In this paper, we theoretically propose an optomechanical scheme to thermalize a two-dimensional photon gas in a hybrid optomechanical microcavity composed of a two-level atomic ensemble and a membrane oscillator enclosed in an optical cavity. The thermalization process is based on a phonon-induced asymmetry between the emission and the absorption rates of the atoms. We show that whenever this asymmetry obeys the detailed balance condition and if the photon lifetime is high enough, the steady-state photon number distribution matches the Bose–Einstein distribution. Furthermore, in order to study the effect of the optomechanical coupling on the Bose–Einstein condensation of photons, we calculate the critical photon number as a function of the temperature. We find that the optomechanically induced nonlinearity leads to the increase of the critical photon number, which can be controlled by tuning the optomechanical parameters.
In this paper, we theoretically propose an optomechanical scheme to thermalize a two-dimensional photon gas in a hybrid optomechanical microcavity composed of a two-level atomic ensemble and a membrane oscillator enclosed in an optical cavity. The thermalization process is based on a phonon-induced asymmetry between the emission and the absorption rates of the atoms. We show that whenever this asymmetry obeys the detailed balance condition and if the photon lifetime is high enough, the steady-state photon number distribution matches the Bose–Einstein distribution. Furthermore, in order to study the effect of the optomechanical coupling on the Bose–Einstein condensation of photons, we calculate the critical photon number as a function of the temperature. We find that the optomechanically induced nonlinearity leads to the increase of the critical photon number, which can be controlled by tuning the optomechanical parameters.
We propose to thermalize a low-dimensional photon gas and obtain photonic Bose-Einstein condensation by optomechanical interactions in a microscopic optical cavity, with a single longitudinal mode and many transverse modes. The geometry of the short cavity is such that it provides a low-frequency cutoff at a photonic energy far above the thermal energy, so that thermal emission of photons is suppressed and the photon number is conserved. While previous experiments on photonic Bose-Einstein condensation have used dye molecules for photon gas thermalization, we here investigate thermalization owing to interactions with thermally fluctuating nanomechanical oscillators forming the cavity mirrors. In the quantum degenerate regime, the nanomechanical cavity converts broadband optical radiation into tuneable coherent radiation.
W present time-resolved studies of the thermalization and condensation process of a two-dimensional photon gas in an optical microcavity. In our experiment, a two-dimensional photon gas is confined in a high finesse microresonator containing a dye medium. If this system is operated in a regime in which reabsorption of cavity photons by the dye medium dominates over photon loss, e.g. by mirror transmission, a thermalization process of the photon gas to the temperature of the resonator (room temperature) takes place. In earlier work, we have experimentally observed both the thermalization process and, at sufficiently high photon densities, a condensation in the resonator ground mode. In recent experiments, we have studied the thermalization and condensation dynamics of the system after excitation with a short laser pulse. The timescale on which the photon gas becomes thermal (Bose-Einstein distribution) is found to be in the picosecond to nanosecond regime and is tunable by various system parameters e.g. by the dye concentration. Upon spatially displacing the pump spot from the optical axis, a transient laser-like oscillation of higher order cavity modes can be observed. These laser-like oscillations decay after several hundred picoseconds when the majority of photons have relaxed to the resonator ground state.
