Bose-Einstein Condensation Of Polaritons Research Articles

Room Temperature Current Injection Polariton Light Emitting Diode with a Hybrid Microcavity

The strong light-matter interaction within a semiconductor high-Q microcavity has been used to produce half-matter/half-light quasiparticles, exciton-polaritons. The exciton-polaritons have very small effective mass and controllable energy-momentum dispersion relation. These unique properties of polaritons provide the possibility to investigate the fundamental physics including solid-state cavity quantum electrodynamics, and dynamical Bose-Einstein condensates (BECs). Thus far the polariton BEC has been demonstrated using optical excitation. However, from a practical viewpoint, the current injection polariton devices operating at room temperature would be most desirable. Here we report the first realization of a current injection microcavity GaN exciton-polariton light emitting diode (LED) operating under room temperature. The exciton-polariton emission from the LED at photon energy 3.02 eV under strong coupling condition is confirmed through temperature-dependent and angle-resolved electroluminescence spectra.

Ground-state properties of microcavity polariton condensates at arbitrary excitation density

The ground state of microcavity polariton Bose-Einstein condensates (BEC's) is determined as a function of experimentally tunable parameters (the excitation density and the detuning of cavity photons), and also a material parameter (the ultraviolet cutoff). To obtain the ground state at an arbitrary excitation density, an interpolation method for the BEC-BCS crossover of excitonic insulators is extended to microcavity polariton systems in two or three dimensions. The ground state of the condensate changes from excitonic to photonic with an increase in the excitation density. This change is accompanied by several interesting features: (i) A laserlike input (excitation density) and output (photon density) relation with a sharp onset for largely detuned systems, which changes to that with a smooth onset for slightly detuned systems. (ii) The origin of the binding force of electron-hole pairs changes from Coulomb attraction to photon-mediated interactions, resulting in the formation of strongly bound pairs with a small radius, such as 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-mentioned parameters, and is studied by plotting phase diagrams.

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

Bose-Einstein condensation (BEC) is a thermodynamic phase transition of an interacting Bose gas. Its key signatures are remarkable quantum effects like superfluidity and a phonon-like Bogoliubov excitation spectrum, which have been verified for atomic BECs. In the solid state, BEC of exciton-polaritons has been reported. Polaritons are strongly coupled light-matter quasiparticles in semiconductor microcavities and composite bosons. However, they are subject to dephasing and decay and need external pumping to reach a steady state. Accordingly the polariton BEC is a nonequilibrium process of a degenerate polariton gas in self-equilibrium, but out of equilibrium with the baths it is coupled to and therefore deviates from the thermodynamic phase transition seen in atomic BECs. Here we show that key signatures of BEC can even be observed without fulfilling the self-equilibrium condition in a highly photonic quantum degenerate nonequilibrium system.

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

The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density and detuning. During a change in the ground state of Bose-Einstein condensate from excitonic to photonic, which occurs as the excitation density is increased, 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 phase diagram obtained provides valuable information that can be used to build theoretical models for each regime.

Exciton-polariton Bose-Einstein condensation

In the past decade, a two-dimensional matter-light system called the microcavity exciton-polariton has emerged as a new promising candidate of Bose-Einstein condensation (BEC) in solids. Many pieces of important evidence of polariton BEC have been established recently in GaAs and CdTe microcavities at the liquid helium temperature, opening a door to rich many-body physics inaccessible in experiments before. Technological progress also made polariton BEC at room temperatures promising. In parallel with experimental progresses, theoretical frameworks and numerical simulations are developed, and our understanding of the system has greatly advanced. In this article, recent experiments and corresponding theoretical pictures based on the Gross-Pitaevskii equations and the Boltzmann kinetic simulations for a finite-size BEC of polaritons are reviewed.

Exciton-polariton Bose-Einstein condensation: advances and issues

In this review, we present a comprehensive set of experimental results on microcavity-polariton Bose-Einstein Condensation (BEC), obtained within a close collaboration between Institut Neel, Grenoble, France and EPFL, Lausanne, Switzerland. First, we recall the main observations, i.e., massive occupation of the ground state and build-up of long range order, which led us to conclude that polariton BEC indeed occurs. Then, the highly disordered environment in which the condensation takes place is considered: we show how interactions are a necessary ingredient for polariton BEC. Finally we discuss quantised vortices observed for the first time in polariton condensates. Their unusual features are shown to be inherited from the disordered environment and the driven-dissipative character of the polariton BEC.

