Coherence properties and luminescence spectra of condensed polaritons in CdTe microcavities

We analyse the spatial and temporal coherence properties of a two-dimensional and finite sized polariton condensate with parameters tailored to the recent experiments which have shown spontaneous and thermal equilibrium polariton condensation in a CdTe microcavity [J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J.M.J. Keeling, F.M. Marchetti, M.H. Szymanska, R. Andre, J.L. Staehli, et al., Nature 443 (7110) (2006) 409]. We obtain a theoretical estimate of the thermal length, the lengthscale over which full coherence effectively exists (and beyond which power-law decay of correlations in a two-dimensional condensate occurs), of the order of 5 μm. In addition, the exponential decay of temporal coherence predicted for a finite size system is consistent with that found in the experiment. From our analysis of the luminescence spectra of the polariton condensate, taking into account pumping and decay, we obtain a dispersionless region at small momenta of the order of 4 degrees. In addition, we determine the polariton linewidth as a function of the pump power. Finally, we discuss how, by increasing the exciton-photon detuning, it is in principle possible to move the threshold for condensation from a region of the phase diagram where polaritons can be described as a weakly interacting Bose gas to a region where instead the composite nature of polaritons becomes important.     

Evidence for spontaneous interlayer phase coherence in a bilayer quantum Hall exciton condensate

Recent experimental work on the quantized Hall state at total filling factor ν_T=1 in bilayer 2D electron systems has revealed a number of striking phenomena, including a giant and sharply resonant enhancement of the interlayer tunneling conductance at zero bias. The tunneling enhancement is a compelling indicator of spontaneous interlayer phase coherence among the electrons in the system. Such phase coherence is perhaps the single most important attribute of the excitonic Bose condensate which describes this remarkable quantum Hall state.     

Secondary peak in the optical absorption spectra: A possible criterion for Bose condensation of excitons

By solving the BCS and Bethe-Salpeter equations, we confirm the result by Chu and Chang that a secondary peak appears in the optical absorption spectrum immediately after the 1S-exciton peak in the presence of a condensed phase. The observation of the secondary peak indicates the presence of exciton condensate.     

Bose glass and superfluid phase transitions of exciton-polaritons in GaN microcavities

Microcavity exciton-polaritons within GaN-based structures are the object of the present work. The impact of the structural imperfections on the properties of the two-dimensional polariton gas is investigated through the calculation of its phase diagram. We demonstrate that the presence of disorder first induces a quasi-phase transition of the polariton system towards a Bose-glass phase before it becomes superfluid as its density increases. Calculations of the density of states as well as the condensate wavefunction and the related spectrum of elementary excitations in the framework of the Gross-Pitaevskii theory provide further insight into the properties of exciton-polaritons in GaN-based microcavities.     

Polariton condensation in a one-dimensional disordered potential

We study the coherence and density modulation of a nonequilibrium exciton-polariton condensate in a one-dimensional valley with disorder. By means of interferometric measurements we evidence a modulation of the first-order coherence function and we relate it to a disorder-induced modulation of the condensate density, that increases as the pump power is increased. The nonmonotonic spatial coherence function is found to be the result of the strong nonequilibrium character of the one-dimensional system, in the presence of disorder.     

Anomalous dephasing of bosonic excitons interacting with phonons in the vicinity of the Bose-Einstein condensation

The dephasing and relaxation kinetics of bosonic excitons interacting with a thermal bath of acoustic phonons is studied after coherent pulse excitation. The kinetics of the induced excitonic polarization is calculated within Markovian equations both for subcritical and supercritical excitation with respect to a Bose-Einstein condensation (BEC). For excited densities n below the critical density , an exponential polarization decay is obtained, which is characterized by a dephasing rate . This dephasing rate due to phonon scattering shows a pronounced exciton-density dependence in the vicinity of the phase transition. It is well described by the power law that can be understood by linearization of the equations around the equilibrium solution. Above the critical density we get a non-exponential relaxation to the final condensate value p⁰ with that holds for all densities. Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB) terms due to the exciton-exciton interaction and the kinetics of the anomalous functions . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent exciton-exciton interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density. Received 13 December 1999     

Coherence matrices of radiation from an excited system

A new basis for the calculation of the coherence matrices of the radiation emitted by a system is introduced. The utility of this representation is demonstrated by calculating the coherence matrices of the radiation in scattering problems as well as in transitions involving a multiplet of states.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.     

Towards thermal equilibrium in the Bose-Einstein condensation of microcavity polaritons

By comparing a kinetic and a thermal-equilibrium theory of polariton Bose-Einstein condensation, we study under what conditions the dynamical condensation under steady-state non-resonant pumping can approach thermal equilibrium. In particular, we study the dependence on two material parameters: the vacuum-field Rabi-splitting and the polariton radiative lifetime. When increasing the Rabi splitting, condensation takes place under strong non-equilibrium conditions, with dominating quantum fluctuations. Increasing the polariton lifetime above 10 ps at moderate Rabi splitting, instead, produces a quasi-equilibrium condensate at low exciton density, consistently with the picture of a weakly interacting Bose gas.     

Subradiant split Cooper pairs

We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of cavity quantum electrodynamics could be generalized to many other nanoscale circuits.     

