A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. In contrast to typical discussions of BEC, our system is better treated with a controlled chemical potential rather than a controlled particle number, and is subject to energy-dependent loss. Here, we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline-earth atoms) inside a Fabry-Pérot cavity.
A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. In contrast to typical discussions of BEC, our system is better treated with a controlled chemical potential rather than a controlled particle number, and is subject to energy-dependent loss. Here, we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline-earth atoms) inside a Fabry-Pérot cavity.
Light is a paradigmatic quantum field, with individual excitations---photons---that are the most accessible massless particles known. However, their lack of mass and extremely weak interactions mean that typically the thermal description of light is that of blackbody radiation. As the temperature of the light decreases, the overall number of photons approaches zero. Therefore, efforts for quantum optics and optical physics have mostly focused on driving systems far from equilibrium to populate sufficient numbers of photons. While lasers provide a severe example of a nonequilibrium problem, recent interests in the near-equilibrium physics of so-called photon gases, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one re-examine near-equilibrium cases. In this thesis, we consider peculiar driven open quantum system scenarios where near-equilibrium dynamics can lead to equilibration of photons with a finite number, following a thermal description closer to that of an ideal gas than to blackbody radiation. Specifically, we show how laser cooling of a well-isolated mechanical mode or atomic motion can provide an effective bath which enables control of both the chemical potential and temperature of the resulting grand canonical ensemble of photon. We then theoretically demonstrate that Bose condensation of photons can be realized by cooling an ensemble of two-level atoms inside a cavity. Finally, we find that the engineered chemical potential for light not only admits future applications in many-body quantum simulations, facilitates preparation of near-equilibrium photonic states, but also enables an analogous voltage bias for photonic circuit elements.
The interesting question if and how can Bose-Einstein condensation (BEC) occur with photons has received a boost by a recent experiment that reported on the observation of photon-BEC condensation in an optical microcavity [1]. Here we present a different laser light condensation (LC) phenomenon [2], while discussing and questioning the meaning and the possibility to observe thermal photon-BEC in laser cavities. LC is a classical condensation effect that is based on very different grounds than the regular BEC. Its “energy” levels are measured in a loss-gain scale inherent in laser cavities, where the “ground-state” is the lowest-loss mode, and noise has the role of temperature. The loss scale gives a power occupation hierarchy and power spectra similar to Bose-Einstein statistics with an effective chemical potential parameter and eventually laser light-condensation (LC) which is formally very similar to BEC in a potential-well [3].
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.
Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, has been observed in cold atomic gases and solid-state physics quasiparticles. In contrast, photons do not show this phase transition usually, because in Planck's blackbody radiation the particle number is not conserved and at low temperature the photons disappear in the walls of the system. Here we report on the realization of a photon Bose-Einstein condensate in a dye-filled optical microcavity, which acts as a "white-wall" photon box. The cavity mirrors provide a trapping potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped massive bosons. Thermalization of the photon gas is reached in a number conserving way by multiple scattering off the dye molecules. Signatures for a BEC upon increased photon density are: a spectral distribution that shows Bose-Einstein distributed photon energies with a macroscopically populated peak on top of a broad thermal wing, the observed threshold of the phase transition showing the predicted absolute value and scaling with resonator geometry, and condensation appearing at the trap centre even for a spatially displaced pump spot.
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.
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.