Dynamics of Long-Range Ordering in an Exciton-Polariton Condensate

We report on time-resolved measurements of the first order spatial coherence in an exciton-polariton Bose-Einstein condensate. Long-range spatial coherence is found to set in right at the onset of stimulated scattering, on a picosecond time scale. The coherence reaches its maximum value after the population and decays slowly, staying up to a few hundred picoseconds. This behavior can be qualitatively reproduced, using a stochastic classical field model describing interaction between the polariton condensate and the exciton reservoir within a disordered potential.

Quantum phase transitions in an array of coupled nanocavity quantum dots

We investigate exciton-photon quantum phase transitions in a planar lattice of one-mode cavities containing one quantum dot. The quantum dot can be occupied by up to two excitons with opposite spin. We adopt the well-established mean-field approximation comprising an exciton order parameter and a photon coherence parameter. Calculating exciton- and photon-phase diagrams it is demonstrated that by controlling exciton- and photon-hopping energies a very rich scenario of coupled fermionic-bosonic quantum phase transitions, including, e.g., quantum phase transitions of the Hubbard model or quantum phase transitions of the light, is revealed. Moreover, our results support the interpretation of polariton Bose-Einstein condensation as only (polariton) laser coherence.

Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate

The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ( approximately 150 ps) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.

Large vacuum Rabi splitting in a multiple quantum well GaN-based microcavity in the strong-coupling regime

An $\mathrm{Al}\mathrm{In}\mathrm{N}∕\mathrm{Al}\mathrm{Ga}\mathrm{N}$ microcavity (MC) containing a $\mathrm{Ga}\mathrm{N}∕{\mathrm{Al}}_{0.2}{\mathrm{Ga}}_{0.8}\mathrm{N}$ multiple quantum well (MQW) structure is investigated through room temperature (RT) photoluminescence and reflectivity experiments. A vacuum Rabi splitting as large as $50\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ at RT is reported for this MC structure, the highest value reported so far for a semiconductor MC containing QWs. This is shown to result from a geometry combining a state of the art nitride-based MC with a MQW system where the built-in electric field has a reduced impact on the oscillator strength of optical transitions. The contribution of Bragg modes seen in optical spectra is well accounted for by transfer matrix simulations. In addition, the sensitivity of the present system to the tuning between the various optical components of the microcavity (bottom and top Bragg reflectors and active cavity region) to maximize the strong-coupling regime is also shown through simulations. Prospects regarding the nonlinear polariton emission from such a structure indicate that this type of MCs could potentially sustain ultrafast polariton parametric amplification up to $440\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, thanks to an increased exciton binding energy. More generally, it is predicted that, owing to a large exciton saturation density in excess of $1\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ per QW, such a MC structure would be suitable for the observation of nonlinear effects associated with cavity polaritons (polariton lasing and polariton Bose-Einstein condensates) at RT and above.

Photon lasing inGaAsmicrocavity: Similarities with a polariton condensate

We study experimentally the lasing regime of a $\mathrm{GaAs}$ based microcavity sample under strong optical pumping. The very same sample exhibits the strong coupling regime at low excitation power with a Rabi splitting as large as $15\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. We show that some features which may be considered as experimental evidence of polariton Bose-Einstein condensation are also observed in the weak coupling regime when the cavity is behaving as a regular photon laser. In particular, the emission pattern in the lasing regime displays a sharp peak near the energy minimum followed by a Boltzmann distribution at higher energies.

Towards thermal equilibrium in the Bose–Einstein condensation of microcavity polaritons

By comparing a kinetic and a thermal-equilibrium theory of polariton Bose–Einstein condensation, we study under what conditions the dynamical condensation under steady-state non-resonant pumping can approach thermal equilibrium. In particular, we study the dependence on two material parameters: the vacuum-field Rabi-splitting and the polariton radiative lifetime. When increasing the Rabi splitting, condensation takes place under strong non-equilibrium conditions, with dominating quantum fluctuations. Increasing the polariton lifetime above 10 ps at moderate Rabi splitting, instead, produces a quasi-equilibrium condensate at low exciton density, consistently with the picture of a weakly interacting Bose gas.

