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International Journal of Modern Physics B

ORDER FORMATION AND ELEMENTARY EXCITATIONS IN TYPE-II QUANTUM-WELL EXCITON SYSTEM

T. Iida, Makoto Tsubota

Published Dec 10, 2001• 1 citation
Publisher

Abstract

The ordered state and the elementary excitations are theoretically studied in an interacting dilute quasi-two-dimensional Bose gas of excitons in a type-II quantum well. This system is advantageous for studying the macroscopic quantum phenomena because those excitons have a long lifetime of the order of 10-6 s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the obtained dispersion relations for excitations, we examine the Landau criterion for exciton superflow and the temperature dependence of the off-diagonal long-range order which characterizes the quasi-Bose-Einstein condensation in two-dimensional systems.

DOI
10.1142/s0217979201008706

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The ordered state and the elementary excitations are theoretically studied in an interacting dilute quasi-two-dimensional Bose gas of excitons in a type-II quantum well. This system is advantageous for studying the macroscopic quantum phenomena because those excitons have a long lifetime of the order of 10-6 s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the obtained dispersion relations for excitations, we examine the Landau criterion for exciton superflow and the temperature dependence of the off-diagonal long-range order which characterizes the quasi-Bose-Einstein condensation in two-dimensional systems.
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Summary form only given. In the dilute limit excitons behave as weakly interacting Bose particles and are expected to undergo the Bose-Einstein condensation (BEC). Because the exciton mass is very small at experimentally accessible exciton densities the critical temperature for exciton BEC should reach several Kelvins, i.e., about six orders of magnitude higher than the T/sub c/ for atom BEC. To create degenerate Bose-gas of excitons we propose quasi-2D gas of indirect excitons in coupled quantum wells (CQWs) which have two primary advantages for realizing a quantum degenerate exciton gas and, ultimately, the BEC-like phase transition: (i) the long lifetime of indirect excitons and (ii) the short exciton cooling time.
This paper deals with ordinary material systems whose elementary constitutents are fermions. It is pointed out that in such systems there can occur two kinds of bosons with quite different physical and mathematical characteristics. Type I bosons are bound complexes of an even number of fermions (such as 4He^{4}\mathrm{He}4He); and type II bosons are elementary excitations which are bound complexes of fermions and their holes (such as excitons). When the first type condenses, a superfluid state results with so-called off-diagonal, long-range order; while when the second type condenses, there is no superfluidity, but a change in spatial order. Thus both kinds of long-range order are related to Bose condensation.
The transition of atomic, electronic, or e-h systems to quantum phases is an extraordinary process when both microscopic and macroscopic properties of the system undergo fundamental changes. Bose-Einstein condensation, has been observed in a number of physical systems, including super-cold atomic gases and solid- state quasiparticles. The most typical example of equilibrium condensation is the superconducting state of Cooper pairs in metals. However, in many cases the lifetime of particles or quasiparticles under study is finite, ranging from picoseconds to milliseconds. And even in this case condensation is possible. It is generally understood at present that coherence and off-diagonal long-range order in the density matrix are the most important characteristic features of condensed quantum states. Phase coherence established over microscopic distances is an intrinsic property of all Bose condensates. Experiments featuring interference between either two condensates or two separate parts of the same condensate are often considered as more convincing than observation of the macroscopic occupation of the ground state. The formation of long-range order and spatial phase coherence can be measured by studying interference patterns using either a Michelson interferometer or Young double slit arrangement. Here we present experimental results of observation of long-range temporal and spatial coherence of a macroscopically ordered state of a high-density e-h system in GaAs during the generation of femtosecond superradiant emission at room temperature
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.