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Register a new userFinite-temperature Hatree-Fock-Bogoliubov theory for exciton-polaritons
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Microcavity exciton-polaritons, known to exhibit non-equilibrium Bose condensation at high critical temperatures, can be also brought in thermal equilibrium with the surrounding medium and form a quantum degenerate Bose-Einstein distribution. It happens when their thermalization time in the regime of positive detunings -- or, alternatively, for high-finesse microcavities -- becomes shorter than their lifetime. Here we present the self-consistent finite-temperature Hartree-Fock-Bogoliubov description for such a system of polaritons, universally addressing the excitation spectrum, momentum-dependent interactions, condensate depletion, and the background population of dark excitons that contribute to the systems chemical potential. Employing the derived expressions, we discuss the implications for the Bogoliubov sound velocity, confirmed by existing experiments, and define the critical temperatures of (quasi-)condensation and the integral particle lifetime dependencies on the detuning. Large positive detunings are shown to provide conditions for the total lifetime reaching nanosecond timescales. This allows realization of thermodynamically-equilibrium polariton systems with Bose-Einstein condensate forming at temperatures as high as tens of Kelvin.
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We demonstrate, experimentally and theoretically, a Talbot effect for hybrid light-matter waves -- exciton-polariton condensate formed in a semiconductor microcavity with embedded quantum wells. The characteristic Talbot carpet is produced by loading the exciton-polariton condensate into a microstructured one dimensional periodic array of mesa traps, which creates an array of sources for coherent polariton flow in the plane of the quantum wells. The spatial distribution of the Talbot fringes outside the mesas mimics the near-field diffraction of a monochromatic wave on a periodic amplitude and phase grating with the grating period comparable to the wavelength. Despite the lossy nature of the polariton system, the Talbot pattern persists for distances exceeding the size of the mesas by an order of magnitude.
Bogoliubovs theory states that self-interaction effects in Bose-Einstein condensates produce a characteristic linear dispersion at low momenta. One of the curious features of Bogoliubovs theory is that the new quasiparticles in the system are linear combinations of creation and destruction operators of the bosons. In exciton-polariton condensates, this gives the possibility of directly observing the negative branch of the Bogoliubov dispersion in the photoluminescence (PL) emission. Here we theoretically examine the PL spectra of exciton-polariton condensates taking into account of reservoir effects. At sufficiently high excitation densities, the negative dispersion becomes visible. We also discuss the possibility for relaxation oscillations to occur under conditions of strong reservoir coupling. This is found to give a secondary mechanism for making the negative branch visible.
Recently, the zero-pairing limit of Hartree-Fock-Bogoliubov (HFB) mean-field theory was studied in detail in arXiv:2006.02871. It was shown that such a limit is always well-defined for any particle number A, but the resulting many-body description differs qualitatively depending on whether the system is of closed-(sub)shell or open-(sub)shell nature. Here, we extend the discussion to the more general framework of Finite-Temperature HFB (FTHFB) which deals with statistical density operators, instead of pure many-body states. We scrutinize in detail the zero-temperature and zero-pairing limits of such a description, and in particular the combination of both limits. For closed-shell systems, we find that the FTHFB formulism reduces to the (zero-temperature) Hartree-Fock formulism, i.e. we recover the textbook solution. For open-shell systems, however, the resulting description depends on the order in which both limits are taken: if the zero-temperature limit is performed first, the FTHFB density operator demotes to a pure state which is a linear combination of a finite number of Slater determinants, i.e. the case of arXiv:2006.02871. If the zero-pairing limit is performed first, the FTHFB density operator remains a mixture of a finite number of Slater determinants with non-zero entropy, even as the temperature vanishes. These analytical findings are illustrated numerically for a series of Oxygen isotopes.
We present experimental observations of a non-resonant dynamic Stark shift in strongly coupled microcavity quantum well exciton-polaritons - a system which provides a rich variety of solid-state collective phenomena. The Stark effect is demonstrated in a GaAs/AlGaAs system at 10K by femtosecond pump-probe measurements, with the blue shift approaching the meV scale for a pump fluence of 2 mJcm^-2 and 50 meV red detuning, in good agreement with theory. The energy level structure of the strongly coupled polariton Rabi-doublet remains unaffected by the blue shift. The demonstrated effect should allow generation of ultrafast density-independent potentials and imprinting well-defined phase profiles on polariton condensates, providing a powerful tool for manipulation of these condensates, similar to dipole potentials in cold atom systems.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.
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