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Publication# Bose-Einstein condensation of exciton polaritons

Abstract

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.

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Polariton

In physics, polaritons pəˈlærᵻtɒnz,_poʊ- are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of

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In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolut

Temperature

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperatur

Cristiano Ciuti, Benoît Marie Joseph Deveaud, Stefan Kundermann, Michele Saba

Microcavity exciton polaritons, the fundamental optical excitations of semiconductor microcavities with quantum wells inside, have been proposed as promising candidates for observing stimulated scattering, condensation and other phenomena related to the bosonic nature of excitons. Having a light mass, quantum degeneracy of polaritons can be reached at low densities and high temperatures. But the radiative time of polaritons is very short (in the picosecond range) and usually prevents an efficient thermalization and cooling of the excited cloud of polaritons. A 'coherently driven condensate', not corresponding to a thermal equilibrium, but featuring multiple occupation of single-particle states, can however be created by an external laser source resonantly exciting polaritons. Under this condition, stimulated parametric scattering of polaritons can provide huge optical gain on a weak probe pulse shined on the sample. In this work we demonstrate that this phenomenon can survive at temperatures close to room temperature and could be achieved in the future even above this limit. Clever sample designs favour the thermal robustness of polariton parametric amplification, but from the experimental data it turns out that the parameter that ultimately limits the highest temperature for polariton parametric scattering is the exciton binding energy.

2003Cristiano Ciuti, Benoît Marie Joseph Deveaud, Stefan Kundermann, Michele Saba

Microcavity exciton polaritons, the fundamental optical excitations of semiconductor microcavities with quantum wells inside, have been proposed as promising candidates for observing stimulated scattering, condensation and other phenomena related to the bosonic nature of excitons. Having a light mass, quantum degeneracy of polaritons can be reached at low densities and high temperatures. But the radiative time of polaritons is very short (in the picosecond range) and usually prevents an efficient thermalization and cooling of the excited cloud of polaritons. A 'coherently-driven condensate', not corresponding to a thermal equilibrium, but featuring multiple occupation of single-particle states, can however be created by an external laser source resonantly exciting polaritons. Under this condition, stimulated parametric scattering of polaritons can provide huge optical gain on a weak probe pulse shined on the sample. In this work we demonstrate that this phenomenon can survive at temperatures close to room temperature and could be achieved in the next future even above this limit. Clever sample designs favour the thermal robustness of polariton parametric amplification, but from the experimental data it turns out that the parameter that ultimately limits the highest temperature for polariton parametric scattering is the exciton binding energy. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

2003This thesis presents a theoretical description of the phase transition, with formation of long-range spatial coherence, occurring in a gas of exciton-polaritons in a semiconductor microcavity structure. The results and predictions of the theories developed in this thesis suggest that this phase transition, recently observed in experiments, can be interpreted as the Bose-Einstein Condensation (BEC) of microcavity polaritons. Our theoretical framework is conceived as a generalization to the microcavity polariton system of the standard theories describing the BEC of a weakly interacting Bose gas. These latter are reviewed in Chapter 2, where an introduction to the physics of polaritons is also given. The polariton system is peculiar, basically due to three main features, i.e. the composite nature of polaritons, which are a linear superposition of photon and exciton states, their intrinsic 2-D nature, and the presence of two-body interactions, arising both from the mutual interaction between excitons and from the saturation of the exciton oscillator strength. Therefore it is not clear whether the observed phase transition can be properly described in terms of BEC of a trapped gas. To clarify this point, one has to describe self-consistently the linear exciton-photon coupling giving rise to polariton quasiparticles, and the exciton-nonlinearities. This is made in Chapter 3, where a bosonic theory is developed by generalizing the Hartree-Fock-Popov description of BEC to the case of two coupled Bose fields at thermal equilibrium. Hence, we derive the classical equations describing the condensate wave function and the Dyson-Beliaev equations for the field of collective excitations. In this way, for each value of the temperature and of the total polariton density, a self-consistent solution can be obtained, fixing the populations of the condensate and of the excited states. In particular, the theory allows to describe simultaneously the properties of the polariton, the exciton and the photon fields, this latter being directly investigated in the typical optical measurements. The predicted phase diagram, the energy shifts, the population energy distribution and the behavior of the resulting first order spatial correlation function agree with the recent experimental findings [Kasprzak 06, Balili 07]. These results thus support the idea that the observed experimental signatures are a clear evidence of polariton BEC. However, from a quantitative pint of view, the measured coherence amount in the condensed regime is significantly lower than the predicted one. This discrepancy could be due to deviations from the weakly interacting Bose gas picture and/or to deviations from the thermal equilibrium regime. In particular, these latter are expected to be strong in current experiments, because polaritons have a short radiative lifetime, while the rate of the energy-relaxation mechanisms is very slow. To investigate how the deviations from equilibrium could affect the condensate fraction and the formation of off-diagonal long-range correlations, in Chapter 4, we develop a kinetic theory of the polariton condensation, accounting for both the relaxation mechanisms and for the field dynamics of fluctuations. Within the Hartree-Fock-Bogoliubov limit, we derive a set of coupled equations of motion for the one-particle populations and for the two particle correlations describing quantum fluctuations. We account for the relaxation processes due both to the polariton-phonon coupling and to the exciton-exciton scattering. The actual spectrum of the system is evaluated within the Popov limit, during the relaxation kinetics. Within this model, we solve self-consistently the populations kinetics and the dynamics of the excitation field, for typical experimental conditions. In particular, we show that the role of quantum fluctuations is amplified by non-equilibrium, resulting in a significant condensate depletion. This behavior could explain the partial suppression of off-diagonal long-range coherence reported in experiments [Kasprzak 06, Balili 07]. We complete the analysis, by studying how the deviations from equilibrium depend on the system parameters. Our results show that the polariton lifetime plays a crucial role. In particular, we expect that the increase of the polariton lifetime above 10 ps would lead to thermal-equilibrium polariton BEC in realistic samples. In Chapter 5, devoted to the conclusions, we discuss which issues of BEC could be clarified, by achieving polariton BEC at thermal-equilibrium, and which extensions of the present work would be most promising in this respect.