing are discussed. Experimental work on saturation characteristic of InGa/GaAs quantum dots close to the telecommunication O-band (1.24-1.28 mm) and of InAlAs/GaAlAs quantum dots at 780 nm is described and the first demonstration of the cw saturation of absorption in room temperature quantum dot samples is discussed in detail