Optomechanical cavity is a powerful connection between a nanomechanical oscillator and a quantized electromagnetic field. In this system, a novel photon-phonon nonlinear interaction arising from the nanomechanical oscillation is produced through the radiation pressure. Now this nonlinear photon-phonon interaction has become an important resource for implementing high-precision measurements and processing quantum information. Motivated by T. Esslinger group’s experiment, it is very meaningful to explore the exotic quantum phenomena when a ultra-cold BEC is trapped in an optomechanical cavity. In this paper, we mainly investigate phase transition and the finite-temperature thermodynamic properties of a Bose-Einstein condensate in an optomechanical cavity. It’s worth mentioning that at zero temperature many different mean-field approximate methods have been used to analyze the ground state properties of a Bose-Einstein condensate in an optomechanical cavity. Two common methods are Holstein-Primakoff transformation and spin coherent state variation. In this paper, an interesting imaginary-time path integral approach has been introduced to study finite temperature thermodynamic properties and phase transition of a Bose-Einstein condensate in an optomechanical cavity. First, we obtained system's partition function by taking imaginary-time path integration. Meanwhile, an effective action has been obtained by means of this method, which is the basic of the variation to get the numerical solution of photon number and the expression of the atomic number. At zero temperature, these results are consistent with what we have obtained by Holstein-Primakoff transformation or spin coherent state variational method. By adjusting the atom-field coupling strength and other parameters the second-order phase transition from the normal phase to the superradiant phase has been revealed. Meanwhile, a new unstable superradiant state was also found. And we found that in addition to the normal phase and superradiation phase, there exists an un-solution region of the mean photon number. Meanwhile, we find that the nonlinear photon-phonon interaction does not affect the normal phase. However, in the superradiant phase, the nonlinear photon-phonon interaction can enhance the macroscopic collective excitations. At the same time, the thermodynamic properties of the system are also discussed. According to the obtained distribution function, we can derive the analytical expression of the average energy and the free energy. Furthermore, the expression of entropy at finite temperature can also be obtained. we find the nonlinear photon-phonon interaction does not affect the average energy in the normal phase, but the average energy in the superradiant phase can deeply deviate in the large nonlinear photon-phonon interaction. It’s worth mentioning that the mean photon number and average energy in the finite-temperature tend to be consistent with the case in absolute zero temperature in the strong coupling region, while the entropy in the superradiant phase is rapidly reduced to zero as the atom-field coupling strength increases. In other words, strongly coupled collective excited states are highly ordered and are not affected by thermal fluctuations in the temperature range we are considering. The thermodynamic properties, such as the entropy and corresponding specific heat, characterize the Dicke phase transition.
We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser-driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanical coupling (QOC), one can achieve a very high degree of squeezing in the mechanical mode and a strong entanglement between the mechanical and atomic modes without the necessity of using squeezed light injection. Furthermore, the QOC changes the effective oscillation frequencies of both the mechanical and the atomic modes and affects their relaxation times. It can also make the system switch from optical bistability to tristability.
A system of identical bosons can exhibit a state of matter in which the ground state is macroscopically occupied. This special state is called Bose-Einstein condensation, and was predicted by Satyendra Nath Bose and Albert Einstein in 1924. It took some time before physicists achieved this experimentally, but in 1995 it was done by Eric Cornell and Carl Wieman. Since photons are also bosonic particles, they should be able to achieve Bose-Einstein condensation in thermal equilibrium. However this is not as easy for photons as it is for atoms, since the number of photons depends on the temperature. But in 2010 the group of Martin Weitz in Bonn was able to produce a photon Bose-Einstein condensate. This was done using a dye-filled microcavity which is optically pumped. The same principles are used in our setup. Photons inside the cavity thermalize with a fluorescent dye through multiple absorption and emission cycles. The effectively two-dimensional photon gas is trapped by a harmonic potential induced by the shape of the cavity mirrors. This results in photons with eigenenergies of the quantum harmonic oscillator. The minimal energy is determined by the cutoff frequency, set by the cavity length. The thermalization of the photon gas depends on this cutoff frequency, and the total pump power. Jonathan Keeling and Peter Kirton developed a theoretical model describing this system and its thermalization, and simulated it in one dimension.\nWe simulate the same model, in two dimensions using radially averaged photon modes. Threshold for Bose-Einstein condensation is determined for different cutoff frequencies. Our results show good agreement with those of Keeling and Kirton, below, at and above threshold. Multimode condensation and gain clamping of the molecular excitation density are observed above threshold. Comparison with experimental data can only be done qualitatively since it currently is uncalibrated.
Abstract We theoretically study photothermally and optomechanically induced transparency in a hybrid system of two coupled Fabry-Peŕot cavities. The left cavity hosts a dual-species Bose-Einstein condensate driven by pump and probe fields, while the right cavity couples to a mechanical resonator via photothermal effects. By tuning intercavity, optomechanical, and condensate-cavity couplings, both single and multiple transparency windows emerge. Interspecies and intraspecies interactions, along with effective coupling parameters, govern the transparency conditions, while the photothermal coefficient shapes the profiles. Absorption and dispersion spectra reveal that strong coupling enhances slow-light effects and group delay. These findings provide insights into tunable light-matter interactions for optical communication and photonic applications.