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AIP conference proceedings

Can Exciton BEC be observed via multi-level PL Kinetics?

Boris Laikhtman, Leonid D. Shvartsman

Published Jan 1, 2007• 0 citations
Publisher

Abstract

It is shown that the transition process to BEC phase of excitons can be manifested as non‐monotonic kinetics of photoluminescence decay. This decay looks as a series of subsequent peaks resulting from superradiance phenomenon. We show that decay of PL of certain InAs‐GaSb coupled quantum wells having, for instance, in average 5 ground state excitons per island may demonstrate up to 5 consecutive maximums followed by exponential decay. This dependence may be considered as a manifestation of transition to the Bose condensate phase. The radiation kinetics of such a system is a generalization of the known two‐level Dicke superradiance to an ensemble of multilevel systems.

DOI
10.1063/1.2729941

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Physical review. B, Condensed matter•Aug 15, 1997•23 citations
It is shown that the transition process to BEC phase of excitons can be manifested as non‐monotonic kinetics of photoluminescence decay. This decay looks as a series of subsequent peaks resulting from superradiance phenomenon. We show that decay of PL of certain InAs‐GaSb coupled quantum wells having, for instance, in average 5 ground state excitons per island may demonstrate up to 5 consecutive maximums followed by exponential decay. This dependence may be considered as a manifestation of transition to the Bose condensate phase. The radiation kinetics of such a system is a generalization of the known two‐level Dicke superradiance to an ensemble of multilevel systems.
We suggest a system of ground state excitons in multiple InAs-GaSb coupled quantum wells as a new source of superradiance. Coupled InAs-GaSb quantum wells can be tuned to a very large wavelength that makes it possible to fabricate a sample with a large number of quantum wells radiating in phase, and in this way to increase the superradiant effect. Depending on the parameters of the system, this superradiance may be a direct analogy of the known Dicke case, or a realization of new type NNN-level superradiance. In the last case, the time dependence of the luminescence presents NNN decaying peaks. This dependence may be considered as a manifestation of transition to the Bose condensate phase.
The influence of the radiative decay of excitonic molecules on a possible quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecule's is examined with respect to the radiative renormalization of the excitonic molecule energy (excitonic molecule Lamb shift). For the excitonic molecule wave function, a Schrödinger equation which contains polariton effects is derived and analyzed. Both the inverse excitonic molecule radiative lifetime γ m and the biexciton Lamb shift Δ m depend strongly on the total excitonic molecule momentum K. The energy renormalization Δ m (K) leads to the excitonic molecule effective mass modification and can result in a camel-back structure at K = 0, which opposes a BEC of excitonic molecules at K = 0. Introduction Observations of a quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecules (EM) have been attempted [1, 2, 3] following its theoretical prediction [4, 5] (for reviews see, e.g. [6, 7]). Recent approaches [8, 9] with high-precision techniques renewed the interest in this phenomenon. Traditionally, one tries to detect BEC of the EMs in luminescence. In the new approach the appearance of coherence in the thermal system of the EMs has been tested by means of four-wave mixing and treated as a fundamental manifestation of BEC. (See the paper by Hasuo et al . in this book.) Both optical methods for the BEC detection imply that the optical transition to the corresponding intermediate exciton (IE) state is dipole-active. In this case the EM state is unstable against optical decay with a “giant” oscillator strength [6].
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.
We develop a microscopic theory for the relaxation dynamics of an optically pumped two-level system (TLS) coupled to a bath of weakly interacting Bose gas. Using Keldysh formalism and diagrammatic perturbation theory, expressions for the relaxation times of the TLS Rabi oscillations are derived when the boson bath is in the normal state and the Bose-Einstein condensate (BEC) state. We apply our general theory to consider an irradiated quantum dot coupled with a boson bath consisting of a two-dimensional dipolar exciton gas. When the bath is in the BEC regime, relaxation of the Rabi oscillations is due to both condensate and non-condensate fractions of the bath bosons for weak TLS-light coupling and pre dominantly due to the non-condensate fraction for strong TLS-light coupling. Our theory also shows that a phase transition of the bath from the normal to the BEC state strongly influences the relaxation rate of the TLS Rabi oscillations. The TLS relaxation rate is approximately independent of the pump field frequency and monotonically dependent on the field strength when the bath is in the low-temperature regime of the normal phase. Phase transition of the dipolar exciton gas leads to a non-monotonic dependence of the TLS relaxation rate on both the pump field frequency and field strength, providing a characteristic signature for the detection of BEC phase transition of the coupled dipolar exciton gas.
Time-resolved photoluminescence (PL) of excitonic molecules in GaAs quantum wells (QW's) reveals an initial transient characterized by a finite rise and an extremely fast nonexponential decay [H. Wang, J. Shah, and T. C. Damen et al., Solid State Commun. 98, 807 (1996)]. The transient is attributed to coherent quantum evolution towards the molecule ground state of two optically correlated excitons, ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}},$ which undergo the Coulombic attraction. In the present paper, we develop a theory of the transient PL and fit the experimental data. The radiative decay of a quasi-two-dimensional (2D) excitonic molecule is analyzed with the giant oscillator strength model adapted to QW's and with the bipolariton model. Within the 2D bipolariton model, the main ``hidden'' channel of the radiative decay of an excitonic molecule is the resonant dissociation into two outgoing interface (surface) polaritons rather than the observable decay into the bulk radiative modes. We conclude that quasi-2D molecules dissociate already within the initial transient of PL, while the following exponential decay of the molecule-mediated PL is due to the escape of secondary interface polaritons into the bulk modes. According to the 2D bipolariton model, the sequence ``two incoming $\mathrm{photons}\ensuremath{\rightarrow}\mathrm{two}$ virtual $\mathrm{excitons}\ensuremath{\rightarrow}2\mathrm{D}$ $\mathrm{molecule}\ensuremath{\rightarrow}\mathrm{two}$ outgoing interface polaritons'' is a completely coherent process. The fit of the time-resolved molecule-mediated PL provides us with numerical estimates of the exciton-photon coupling in GaAs QW's.