What Determines the Wave Function of Electron-Hole Pairs in Polariton Condensates?

Abstract

The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density, detuning, and ultraviolet cutoff. During a change in the ground state of Bose-Einstein condensate from excitonic to photonic, which occurs as increasing the excitation density, the origin of the binding force of electron-hole pairs changes from Coulomb to photon-mediated interactions. The change in the origin gives rise to the strongly bound pairs with a small radius, like Frenkel excitons, in the photonic regime. The change in the ground state can be a crossover or a first-order transition, depending on the above-mentionsed parameters, and is outlined by a phase diagram. Our result provides valuable information that can be used to build theoretical models for each regime.PACS numbers: 71.36.+c, 71.35.Lk, 03.75.Hh, 42.50.Gy Microcavity polaritons-photoexcited electrons and holes strongly coupled with photons in a semiconductor microcavity-have been observed to exhibit BoseEinstein condensation (BEC) [1,2]. Due to the lightmatter coupling, the polariton has an extremely small mass about 10 −4 times the free-electron mass; the small mass results in a high critical temperature and low critical density. BEC can be realized even at room temperature [3], which is remarkable considering that it had been difficult to realize BEC in exciton systems for a long time [4]. Microcavity polaritons are dissipative particles due to the short lifetime of photons and inelastic scattering of excitons by phonons. Therefore, the polariton BEC is in a nonequilibrium stationary state with a balance between pumping and losses [5,6,7]. However, the polariton BEC has many similarities with BEC of neutral atoms in a thermal equilibrium [8]. It shows several evidences for the superfluidity: the Goldstone mode [9], the quantized vortices [10], and the collective fluid dynamics [11].Such a stationary state appears to be well described by the ground state of a closed microcavity polariton system, when the polariton lifetime is longer than the thermalization time [6,12]. In this paper, assuming such a situation, we determine the ground state with a fixed excitation density at absolute zero as a function of experimentally variable parameters: excitation density, detuning [13], and ultraviolet cutoff determined by the lattice constant. In past studies, mean-field theories have been used to discuss the two limits-low excitation density [14,15] and high excitation density [16]-by considering two different models. These theories are complementary [17], but their relation is somewhat ambiguous. We investigate the intermediate density region as well, where the electronhole (eh) wave function of the relative motion becomes important. We show that the ground state energy and wavefuction gradually change from those of excitons to photons as the excitation density increases. It is also shown that the change can be a crossover or a first-order transition, depending on the parameters considered. T...

PIPT from the Beginning to Future

“…Another kind of cooperative photoinduced phenomena, not discussed here, concerns the photostationary macroscopic state originating from the quantum condensation of electron-hole-photon systems [76].…”

Temperature Dependence of Highly Excited Exciton Polaritons in Semiconductor Microcavities

“…The polariton condensate is expected to experience several phases governed by the excitation density and detuning, for which different signatures of the photon laser have been theoretically determined under suitable conditions. [19][20][21][22][23] In particular, the work described in refs. 22 and 23 utilized the framework of a nonequilibrium system caused by pumping and decay, 33 which is very close to the actual experimental conditions.…”

“…Population inversion then occurs, and photon lasing is observed after the second nonlinear increase, which is often called the second threshold in contrast to the first or condensation threshold. [11][12][13][14][15][16][17][18] However, recent theoretical studies [19][20][21][22][23] have indicated that some e-h pairs can remain in the high-density regime.…”

“…Our results suggest that e-h binding is present in the high-excitation regime at low temperatures, supporting the theoretical considerations. [19][20][21][22][23] Appendix A: Parameters for the Estimation of Effective Masses…”

From polariton condensates to highly photonic quantum degenerate states of bosonic matter

“…Recent theoretical analysis (16) predicts condensation effects even when the local self-equilibrium condition is not fulfilled and also not only for the equilibrium Bose-Einstein distribution, but also for a wide range of nonequilibrium distribution functions. However, although there are theoretical studies classifying the condensate ground state for different detunings and mean polariton separations (17), from an experimental point of view, detailed studies of this regime without local self-equilibrium are still missing.…”