Angular distribution of photoluminescence as a probe of bose condensation of trapped excitons

Recent experiments on two-dimensional exciton systems have shown that excitons collect in shallow in-plane traps. We find that Bose condensation in a trap results in a dramatic change of the exciton photoluminescence (PL) angular distribution. The long-range coherence of the condensed state gives rise to a sharply focused peak of radiation in the direction normal to the plane. By comparing the PL profile with and without Bose condensation, we provide a simple diagnostic for the existence of a Bose condensate. The PL peak has strong temperature dependence due to the thermal order parameter phase fluctuations across the system. The angular PL distribution can also be used for imaging vortices in the trapped condensate. Vortex phase spatial variation leads to destructive interference of PL radiation in certain directions, creating nodes in the PL distribution that imprint the vortex configuration.     

Interacting bosons in an optical lattice

A strongly interacting Bose gas in an optical lattice is studied using a hard‐core interaction. Two different approaches are introduced, one is based on a spin‐1/2 Fermi gas with attractive interaction, the other one on a functional integral with an additional constraint (slave‐boson approach). The relation between fermions and hard‐core bosons is briefly discussed for the case of a one‐dimensional Bose gas. For a three‐dimensional gas we identify the order parameter of the Bose‐Einstein condensate through a Hubbard‐Stratonovich transformation and treat the corresponding theories within a mean‐field approximation and with Gaussian fluctuations. This allows us to evaluate the phase diagram, including the Bose‐Einstein condensate and the Mott insulator, the density‐density correlation function, the static structure factor, and the quasiparticle excitation spectrum. The role of quantum and thermal fluctuations are studied in detail for both approaches, where we find good agreement with the Gross‐Pitaevskii equation and with the Bogoliubov approach in the dilute regime. In the dense regime, which is characterized by the phase transition between the Bose‐Einstein condensate and the Mott insulator, we discuss a renormalized Gross‐Pitaevskii equation. This equation can describe the macroscopic wave function of the Bose‐Einstein condensate in the dilute regime as well as close to the transition to the Mott insulator. Finally, we compare the results of the attractive spin‐1/2 Fermi gas and those of the slave‐boson approach and find good agreement for all physical quantities.     

Dynamical processes related to the Bose condensation of excitonic molecules in CdSe

The time dependences in the picosecond region of various dynamical processes of single excitons and excitonic molecules in CdSe are studied experimentally. The results are discussed in relation to the realization of the Bose condensation of excitonic molecules by the use of picosecond pulse excitation.     

Quantum phase transition in an atomic bose gas with a feshbach resonance

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.     

Bose glass and superfluid phases of cavity polaritons

We report the calculation of cavity exciton-polariton phase diagram including realistic structural disorder. With increasing density polaritons first undergo a quasiphase transition toward a Bose glass: the condensate is localized in at least one minimum of the disorder potential. A further increase of the density leads to a percolation process of the polariton fluid giving rise to a Kosterlitz-Thouless phase transition toward superfluidity. The spatial representation of the condensate wave function as well as the spectrum of elementary excitations are obtained from the Gross-Pitaevskii equation for all the phases.     

Response of a Bose-Einstein condensate of dipole excitons to static and dynamic perturbations

Studies of the interaction of a Bose-Einstein condensate of two-dimensional spatially indirect excitons with the static fields of impurities, surface acoustic waves, and elementary excitations of a degenerate electron gas have been reviewed. The effects of screening of charged impurities and absorption of a Bleustein-Gulyaev surface acoustic wave by an exciton condensate have been considered. Friedel oscillations of the exciton density in a hybrid electron-exciton system, which consists of spatially separated layers of condensed exciton gas and degenerate electron gas, have been studied. The lifetimes of quasiparticle excitations (electrons, plasmons, and bogolons) in the hybrid system have been calculated. The contributions to the effects under study from condensate and above-condensate particles have been determined. The properties of an excitonic insulator have been analyzed within the Bardeen-Cooper-Schrieffer model with a built-in dissipation-free current.     

