59 research outputs found
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 =2 Bilayer Quantum Hall Systems
At the filling factor =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 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 -component electrons at the integer filling factor .
The basic algebra is the SU(N)-extended W. 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 sigma model, and the dynamical field
is the Grassmannian field, describing 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
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