Bose-Einstein condensation of photons in an erbium-ytterbium co-doped fiber cavity

Bose-Einstein condensation of photons in microcavity plasmas

Bose-Einstein condensation of a finite number of photons propagating inside a plasma-filled microcavity is investigated. The nonzero chemical potential is provided by the electrons, which induces a finite photon mass and allows condensation to occur. We derive an equation that models the evolution of the photon-mode occupancies, with Compton scattering taken into account as the mechanism of thermalization. The kinetic evolution of the photon spectrum is solved numerically, and we find evidence of condensation down to nanosecond timescales for typical microplasma conditions, n_{e}∼10^{14}-10^{15}cm^{-3}. The critical temperature scales almost linearly with the number of photons, and we find high condensate fractions at microcavity-plasma temperatures, for experimentally achievable cavity lengths (100-500µm) and photon numbers (10^{10}-10^{12}).

Observation of Light Thermalization to Negative-Temperature Rayleigh-Jeans Equilibrium States in Multimode Optical Fibers

Although the temperature of a thermodynamic system is usually believed to be a positive quantity, under particular conditions, negative-temperature equilibrium states are also possible. Negative-temperature equilibriums have been observed with spin systems, cold atoms in optical lattices, and two-dimensional quantum superfluids. Here we report the observation of Rayleigh-Jeans thermalization of light waves to negative-temperature equilibrium states. The optical wave relaxes to the equilibrium state through its propagation in a multimode optical fiber-i.e., in a conservative Hamiltonian system. The bounded energy spectrum of the optical fiber enables negative-temperature equilibriums with high energy levels (high-order fiber modes) more populated than low energy levels (low-order modes). Our experiments show that negative-temperature speckle beams are featured, in average, by a nonmonotonic radial intensity profile. The experimental results are in quantitative agreement with the Rayleigh-Jeans theory without free parameters. Bringing negative temperatures to the field of optics opens the door to the investigation of fundamental issues of negative-temperature states in a flexible experimental environment.

Exact Analytical Solution for the Density Matrix of a Nonequilibrium Polariton Bose-Einstein Condensate

In this Letter, we give an analytical quantum description of a nonequilibrium polariton Bose-Einstein condensate (BEC) based on the solution of the master equation for the full polariton density matrix in the limit of fast thermalization. We find the density matrix of a nonequilibrium BEC, that takes into account quantum correlations between all polariton states. We show that the formation of BEC is accompanied by the build-up of cross-correlations between the ground state and the excited states reaching their highest values at the condensation threshold. Despite the nonequilibrium nature of polariton systems, we show the average population of polariton states exhibits the Bose-Einstein distribution with an almost zero effective chemical potential above the condensation threshold similar to an equilibrium BEC. We demonstrate that above threshold the effective temperature of polaritons drops below the reservoir temperature.

Realizing Einstein's Mirror: Optomechanical Damping with a Thermal Photon Gas

Einstein described the damping and thermalization of the center-of-mass motion of a mirror placed inside a blackbody cavity by collisions with thermal photons. While the time for damping even a microscale or nanoscale object is so long that it is not experimentally viable, we show that this damping is feasible using the high-intensity light from an amplified thermal light source with a well-defined chemical potential. We predict this damping of the center-of-mass motion will occur on timescales of tens of seconds for small optomechanical systems.

A Bose–Einstein condensate is a Bose condensate in the laboratory ground state

Bose–Einstein condensates of weakly interacting, ultra-cold atoms have become a workhorse for exploring quantum effects on atomic motion, but does this condensate need to be in the ground state of the system? Researchers often perform transformations so that their Hamiltonians are easier to analyse. However, changing Hamiltonians can require an energy shift. We show that transforming into a rotating or oscillating frame of reference of a Bose condensate does not then satisfy Einstein’s requirement that a condensate exists in the zero kinetic energy state. We show that Bose condensation can occur above the ground state and at room temperature, referring to recent literature.

Bose-Einstein condensation of photons in a long fiber cavity

We demonstrate photon Bose-Einstein condensation (photon-BEC) at a broad temperature range that is valid also in the long 1D fiber cavity limit. It is done with an erbium-ytterbium co-doped fiber (EYDF) cavity by overcoming the challenging requirement of sublinear light dispersion for BEC in 1D using a chirped-gratings Fabry-Perot. We experimentally show with a square-root mode-dispersion, a quadratic temperature dependence of the critical power for condensation (compared to a linear dependence in finite regular fiber-cavities) between 90 K and 382 K, as the theory predicts.

Learning the Fuzzy Phases of Small Photonic Condensates

Phase transitions, being the ultimate manifestation of collective behavior, are typically features of many-particle systems only. Here, we describe the experimental observation of collective behavior in small photonic condensates made up of only a few photons. Moreover, a wide range of both equilibrium and nonequilibrium regimes, including Bose-Einstein condensation or laserlike emission are identified. However, the small photon number and the presence of large relative fluctuations places major difficulties in identifying different phases and phase transitions. We overcome this limitation by employing unsupervised learning and fuzzy clustering algorithms to systematically construct the fuzzy phase diagram of our small photonic condensate. Our results thus demonstrate the rich and complex phase structure of even small collections of photons, making them an ideal platform to investigate equilibrium and nonequilibrium physics at the few particle level.

Photon thermalization and a condensation phase transition in an electrically pumped semiconductor microresonator

We report on an experimental study of photon thermalization and condensation in a semiconductor microresonator in the weak-coupling regime. We measure the dispersion relation of light and the photon mass in a single-wavelength, broad-area resonator. The observed luminescence spectrum is compatible with a room-temperature, thermal-equilibrium distribution. A phase transition, identified by a saturation of the population at high energies and a superlinear increase of the occupation at low energy, takes place when the phase-space density is of order unity. We explain our observations by Bose-Einstein condensation of photons in equilibrium with a particle reservoir and discuss the relation with laser emission.

Classical Rayleigh-Jeans Condensation of Light Waves: Observation and Thermodynamic Characterization

Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the nonequilibrium formation of nonlinear coherent structures (solitons, vortices,…), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the first demonstration of a coherent phenomenon of self-organization that is exclusively driven by optical thermalization toward the Rayleigh-Jeans equilibrium.

Sub-picosecond thermalization dynamics in condensation of strongly coupled lattice plasmons

Bosonic condensates offer exciting prospects for studies of non-equilibrium quantum dynamics. Understanding the dynamics is particularly challenging in the sub-picosecond timescales typical for room temperature luminous driven-dissipative condensates. Here we combine a lattice of plasmonic nanoparticles with dye molecule solution at the strong coupling regime, and pump the molecules optically. The emitted light reveals three distinct regimes: one-dimensional lasing, incomplete stimulated thermalization, and two-dimensional multimode condensation. The condensate is achieved by matching the thermalization rate with the lattice size and occurs only for pump pulse durations below a critical value. Our results give access to control and monitoring of thermalization processes and condensate formation at sub-picosecond timescale.

Nonlinear light mode dispersion and nonuniform mode comb by a Fabry-Perot with chirped fiber gratings

We demonstrate a nonlinear light mode dispersion and a nonuniform frequency mode comb by a chirped fiber Bragg gratings (CFBG) Fabry-Perot (FP) at the 1550 nm wavelength regime. We give analytical expressions for the general chirp case, and an experimental demonstration with a linear chirp, showing a square-root dependence of the dispersion as a function of the FP mode number. Such sublinear dispersion is required, for example, for photon Bose-Einstein condensation (BEC) in a one-dimensional (1D) system like fiber cavities.