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Acta Physica Sinica

Influence of temperature on the Bose condensation of photons and excitons in optic microcavity

Zhengfu Cheng, Long Xiao-Xia, Zheng Rui-Lun

Published Jan 1, 2010• 0 citations
Publisher

Abstract

In this paper, an exciton-photon model is created in an optic microcavity, and then in Bose condensation (BC), the variations of chemical potential range and number density of particles with temperature and position are studied in cases: constant width and varying width. Taking a semiconductor optic microcavity GaAs as example, the influence of temperature on BC is analyzed. The result shows that the range of chemical potential is related to dielectric function and microcavity width, while the number densities of photons and excitons and the sum of both particle numbers are related not only to them but also to temperature. The theoretical temperature of BC of GaAs is close to the experimental value. The densities of photons and excitons are almost equal, and their distributions are restricted to r=0 when BC occurs. With the reduction of temperature the number densities of both particles increase and their distributions expand, and the number of photons is more than that of excitons no matter how the width of optic microcavity changes.

DOI
10.7498/aps.59.8377

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In this paper, an exciton-photon model is created in an optic microcavity, and then in Bose condensation (BC), the variations of chemical potential range and number density of particles with temperature and position are studied in cases: constant width and varying width. Taking a semiconductor optic microcavity GaAs as example, the influence of temperature on BC is analyzed. The result shows that the range of chemical potential is related to dielectric function and microcavity width, while the number densities of photons and excitons and the sum of both particle numbers are related not only to them but also to temperature. The theoretical temperature of BC of GaAs is close to the experimental value. The densities of photons and excitons are almost equal, and their distributions are restricted to r=0 when BC occurs. With the reduction of temperature the number densities of both particles increase and their distributions expand, and the number of photons is more than that of excitons no matter how the width of optic microcavity changes.
Taking semiconductor GaAs optical micro-cavity for example,the impact of the optical micro-cavity on the temperature and heat capacity of Bose condensation in exciton-photon system are researched in this paper.It shows that critical temperature of Bose condensation increases with rising of micro-cavity's width,but it is significant only when the width of micro-cavity is small.There's not Bose condensation in the system when the width of micro-cavity is very small.The variety of Bose condensation's critical temperature is little with the position in micro-cavity.The critical temperature is high in the vicinity of in micro-cavity.Photon and exciton contribute on heat capacity nearly the same.They are both increasing with temperature,and decreasing with the width of micro-cavity.The impact of micro-cavity shape on the temperature and heat capacity of Bose condensation is little.The change of heat capacity with position is obvious only when the width of micro-cavity is very small.
We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon number can be tuned independently of each other or, correspondingly, for a nonvanishing photon chemical potential. We here describe experiments demonstrating the fluorescence-induced thermalization and Bose-Einstein condensation of a two-dimensional photon gas in the dye microcavity. Moreover, recent measurements on the photon statistics of the condensate, showing Bose-Einstein condensation in the grand-canonical ensemble limit, will be reviewed. Introduction Quantum statistical effects become relevant when a gas of particles is cooled, or its density is increased, to the point where the associated de Broglie wavepackets spatially overlap. For particles with integer spin (bosons), the phenomenon of Bose-Einstein condensation (BEC) then leads to macroscopic occupation of a single quantum state at finite temperatures [1]. Bose-Einstein condensation in the gaseous case was first achieved in 1995 by laser and subsequent evaporative cooling of a dilute cloud of alkali atoms [2, 3, 4], as detailed in Chapter 3 of this volume. The condensate atoms can be described by a macroscopic singleparticle wavefunction, similar to the case of liquid helium [1]. Bose-Einstein condensation has also been observed for exciton-polaritons, which are hybrid states of matter and light [5, 6, 7] (see Chapter 4), magnons [8] (see Chapter 25), and other physical systems. Other than material particles, photons usually do not show Bose-Einstein condensation [9]. In blackbody radiation, the most common Bose gas, photons at low temperature disappear, instead of condensing to a macroscopically occupied ground-state mode. In this system, photons have a vanishing chemical potential, meaning that the number of photons is determined by the available thermal energy and cannot be tuned independently from temperature.
The effect of the particle position-dependent effective mass on the behavior of quasi-two-dimensional photon and exciton-polariton condensates in a parabolic trap in a semiconductor optical microcavity is investigated. It is demonstrated that the correct inclusion of the coordinate dependence of the effective mass in the kinetic-energy operator modifies the effective confining potential for the particles. Corrections to the energy and wavefunction of the photon Bose condensate are derived. For exciton-polaritons, it is shown that the choice of specific mirror geometry can lead to the change from repulsive to attractive particle–particle interaction.
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.
Abstract When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-filled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells offer stronger photon–photon scattering. We measure an unoptimized interaction parameter ( g~\tilde{{{{{g}}}}}g~​ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
When particles with integer spin accumulate at low temperature and high density they undergo Bose-Einstein condensation (BEC). Atoms, solid-state excitons and excitons coupled to light all exhibit BEC, which results in high coherence due to massive occupation of the respective system's ground state. Surprisingly, photons were shown to exhibit BEC much more recently in organic dye-filled optical microcavities, which, owing to the photon's low mass, occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalise and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalisation in our system where we can clearly distinguish laser action from BEC. Based on well-developed technology, semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. Notably, photon BEC is an alternative to exciton-based BECs, which dissociate under high excitation and often require cryogenic operating conditions. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages of photon BEC in semiconductor materials: the lack of dark electronic states allows these BECs to be sustained continuously; and semiconductor quantum wells offer strong photon-photon scattering. We measure an unoptimised interaction parameter, g~=0.0023±0.0003\tilde{g}=0.0023\pm0.0003g~​=0.0023±0.0003, which is large enough to access the rich physics of interactions within BECs, such as superfluid light or vortex formation.