Bose–Einstein condensation of exciton polaritons

Phase transitions to quantum condensed phases--such as Bose-Einstein condensation (BEC), superfluidity, and superconductivity--have long fascinated scientists, as they bring pure quantum effects to a macroscopic scale. BEC has, for example, famously been demonstrated in dilute atom gas of rubidium atoms at temperatures below 200 nanokelvin. Much effort has been devoted to finding a solid-state system in which BEC can take place. Promising candidate systems are semiconductor microcavities, in which photons are confined and strongly coupled to electronic excitations, leading to the creation of exciton polaritons. These bosonic quasi-particles are 10(9) times lighter than rubidium atoms, thus theoretically permitting BEC to occur at standard cryogenic temperatures. Here we detail a comprehensive set of experiments giving compelling evidence for BEC of polaritons. Above a critical density, we observe massive occupation of the ground state developing from a polariton gas at thermal equilibrium at 19 K, an increase of temporal coherence, and the build-up of long-range spatial coherence and linear polarization, all of which indicate the spontaneous onset of a macroscopic quantum phase.

Polariton lasing in a microcavity

We review our recent observation of exciton-polariton lasing and discuss new time-resolved spectra, imaging and angular dispersion data with regards to a possible Bose-Einstein condensate of polaritons. A brief outlook on our activities towards a clearer observation of polariton lasing is given.

Polariton dynamics and Bose-Einstein condensation in semiconductor microcavities

We present a theoretical model that allows us to describe the polariton dynamics in a semiconductor microcavity at large densities, for the case of non-resonant excitation. Exciton-polariton scattering from a thermalized exciton reservoir is identified as the main mechanism for relaxation into the lower polariton states. A maximum in the polariton distribution that shifts towards lower energies with increasing pump-power or temperature is shown, in agreement with recent experiments. Above a critical pump-power, macroscopic occupancies (5 \times 10^4) can be achieved in the lowest energy polariton state. Our model predicts the possibility of Bose-Einstein Condensation of polaritons, driven by exciton-polariton interaction, at densities well below the saturation density for CdTe microcavities.

Bose-Einstein Condensation of Polaritons in Organic Semiconducting Microcavities

Bose-Einstein Condensation of Polaritons in Organic Semiconducting Microcavities

Bose-Einstein Condensation of Polaritons in Organic Semiconducting Microcavities

Anti-crossing of organic exciton and photon modes and a room temperature Rabi splitting that is an order of magnitude larger than the highest values reported for inorganic semiconductor quantum wells are observed in organic microcavity embedded quantum wells. Also, this larger splitting due to the large oscillator strength of organic excitons is easily achieved with many organic systems and gives reasonable hope for reaching the strong coupling regime. However, dynamic condensation clearly involving stimulated emission of the k ≈ 0 lower polaritons is expected at relatively low exciton density, due to the very small polariton mass. We report on the theoretical study of non-linear emission of organic microcavity polaritons. In the ‘Boser’ model at low density, we include the acoustic phonon-assisted relaxation and polariton–polariton scattering stimulated by the quasi-bosonic polariton final state population.

Induced coherent macroscopic states of excitons and biexcitons in a microcavity-embedded Zn 1− xCd xSe-type quantum well

The conditions of induced and spontaneous Kosterlitz–Thouless-type Bose–Einstein condensation (BEC) of excitons and biexcitons in a microcavity-embedded quantum well are discussed. As an example the Zn 1− x Cd x Se/ZnSe quantum well is considered, where the HH-exciton electronic structure consisting of four types of excitons – E( x), E( y), A 1, A 2 is taken into account. A polarized strong pump pulse with the frequency in the polariton region induces the BEC of polaritons and biexcitons. The biexciton is formed from the above-mentioned four types of excitons. The coherent polariton and biexciton concentration were obtained. It was proved that if the cavity photon mode E ph(0) is below the exciton resonance E ex(0), the biexciton is always polarized. If E ph(0)> E ex(0) and the pump frequency is in the electron–hole transition region, optical nonactive A 1, A 2 HH-excitons can be accumulated and spontaneous Kosterlitz–Thouless-type BEC of biexcitons and “dark” excitons can occur.