Bose–Einstein condensation (BEC) of dressed photons in a Kerr nonlinear optical microcavity is investigated. Our experimental scheme is based on an optical microcavity filled with a Kerr nonlinear nonpolar crystal. The pump photons interact with the Raman phonons in the crystal and hence are converted into new quasiparticles, which we refer to as dressed photons. A dressed photon is a photon dressed with a cloud of virtual transverse-optical phonons. The first main finding is that two-dimensional (2D) dressed photons have an increased inert mass. The second main finding is that the lower cutoff frequency of a nonlinear optical microcavity becomes larger. The third main finding is that the incident laser intensity is a moderate laser intensity ([Formula: see text]10[Formula: see text] W/cm2). The fourth main finding is that the critical optical power of a nonlinear optical microcavity is increased. The fifth main finding is that the radiation emitted by 2D dressed photons has an ultrahigh intensity.
Bose–Einstein condensation (BEC) of dressed photons in a Kerr nonlinear optical microcavity is investigated. Our experimental scheme is based on an optical microcavity filled with a Kerr nonlinear nonpolar crystal. The pump photons interact with the Raman phonons in the crystal and hence are converted into new quasiparticles, which we refer to as dressed photons. A dressed photon is a photon dressed with a cloud of virtual transverse-optical phonons. The first main finding is that two-dimensional (2D) dressed photons have an increased inert mass. The second main finding is that the lower cutoff frequency of a nonlinear optical microcavity becomes larger. The third main finding is that the incident laser intensity is a moderate laser intensity ([Formula: see text]10[Formula: see text] W/cm2). The fourth main finding is that the critical optical power of a nonlinear optical microcavity is increased. The fifth main finding is that the radiation emitted by 2D dressed photons has an ultrahigh intensity.
The photo-polaron in a two-dimensional optical microcavity is investigated within the framework of quantum statistical mechanics. Our experimental setup is based on a planar Fabry-P\'erot cavity filled with a nonlinear nonpolar crystal. The Fabry-P\'erot cavity provides a chemical potential and an effective mass for a photon, making the system formally equivalent to a two-dimensional gas of number-conserving, massive bosons. The incident photons interact with the Raman phonons in the crystal and hence are converted into quasiparticles, which we refer to as photo-polarons. A photo-polaron is a photon dressed with a cloud of virtual transverse-optical phonons, namely, the dressed photon. One of the most important properties of photo-polaron is an increased inert mass. Because of the effect of photo-polarons, we find that the photon-photon interaction is enhanced greatly. The photo-polaron is a quantum effect of cavity nonlinear optics but its increased inert mass is a classical property.
Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.
The photon polaron in a two-dimensional optical micro-cavity is investigated within the framework of quantum statistical mechanics. Our experimental set-up is based on a planar Fabry-Pérot cavity filled with a nonlinear non-polar crystal. The Fabry-Pérot cavity provides a chemical potential and an effective mass for a photon, making the system formally equivalent to a two-dimensional gas of number-conserving, massive bosons. A photon polaron is a photon dressed with a cloud of virtual transverse optical phonons, namely, the dressed photon. One of the most important properties of the photon polaron is an increased inert mass. Because of the effect of photon polarons, we find that the photon-photon interaction is enhanced greatly. The photon polaron is a quantum effect of cavity nonlinear optics but its increased inert mass is a classical property.
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.
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~ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
The advent of controlled experimental accessibility of Bose-Einstein condensates, as realized with e.g. cold atomic gases, exciton-polaritons, and more recently photons in a dye-filled optical microcavity, has paved the way for new studies and tests of a plethora of fundamental concepts in quantum physics. We here describe recent experiments studying a transition between laser-like dynamics and Bose-Einstein condensation of photons in the dye microcavity system. Further, measurements of the second-order coherence of the photon condensate are presented. In the condensed state we observe photon number fluctuations of order of the total particle number, as understood from effective particle exchange with the photo-excitable dye molecules. The observed intensity fluctuation properties give evidence for Bose-Einstein condensation occurring in the grand-canonical statistical ensemble regime.