Dynamical conductivity of the two-dimensional Bose condensate: Superfluid-insulator transition for a long-range random potential

We calculate the dynamical conductivity of a disordered charged Bose condensate in two dimensions with a long-range random potential due to charged impurities with a large spacer width . Analytical results for the frequency-dependent conductivity for weak disorder are derived. For strong disorder the frequency-dependent conductivity is given in terms of a transcendental equation. The disorder-induced transition from a superfluid phase to an insulator phase is discussed. The density-density relaxation function and the screening properties of the disordered Bose gas are calculated. Experimental results for high-T _c superconductors are discussed.     

Superfluid phase transition in two-dimensional excitonic systems

We study the superfluid phase transition in the two-dimensional (2D) excitonic system. Employing the extended Falicov–Kimball model (EFKM) and considering the local quantum correlations in the system composed of conduction band electrons and valence band holes we demonstrate the existence of the excitonic insulator (EI) state in the system. We show that at very low temperatures, the particle phase stiffness in the pure-2D excitonic system, governed by the non-local cross correlations, is responsible for the vortex–antivortex binding phase-field state, known as the Berezinskii–Kosterlitz–Thouless (BKT) superfluid state. We demonstrate that the existence of excitonic insulator phase is a necessary prerequisite, leading to quasi-long-range order in the 2D excitonic system.     

Density of states in the bilayer graphene with the excitonic pairing interaction

In the present paper, we consider the excitonic effects on the single particle normal density of states (DOS) in the bilayer graphene (BLG). The local interlayer Coulomb interaction is considered between the particles on the non-equivalent sublattice sites in different layers of the BLG. We show the presence of the excitonic shift of the neutrality point, even for the noninteracting layers. Furthermore, for the interacting layers, a very large asymmetry in the DOS structure is shown between the particle and hole channels. At the large values of the interlayer hopping amplitude, a large number of DOS at the Dirac’s point indicates the existence of the strong excitonic coherence effects between the layers in the BLG and the enhancement of the excitonic condensation. We have found different competing orders in the interacting BLG. Particularly, a phase transition from the hybridized excitonic insulator phase to the coherent condensate state is shown at the small values of the local interlayer Coulomb interaction.     

Phase diagram of the bose condensation of dipolar excitons in GaAs/AlGaAs quantum-well heterostructures

Experimental studies of the phase diagram of Bose condensation in a system of spatially indirect dipolar excitons in GaAs/AlGaAs quantum wells are reviewed. The properties of spatially periodic patterns arising in the luminescence of the exciton Bose condensate in a ring-shaped potential trap and the coherence of the condensate luminescence are discussed.     

The chiral and deconfinement phase transitions

By introducing the dressed Polayakov loop or dual chiral condensate as a candidate order parameter to describe the deconfinement phase transition for light flavors, we discuss the interplay between the chiral and deconfinement phase transitions, and propose the possible QCD phase diagram at finite temperature and density. We also introduce a dynamical gluodynamic model with dimension-2 gluon condensate, which can describe the color electric deconfinement as well as the color magnetic confinement.     

Exciton Condensation in a Two-Dimensional System with Disorder

The Bose–Einstein condensation of excitons in two-dimensional (2D) systems has been studied theoretically, taking into account both the random potential associated with imperfections of the structure and the finite exciton lifetime. It is shown that the disorder existing in the system makes condensation possible. The finite exciton lifetime limits the thermalization of excitons in the disordered system and sets an additional limit on the critical temperature of the transition. The effects of interparticle interaction and pump fluctuations have been analyzed. The phase correlator has been calculated and the failure of the condensate due to the effects of interaction and fluctuations has been analyzed. The propagation of perturbations in the condensate has been investigated.     

Superfluidity of indirect biexcitons in superlattices

Instability in a system of interacting quasi-two-dimensional excitons in a type II superlattice of a finite thickness due to attraction between oppositely-directed excitonic dipoles in neighboring layers has been discovered. A stable system is that of indirect quasi-two-dimensional biexcitons formed by indirect excitons with dipole moments oriented in opposite directions. The radius and binding energy of indirect biexcitons has been calculated. A collective spectrum of a system of such biexcitons with a weak quadrupole interaction between them has been studied. Feasibility of Bose condensation, the density n _s(T) of the superfluid component, and a phase transition to the superfliud state in a low-density system of indirect biexcitons have been analyzed. Zh. éksp. Teor. Fiz. 115, 1786–1798 (May 1999)     

Internal Structure of Vortices in a Two-Component Exciton-Polariton Condensate

Vortex solutions of coupled Gross–Pitaevskii equations for a two-component Bose–Einstein condensate of exciton polaritons have been described theoretically with the inclusion of the dependence of the Rabi splitting energy on the density of the exciton component. It has been shown that the inclusion of blueshift leads to a considerable decrease in the densities of both components of the condensate. The spatial profiles of excitons and photons in the polariton system, as well as the energy of vortex excitation formation, have been calculated taking into account nonlinear corrections.     

