Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Quantum-kinetic Langevin fluctuations for exciton Bose-Einstein condensation

B. Mieck, H. Haug

Published Aug 15, 2002• 8 citations
Publisher

Abstract

The time-dependent correlation function of the order parameter of Bose-Einstein condensation is calculated for a dilute interacting exciton gas cooled by a cold phonon bath. This calculation is achieved by combining two theoretical concepts: (i) a non-Markovian quantum kinetics, which is necessary in order to include the changing single-particle spectrum during the condensation self-consistently, and (ii) the stochastic non-Markovian Langevin fluctuations which are connected with the dissipative scattering integrals. A linearization around the mean quantum kinetics is used in order to determine the order parameter's fluctuations around its mean value. Similarly as in the laser theory the linewidth or the coherence time of the coherent order parameter amplitude is determined. The results show a clear reduction of the linewidth of the coherent exciton amplitude as the system cools down in time through the threshold of the Bose-Einstein condensation. The observation of this line narrowing by nonlinear optical spectroscopy would give a direct indication of the temporal build-up of an exciton condensate in a semiconductor.

DOI
10.1103/physrevb.66.075111

Related papers

Quantum Kinetics of the Exciton Bose-Einstein Condensation

H. Haug

Photo-excited excitons, i.e. closely bound electron-hole pairs, are in the low-density regime approximately bosons. For sufficiently low temperatures and sufficiently high densities of the exciton gas, a nonequilibrium phase transition in the form of a Bose-Einstein condensation (BEC) can be expected. Various levels of the description of the kinetics of relaxation and condensation due to the coupling of the excitons to a cold reservoir of acoustic phonons are discussed. For noninteracting excitons a rate equation approach with the exciton Boltzmann equation can be used. For interacting excitons the nonmarkovian quantum kinetics is required for the description of the BEC in order to incorporate the changes of the energy spectrum during the condensation self-consistently. Finally colored Langevin fluctuations can be used to calculate the phase diffusion of the condensate.

Phase Transitions•Jan 1, 2002•1 citation

Kinetics of Bose–Einstein Condensate Formation in an Interacting Bose Gas

Yu. Kagan

The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well. Introduction The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].

Cambridge University Press eBooks•Apr 6, 1995•13 citations

Bose-Einstein Condensation Quantum Kinetics for a Gas of Interacting Excitons

O. M. Schmitt, D. B. Tran Thoai, L. Bányai +2 more

A quantum kinetics of the Bose-Einstein condensation in the self-consistent (s.c.) Hartree-Fock-Bogoliubov (HFB) model of the interacting Bose gas is formulated and numerically solved for the example of excitons scattering with a thermal bath of acoustic phonons. The theory describes the condensation in real time starting from a nonequilibrium initial state towards the equilibrium HFB solution. The s.c. changes of the spectrum are automatically incorporated in the scattering terms.

Physical Review Letters•Apr 23, 2001•25 citations

Kinetics of the Dephasing and the Condensation of Excitons

O.M. Schmitt, P. Gärtner, L. B�nyai +2 more

The dephasing and condensation kinetics of bosonic excitons after coherent pulse excitation is studied in the vicinity of a Bose-Einstein condensation (BEC). For a system of excitons interacting with acoustic phonons various excitation conditions are investigated. Significant qualitative changes of the polarization dephasing in the vicinity of the BEC are discussed. Furthermore the kinetics of excitons, interacting via a two particle interaction, is studied. Both the bosonic mean-field terms and the scattering terms are calculated on a microscopic level. As in the phonon-model the dephasing rate of the exciton–exciton scattering diminishes considerably in the vicinity of the BEC. All results are suited as experimentally observable signatures of an excitonic BEC.

physica status solidi (b)•Sep 1, 2000•3 citations

Kinetics of condensation in trapped exciton gases

Wei-Juan Zhao, P. Stenius, Ataç İmamoğlu

We study the kinetics of condensation in a trapped two-dimensional exciton gas using the quantum Boltzmann equation. We assume that the exciton gas interacts with a lattice that is kept at a constant temperature. Our simulations allow us to estimate and compare the condensation time for Bose gases with and without interactions. We find that anti-Stokes Raman-type two-phonon processes dominate the relaxation rate of low-energy states for a noninteracting gas. The presence of dissipation from the low-energy states results in a heating effect for the exciton gas which in turn increases the mean number of Bose particles required for the onset of condensation. Our results indicate that the condensation time scale in trapped two-dimensional excitons is determined by the phonon emission rate into the ground state. This time scale is orders of magnitude shorter than what is predicted for three-dimensional excitons. The steady state in a dissipative gas is a nonequilibrium condensate, or equivalently an exciton matter laser, where the exciton temperature remains above the lattice temperature.

