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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Spectroscopy of Heteronuclear Xenon-noble Gas Dimers – Towards Bose-Einstein Condensation of Vacuum-UV Photons

Eric Boltersdorf, Thilo vom Hövel, Frank Vewinger, Martin Weitz

Published Jun 26, 2023• 0 citations
Publisher

Abstract

Other than for the three-dimensonal case of blackbody radiation, low-dimensional photon gases can exhibit Bose- Einstein condensation, as been experimentally demonstrated in the visible spectral regime first in 2010 using a dye-filled optical microcavity [1]. Here a short, wavelength sized spacing of cavity mirrors provides a low- frequency cutoff imprinting a spectrum of photon energies restricted to well above the thermal energy, and photons thermalize by repeated absorption and (re-)emission processes on the dye molecules to room temperature. As a prominent feature, a Bose-Einstein condensate of photons is as a coherent light source. This is of special interest in the vacuum-ultraviolet spectral regime (100 nm-200 nm, VUV), as it is difficult to realize lasers in this wavelength range. This is mainly due to the$1/\omega^{3}$-scaling of excited state lifetimes, which requires increasingly high pump powers at short wavelengths to create population inversion in a laser medium.

DOI
10.1109/cleo/europe-eqec57999.2023.10231911

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Other than for the three-dimensonal case of blackbody radiation, low-dimensional photon gases can exhibit Bose- Einstein condensation, as been experimentally demonstrated in the visible spectral regime first in 2010 using a dye-filled optical microcavity [1]. Here a short, wavelength sized spacing of cavity mirrors provides a low- frequency cutoff imprinting a spectrum of photon energies restricted to well above the thermal energy, and photons thermalize by repeated absorption and (re-)emission processes on the dye molecules to room temperature. As a prominent feature, a Bose-Einstein condensate of photons is as a coherent light source. This is of special interest in the vacuum-ultraviolet spectral regime (100 nm-200 nm, VUV), as it is difficult to realize lasers in this wavelength range. This is mainly due to the1/ω31/\omega^{3}1/ω3-scaling of excited state lifetimes, which requires increasingly high pump powers at short wavelengths to create population inversion in a laser medium.
Bose-Einstein condensation, the macroscopic ground state occupation of bosonic particles at low temperature and high density, has previously been observed for cold atomic gases and solid-state quasiparticles. In recent work, Bose-Einstein condensation of photons has been realized in a dye-filled optical microcavity at room temperature [1, 2]. The short mirror spacing of the curved mirror microcavity introduces a low-frequency cutoff, and thermal contact to the dye-solution is achieved by subsequent absorption and re-emission processes.
Bose-Einstein condensation, an effect long known for material particles as cold atomic gases, has in recent years also been observed for photons in microscopic optical cavities. Here, we report absorption and emission spectroscopic measurements on the lowest electronic transition ($5{p}^{6}\ensuremath{\rightarrow}5{p}^{5}6s$) of xenon, motivated by the search for a thermalization medium for photon Bose-Einstein condensation in the vacuum-ultraviolet spectral regime. We have recorded pressure-broadened xenon spectra in the 135- to 190-nm wavelength regime at conditions near the critical point. The explored pressure and temperature ranges include high-pressure gaseous xenon below the critical pressure and supercritical xenon at room temperature as well as liquid xenon close to the boiling point near the critical pressure.
Between the absorption and the emission spectral lineshapes of dense atomic and molecular media, such as dye solutions and alkali-noble buffer gas mixtures at high pressure, in many cases there exists a universal scaling, the Kennard-Stepanov relation, which is a manifestation of detailed balance. This relation plays a crucial role in recent Bose-Einstein condensation experiments of visible-spectral-photons in e.g.~dye-solution-filled optical microcavities. It has recently been proposed to use high-pressure xenon-noble gas mixtures as a thermalization medium for vacuum-ultraviolet regime photons, so as to extend the achievable wavelength range of such Bose-Einstein-condensed optical sources from the visible to the vacuum-ultraviolet regime. In this work, we report two-photon excitation spectroscopy measurements of ground state (5p65p^65p6) xenon atoms subject to up to 80bar of helium or krypton buffer gas pressure, respectively, in the 220-260nm wavelength range. The study of such two-photon spectra is of interest e.g.~for the exploration of possible pumping schemes of a future vacuum-ultraviolet photon Bose-Einstein condensate. We have also recorded absorption and emission spectra of the 5p6↔5p56s5p^6 \leftrightarrow 5p^56s5p6↔5p56s single-photon transition near 147nm wavelength of xenon atoms subject to 80bar of krypton buffer gas pressure. We find that the ratio of absorption and emission shows a Kennard-Stepanov scaling, which suggests that such gas mixtures are promising candidates as a thermalization medium for a Bose-Einstein condensate of vacuum-ultraviolet photons.
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 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.