Excitonic condensation under spin-orbit coupling and BEC-BCS crossover

The condensation of electron-hole pairs is studied at zero temperature and in the presence of a weak spin-orbit coupling (SOC) in coupled quantum wells. Under realistic conditions, a perturbative SOC can have observable effects in the order parameter of the condensate. First, the fermion exchange symmetry is absent. As a result, the condensate spin has no definite parity. Additionally, the excitonic SOC breaks the rotational symmetry yielding a complex order parameter in an unconventional way; i.e., the phase pattern of the order parameter is a function of the condensate density. This is manifested through finite off-diagonal components of the static spin susceptibility, suggesting a new experimental method to confirm an excitonic condensate.     

On the type of a phase transition in the system of exciton polaritons in an optical microcavity

The type of a phase transition in the quasi-equilibrium system of exciton polaritons in a two-dimensional optical microcavity has been analyzed. It has been shown that, although the system contains two types of bosons undergoing mutual transformations into each other, only one phase transition to the superfluid state with the quasilong-range order occurs in the two-dimensional system. This phase transition is a Kosterlitz-Thouless phase transition. A new physical implementation—excitons in a photon crystal—has been proposed for the Bose condensation of exciton polaritons. The superfluid properties of the ordered phase are discussed, and the superfluid density and Kosterlitz-Thouless transition temperature have been calculated in the low-density approximation.     

Finite-temperature phase-locking transition in three-dimensional arrays of Josephson coupled Bose–Einstein condensates

We consider theoretically a phase-locking transition in Bose–Einstein condensate in an optical lattice in the regime where system can realized as a three-dimensional Josephson junction array. The coherence between adjacent Bose condensates (trapped in the valleys of the periodic potential) caused by the Josephson tunneling can lead to a phase transition with a global phase coherence at certain critical temperature. Using a model Hamiltonian of Josephson weakly coupled Bose condensates we calculate the critical temperature for the three-dimensional system placed in a simple cubic lattice and discuss the result in the context of system parameters and possible experiments.     

A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.     

Condensate density and superfluid mass density of a dilute Bose-Einstein condensate near the condensation transition

We derive via diagrammatic perturbation theory the scaling behavior of the condensate and superfluid mass density of a dilute Bose gas just below the condensation temperature, T(c). Sufficiently below T(c) particle excitations are described by mean field (Bogoliubov). Near T(c), however, mean field fails, and the system undergoes a second order phase transition, rather than first order as predicted by Bogoliubov theory. Both condensation and superfluidity occur at the same T(c), and have similar scaling functions below T(c), but different finite size scaling at T(c) to leading order in the system size. A self-consistent two-loop calculation yields the condensate fraction critical exponent, 2beta approximately 0.66.     

Exciton condensation in coupled quantum wells

Bound electron-hole pairs—excitons—are Bose particles with small mass. Exciton Bose-Einstein condensation is expected to occur at a few degrees Kelvin—a temperature many orders of magnitude higher than for atoms. Experimentally, an exciton temperature well below 1 K is achieved in coupled quantum well (CQW) semiconductor nanostructures. In this contribution, we review briefly experiments that signal exciton condensation in CQWs: a strong enhancement of the indirect exciton mobility consistent with the onset of exciton superfluidity, a strong enhancement of the radiative decay rate of the indirect excitons consistent with exciton condensate superradiance, strong fluctuations of the indirect exciton emission consistent with critical fluctuations near the phase transition, and a strong enhancement of the exciton scattering rate with increasing concentration of the indirect excitons revealing bosonic stimulation of exciton scattering. Novel experiments with exciton condensation in potential traps, pattern formation in exciton system and macroscopically ordered exciton state will also be reviewed briefly.