Interference and spontaneous emission

The field structure of the spontaneously emitted radiation from a single two-level atom is calculated in terms of atomic source variables and used to discuss the coherence properties of spontaneous emission.     

Dark Matter as a Cosmic Bose-Einstein Condensate and Possible Superfluid

Dark matter arising from spontaneous symmetry breaking of a neutral scalar field coupled to gravity comprises ultra low mass bosons with a Bose-Einstein condensation temperature far above the present background temperature. Assuming galactic halos to consist of a Bose-Einstein condensate of astronomical extent, we calculate the condensate coherence length, transition temperatures, mass distribution, and orbital velocity curves, and deduce the particle mass and number density from the observed rotation curves for the Andromeda and Triangulum galaxies. We also consider the possibility of superfluid behaviour in the halos of rotating galaxies, and estimate the critical angular frequency and line density for formation of quantised vortices.     

Bragg spectroscopy and superradiant Rayleigh scattering in a Bose–Einstein condensate

Two sets of studies concerning the interaction of off-resonant light with a sodium Bose–Einstein condensate are described. In the first set, properties of a Bose–Einstein condensate were studied using Bragg spectroscopy. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum distribution of the condensate. Depending on the momentum transfer, both the phonon regime as well as the free-particle regime could be explored. In the second set of studies, the cigar-shaped condensate was exposed to a single off-resonant laser beam and highly directional scattering of light and atoms was observed. This collective light scattering was caused by the long coherence time of the quasi-particles in the condensate and resulted in a new form of matter wave amplification. Received: 26 June 1999 / Revised version: 21 September 1999 / Published online: 10 November 1999     

Untersuchung der Eigenschaften der Strahlung eines Lasers ohne äußere Rückkopplung

The following article describes the realization of a laser without any external resonance structure and the behaviour of the emitted radiation. The experimental setup consits of a discharge tube closed with Brewster windows and the excitation electronics. The excitation process which brings the atoms to the upper laser level (2 p₆ Neon) will not establish any coherence between the atoms. Space coherence of the radiation has its origin in the correlated behaviour of the radiating atoms. Theoretical and experimental values of the fringe visibility are in close agreement for a path difference till to 440 cm, if temporal coherence is measured in an MICHELSON experiment. Interference fringes result if the radiation emerging from both sides of the tube is superimposed. The contrast decreases rapidly with the number of radiation pulses producing the interference pattern.     

Strong correlation effects in 2D Bose-Einstein condensed dipolar excitons

By doing quantum Monte Carlo ab initio simulations we show that dipolar excitons, which are now under experimental study, actually are strongly correlated systems. Strong correlations manifest in significant deviations of excitation spectra from the Bogoliubov one, large Bose condensate depletion, short-range order in the pair correlation function, and peak(s) in the structure factor.     

Does a Form Factor in Smith–Purcell Radiation Exist Always?

JETP Letters - In the theory of radiation emitted by bunches of charged particles, the effects of coherence are commonly taken into account by multiplying the intensity of radiation generated by a...     

Coherence time of the condensate of a weakly nonideal Bose gas

A system of equations for the density matrix is derived to describe the condensate and quasi-particles of a weakly nonideal spatially homogeneous Bose gas. The equations are used to find the distribution function of the number of particles and the condensate coherence time. A numerical estimate is obtained for a temperature that is significantly lower than the transition temperature. Original Text ? Astro, Ltd., 2009.     

Spatial coherence in the transition radiation spectrum

The formal expression of the spectral distribution of the transition radiation intensity will be here derived in the case of a relativistic three-dimensional charged beam. Charged beams with a particle density such as is typically encountered in a particle accelerator will be considered. In particular, a sufficiently high particle density will be supposed so that a continuous spatial distribution function can be reliably attributed to the charged bunch. The formula of the spectral distribution of the transition radiation intensity originated by a relativistic three-dimensional charged beam - already presented in a previous work - will be here submitted to a formal check and interpreted in the physical consequences. The present work contains an additional mathematical derivation of the radiation energy spectrum consisting in a different method to implement the continuous limit in the distribution function of the particle coordinates. In the former derivation of the formula, the average operation with respect to the continuous distribution function of the particle coordinates was applied to the radiation intensity of a N electron bunch. In the present one, it is applied to the radiation electric field of a N electron bunch. The comparison of the two alternative but in any case equivalent formal routes to the spectral distribution of the transition radiation intensity will offer the possibility to directly cross-check the mathematical self-consistency of the presented results within the limits of applicability of the continuous limit approximation. According to such results, both the flux and the angular distribution of the photons emitted at a given wavelength - even shorter than the longitudinal length of the bunch - are expected to undergo a modification as the beam transverse size is varied with respect to the observed wavelength. As a function of the beam transverse size the spatial coherence degree of the transition radiation source is thus expected to change. The physical consistency of such an effect occurring in the transition radiation emission by a charged beam can be argued on the basis of a compatibility criterion with other similar relativistic electromagnetic radiative phenomena and interpreted in the framework of the temporal causality and the Huygens-Fresnel principles. Finally, the aspect of the applicability of the continuous limit approximation to the case of a charged beam in a particle accelerator is treated in terms of a practical quantitative criterion.