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physica status solidi (b)

Thermal fluctuations in a system of microcavity exciton‐polariton condensations

Dinh‐Hoi Bui, Van‐Nham Phan

Published Sep 21, 2016• 3 citations
Publisher

Abstract

Abstract The exciton‐polariton condensation scenario in a microcavity matter–light system at finite temperature is investigated in the framework of the unrestricted Hartree–Fock approximation applying the two‐dimensional exciton‐polariton model. Treating electron–hole Coulomb interaction and matter–light coupling effects on an equal footing, we analyze the temperature influence on the excitonic and photonic order parameters. In the thermal equilibrium limit, the Kosterlitz–Thouless type phase transition of the exciton‐polariton condensation has been found. Depending on detuning and excitation density one finds that the system either favors the photonic or excitonic condensate. The effect of temperature on a crossover from a BCS‐excitonic to a BEC‐polaritonic condensed state then is discussed.

DOI
10.1002/pssb.201600359

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Abstract The exciton‐polariton condensation scenario in a microcavity matter–light system at finite temperature is investigated in the framework of the unrestricted Hartree–Fock approximation applying the two‐dimensional exciton‐polariton model. Treating electron–hole Coulomb interaction and matter–light coupling effects on an equal footing, we analyze the temperature influence on the excitonic and photonic order parameters. In the thermal equilibrium limit, the Kosterlitz–Thouless type phase transition of the exciton‐polariton condensation has been found. Depending on detuning and excitation density one finds that the system either favors the photonic or excitonic condensate. The effect of temperature on a crossover from a BCS‐excitonic to a BEC‐polaritonic condensed state then is discussed.
In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal-equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. At a given low temperature, the condensate by its nature shows a crossover from an excitonic to a polaritonic and finally photonic condensed state as the excitation density increases at large detuning. Without the detuning, the excitonic condensed state disappears whereas the polaritonic or photonic phases dominate. The crossover is also found by lowering the Coulomb interaction at a finite matter-light coupling. Lowering the Coulomb interaction or increasing the temperature, the excitonic Mott transition occurs, at which the exciton-polariton condensates dissociate to free electron-hole/photon. Depending on temperature and excitation density, the phase transition of the exciton-polariton condensates is also addressed in signatures of photoluminescence mapping to the photonic momentum distribution.
We investigate the thermodynamics and signatures of a polariton condensate over a range of densities, using a model of microcavity polaritons with internal structure. We determine a phase diagram for this system including fluctuation corrections to the mean-field theory. At low densities the condensation temperature Tc{T}_{c}Tc​ behaves like that for point bosons. At higher densities, when Tc{T}_{c}Tc​ approaches the Rabi splitting, Tc{T}_{c}Tc​ deviates from the form for point bosons, and instead approaches the result of a BCS-like mean-field theory. This crossover occurs at densities much less than the Mott density. We show that current experiments are in a density range where the phase boundary is described by the BCS-like mean-field boundary. We investigate the influence of inhomogeneous broadening and detuning of excitons on the phase diagram.
BEC of exciton-polaritons and related effects such as superfluidity1,2, spontaneous symmetry breaking3,4 and quantised vortices5,6 open way to creation of novel light sources7 and optical logic elements8. Remarkable observations of exciton-polariton BEC in microcavities9-12 have been reported in the recent ten years. Very recently, thermalisation and subsequent condensation of cavity photons in a dye-filled microcavity have been observed13. Here we show that BEC of both exciton-polaritons and photons can be created in the same system under different optical excitation conditions. A dynamic phase transition between a photon and a polariton BEC takes place after a single high-power excitation pulse and we find both condensed states in thermal equilibrium with the excited states. At the crossover, photons and polaritons coexist, which results in a decrease in the long-range spatial coherence. Build-up and successive depinning of polarisation is observed at the threshold of both polariton and photon condensation.
Recently, the two-dimensional nanocavity exciton-polariton system confined in semiconductor nanocavities has emerged as a promising alternative of BoseEinstein Condensate (BEC). The strong quantum correlations presents in this system, make it an unique candidate for studying entanglement and quantum phase transitions —qualitative changes in the ground state properties—. In this work, we review previous evidence, obtained by us, in the phase transitions of a finite exciton-polariton system. First, by using a BCS wave function to compute the ground state energy of N excitons without the photonic field, a crossover from the high-density electron-hole phase to the BCS excitonic phase is found, at a density which is roughly four times the close-packing density of excitons. Second, by means of a self-consistent procedure with a trial function composed of a coherent photon field and a BCS function for the electron-hole pairs, we obtain the scaling of the critical temperature with the number of polaritons. Using the method proposed originally by Olliver and Zurek, and subsequently developed by Bo Li and Zhi-Xi Wang , we calculate the discord for a generalized density operator, proposed by Blaizot
Low-energy excitations of the excitonic states in the semimetal and semiconducting materials described by the extended Falicov-Kimball model with phonon correlation are investigated. In the framework of the unrestricted Hartree-Fock approximation, we derive a set of self-consistent equations to find the quasiparticle energies and excitonic condensate order parameters. The real part of the optical conductivity and then the dynamical excitonic susceptibility function are analytically evaluated by means of the linear response theory. Numerical results reveal the significant expansion of the excitonic condensation window in the temperature--Coulomb interaction plane by lowering the mass imbalance. Under the influence of the mass imbalance and thermal fluctuations, the BCS-BEC crossover of the excitonic condensation states has been also addressed in the collective mode signatures of the optical conductivity. Out of the condensation state, the collective excitation of the excitonic bound state is examined by analyzing the imaginary part of the dynamical excitonic susceptibility function. At large mass imbalance and low thermal fluctuations, we find an extremely sharp peak with high intensity at low frequency in the imaginary part of the dynamical excitonic susceptibility spectrum, specifying the long-lifetime exciton existence before it becomes condensed.