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Journal of Southwest China Normal University

Impact of Optical Microcavity on Temperature and Heat Capacity of Bose Condensation in Photon-Exciton System

Long Xiao-xia

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
The paper considers Bose-Einstein condensation (BEC) of light in a cavity with a medium. In the framework of a two-level model we show the effect of gaseous medium on the critical temperature of light condensation in the system. Transition of the system to the state with released light condensate is illustrated in consequent stages. Analytical expressions for a typical spatial extent of the condensed cloud of photons, as well for spectral characteristics of the condensate peak are derived. Energy and heat capacity of photons as functions of temperature are obtained. Finally, we demonstrate that the energy of light can be accumulated in the BEC state.
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.
The condensate density profile of trapped two-dimensional gas of photons in an optical microcavity, filled by a dye solution, is analyzed taking into account a coordinate-dependent effective mass of cavity photons and photon–photon coupling parameter. The profiles for the densities of the superfluid and normal phases of trapped photons in the different regions of the system at the fixed temperature are analyzed. The radial dependencies of local mean-field phase transition temperature Tc0(r) and local Kosterlitz–Thouless transition temperature Tc(r) for trapped microcavity photons are obtained. The coordinate dependence of cavity photon effective mass and photon–photon coupling parameter is important for the mirrors of smaller radius with the high trapping frequency, which provides Bose–Einstein condensation and superfluidity for smaller critical number of photons at the same temperature. We discuss a possibility of an experimental study of the density profiles for the normal and superfluid components in the system under consideration.
Bose-Einstein condensation has in the last two decades been observed in cold atomic gases and in solid-state physics quasiparticles, exciton-polaritons and magnons, respectively. The perhaps most widely known example of a bosonic gas, photons in blackbody radiation, however exhibits no Bose-Einstein condensation, because the particle number is not conserved and at low temperatures the photons disappear in the system’s walls instead of massively occupying the cavity ground mode. This is not the case in a small optical cavity, with a low-frequency cutoff imprinting a spectrum of photon energies restricted to values well above the thermal energy. The here reported experiments are based on a microscopic optical cavity filled with dye solution at room temperature. Recent experiments of our group observing Bose-Einstein condensation of photons in such a setup are described. Moreover, we discuss some possible applications of photon condensates to realize quantum manybody states in periodic photonic lattices and photonic Josephson devices.