Physical review. B, Condensed matter•Sep 1, 1997•18 citations

Quantum kinetic theory. IV. Intensity and amplitude fluctuations of a Bose-Einstein condensate at finite temperature including trap loss

Dieter Jaksch, Crispin W. Gardiner, Klaus M. Gheri +1 more

We use the quantum kinetic theory to calculate the steady state and fluctuations of a trapped Bose-Einstein condensate at a finite temperature. The system is divided in a condensate and a noncondensate part. A quantum-mechanical description based on the number-conserving Bogoliubov method is used for describing the condensate part. The noncondensed particles are treated as a classical gas in thermal equilibrium with temperature $T$ and chemical potential $\ensuremath{\mu}$. We find a master equation for the reduced density operator of the Bose-Einstein condensate, calculate the steady state of the system, and investigate the effect of one-, two-, and three-particle losses on the condensate. Using linearized Ito equations, we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. A Lorentzian line shape is found for the intensity correlation function that is characterized by a time constant ${\ensuremath{\gamma}}_{I}^{\ensuremath{-}1}$ derived in the paper. For the amplitude correlation function, we find ballistic behavior for time differences smaller than ${\ensuremath{\gamma}}_{I}^{\ensuremath{-}1}$, and diffusive behavior for larger time differences.

arXiv:cond-mat/9712206•Physical Review A•Aug 1, 1998•74 citations
The time-dependent correlation function of the order parameter of Bose-Einstein condensation is calculated for a dilute interacting exciton gas cooled by a cold phonon bath. This calculation is achieved by combining two theoretical concepts: (i) a non-Markovian quantum kinetics, which is necessary in order to include the changing single-particle spectrum during the condensation self-consistently, and (ii) the stochastic non-Markovian Langevin fluctuations which are connected with the dissipative scattering integrals. A linearization around the mean quantum kinetics is used in order to determine the order parameter's fluctuations around its mean value. Similarly as in the laser theory the linewidth or the coherence time of the coherent order parameter amplitude is determined. The results show a clear reduction of the linewidth of the coherent exciton amplitude as the system cools down in time through the threshold of the Bose-Einstein condensation. The observation of this line narrowing by nonlinear optical spectroscopy would give a direct indication of the temporal build-up of an exciton condensate in a semiconductor.
Photo-excited excitons, i.e. closely bound electron-hole pairs, are in the low-density regime approximately bosons. For sufficiently low temperatures and sufficiently high densities of the exciton gas, a nonequilibrium phase transition in the form of a Bose-Einstein condensation (BEC) can be expected. Various levels of the description of the kinetics of relaxation and condensation due to the coupling of the excitons to a cold reservoir of acoustic phonons are discussed. For noninteracting excitons a rate equation approach with the exciton Boltzmann equation can be used. For interacting excitons the nonmarkovian quantum kinetics is required for the description of the BEC in order to incorporate the changes of the energy spectrum during the condensation self-consistently. Finally colored Langevin fluctuations can be used to calculate the phase diffusion of the condensate.
The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well. Introduction The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].
The dephasing and condensation kinetics of bosonic excitons after coherent pulse excitation is studied in the vicinity of a Bose-Einstein condensation (BEC). For a system of excitons interacting with acoustic phonons various excitation conditions are investigated. Significant qualitative changes of the polarization dephasing in the vicinity of the BEC are discussed. Furthermore the kinetics of excitons, interacting via a two particle interaction, is studied. Both the bosonic mean-field terms and the scattering terms are calculated on a microscopic level. As in the phonon-model the dephasing rate of the exciton–exciton scattering diminishes considerably in the vicinity of the BEC. All results are suited as experimentally observable signatures of an excitonic BEC.
We study the kinetics of condensation in a trapped two-dimensional exciton gas using the quantum Boltzmann equation. We assume that the exciton gas interacts with a lattice that is kept at a constant temperature. Our simulations allow us to estimate and compare the condensation time for Bose gases with and without interactions. We find that anti-Stokes Raman-type two-phonon processes dominate the relaxation rate of low-energy states for a noninteracting gas. The presence of dissipation from the low-energy states results in a heating effect for the exciton gas which in turn increases the mean number of Bose particles required for the onset of condensation. Our results indicate that the condensation time scale in trapped two-dimensional excitons is determined by the phonon emission rate into the ground state. This time scale is orders of magnitude shorter than what is predicted for three-dimensional excitons. The steady state in a dissipative gas is a nonequilibrium condensate, or equivalently an exciton matter laser, where the exciton temperature remains above the lattice temperature.
We use the quantum kinetic theory to calculate the steady state and fluctuations of a trapped Bose-Einstein condensate at a finite temperature. The system is divided in a condensate and a noncondensate part. A quantum-mechanical description based on the number-conserving Bogoliubov method is used for describing the condensate part. The noncondensed particles are treated as a classical gas in thermal equilibrium with temperature TTT and chemical potential $\ensuremath{\mu}$. We find a master equation for the reduced density operator of the Bose-Einstein condensate, calculate the steady state of the system, and investigate the effect of one-, two-, and three-particle losses on the condensate. Using linearized Ito equations, we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. A Lorentzian line shape is found for the intensity correlation function that is characterized by a time constant ${\ensuremath{\gamma}}_{I}^{\ensuremath{-}1}$ derived in the paper. For the amplitude correlation function, we find ballistic behavior for time differences smaller than ${\ensuremath{\gamma}}_{I}^{\ensuremath{-}1}$, and diffusive behavior for larger time differences.