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arXiv:1212.2748 · Physical Review Letters

Thermodynamic Model of the Macroscopically Ordered Exciton State

S. V. Andreev

Published Apr 2, 2013• 21 citations
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Abstract

We explain the experimentally observed instability of cold exciton gases and the formation of a macroscopically ordered exciton state in terms of a thermodynamic model accounting for the phase fluctuations of the condensate. We show that the temperature dependence of the exciton energy exhibits fundamental scaling behavior with the signature of the second order phase transition.

DOI
10.1103/physrevlett.110.146401

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We explain the experimentally observed instability of cold exciton gases and the formation of a macroscopically ordered exciton state in terms of a thermodynamic model accounting for the phase fluctuations of the condensate. We show that the temperature dependence of the exciton energy exhibits fundamental scaling behavior with the signature of the second order phase transition.
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Dynamical and statistical behaviors of Frenkel excitons in a matter system consisting of N two-level-atoms and interacting with an external field are studied with the molecular field and random phase approximations. Existence of a phase transition is suggested both in the exciton system and exciton-photon coupled system. This phase transition is the second order transition whose order parameter is the polarizability. A new type of condensation of the photon-exciton coupled wave, in which a macroscopic number of excitons and photons participate, has been found as a result of appreciable contribution of photons to the phase transition. When the incident light is coherent, the condition of phase transition is modified by photon induced exciton-exciton interaction. The energy dispersion of elementary excitations is derived.
This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.
This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.
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.
Summary form only given. Phase transitions are among the most dramatic phenomena in nature. Minute variations in the conditions controlling a system trigger a fundamental change of its properties. In the critical regime near a second-order phase transition point the fluctuations of the order parameter are so dominant that they completely govern the behaviour of the system on all length scales. The correlation length of the ultracold gas measures the characteristic length scale of these fluctuations and diverges at the critical temperature. Using cold atomic gases, we have directly observed critical fluctuations of the order parameter near the phase transition of Bose-Einstein condensation. From the divergence of the correlation length of the order parameter versus temperature we have determined its critical exponent v. Despite our densities being ten orders of magnitude smaller and our interactions considerably weaker, we find a remarkable similarity to case of the lambda-transition of helium-4.