Stabilizing optical microcavities in 3D

Optical (micro-)cavities are the workhorse for studying light-matter interactions with important applications in lasing, sensing, and quantum simulations, to name a few. Open resonators in particular offer great versatility due to their tunability but pose challenges in terms of control. This concerns, on the one hand, the control of their length, and on the other hand, the relative orientation (tilt) of the mirror planes to each other. The latter becomes particularly important when working with optically unstable resonators, such as plane-parallel resonators.There are numerous strategies to enhance stability using passive techniques, such as material selection, mechanical damping, or thermal compensation. But especially for tuneable microcavities often an active stabilization method with feedback control systems must be employed. Here, we present a novel method for tilt measurement and stabilization using inverse solving of the Schrödinger equation arising in the paraxial description of the cavity modes. Our method enables the highly precise determination of absolute tilt angles, making it suitable for microcavity applications that require the highest level of cavity parallelism

Quantum Rotor Engines

This chapter presents autonomous quantum engines that generate work in the form of directed motion for a rotor. We first formulate a prototypical clock-driven model in a time-dependent framework and demonstrate how it can be translated into an autonomous engine with the introduction of a planar rotor degree of freedom. The rotor plays both the roles of internal engine clock and of work repository. Using the example of a single-qubit piston engine, the thermodynamic performance is then reviewed. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directed rotation, as well as the intrinsic work based on the exerted torque under autonomous operation; and we compare them with the actual energy output to an external dissipative load. The chapter closes with a quantum-classical comparison of the engine's dynamics. For the single-qubit piston example, we propose two alternative representations of the qubit in an entirely classical framework: (i) a coin flip model and (ii) a classical magnet moment, showing subtle differences between the quantum and classical descriptions.Comment: Chapter of the upcoming book "Thermodynamics in the Quantum Regime - Recent Progress and Outlook

Polariton Condensation and Lasing

The similarities and differences between polariton condensation in microcavities and standard lasing in a semiconductor cavity structure are reviewed. The recent experiments on "photon condensation" are also reviewed.Comment: 23 pages, 6 figures; Based on the book chapter in Exciton Polaritons in Microcavities, (Springer Series in Solid State Sciences vol. 172), V. Timofeev and D. Sanvitto, eds., (Springer, 2012

Bose-Einstein condensation of photons in an optical microcavity

Bose-Einstein condensation, the macroscopic ground state accumulation of particles with integer spin (bosons) at low temperature and high density, has been observed in several physical systems, including cold atomic gases and solid state physics quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition, because the chemical potential of photons vanishes and, when the temperature is reduced, photons disappear in the cavity walls. Theoretical works have considered photon number conserving thermalization processes, a prerequisite for Bose-Einstein condensation, using Compton scattering with a gas of thermal electrons, or using photon-photon scattering in a nonlinear resonator configuration. In a recent experiment, we have observed number conserving thermalization of a two-dimensional photon gas in a dye-filled optical microcavity, acting as a 'white-wall' box for photons. Here we report on the observation of a Bose-Einstein condensation of photons in a dye-filled optical microcavity. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. By multiple scattering off the dye molecules, the photons thermalize to the temperature of the dye solution (room temperature). Upon increasing the photon density we observe the following signatures for a BEC of photons: Bose-Einstein distributed photon energies with a massively populated ground state mode on top of a broad thermal wing, the phase transition occurring both at the expected value and exhibiting the predicted cavity geometry dependence, and the ground state mode emerging even for a spatially displaced pump spot

Does Bose-Einstein condensation of CMB photons cancel {\mu} distortions created by dissipation of sound waves in the early Universe?

The difference in the adiabatic indices of photons and non-relativistic baryonic matter in the early Universe causes the electron temperature to be slightly lower than the radiation temperature. Thermalization of photons with a colder plasma results in the accumulation of photons in the Rayleigh-Jeans tail, aided by stimulated recoil, while the higher frequency spectrum tries to approach Planck spectrum at the electron temperature T_{\gamma}^{final}=\Te; i.e., Bose-Einstein condensation of photons occurs. We find new solutions of the Kompaneets equation describing this effect. No actual condensate is, in reality, possible since the process is very slow and photons drifting to low frequencies are efficiently absorbed by bremsstrahlung and double Compton processes. The spectral distortions created by Bose-Einstein condensation of photons are within an order of magnitude (for the present range of allowed cosmological parameters), with exactly the same spectrum but opposite in sign, of those created by diffusion damping of the acoustic waves on small scales corresponding to comoving wavenumbers $45< k< 10^4\, Mpc^{-1}$. The initial perturbations on these scales are completely unobservable today due to their being erased completely by Silk damping. There is partial cancellation of these two distortions, leading to suppression of $\mu$ distortions expected in the standard model of cosmology. The net distortion depends on the scalar power index $n_S$ and its running $d n_S/d\ln k$, and may vanish for special values of parameters, for example, for a running spectrum with, $n_S=1,d n_S/d\ln k=-0.038$. We arrive at an intriguing conclusion: even a null result, non-detection of $\mu$-type distortion at a sensitivity of $10^{-9}$, gives a quantitative measure of the primordial small-scale power spectrum.Comment: Published versio

Photon condensation in circuit QED by engineered dissipation

We study photon condensation phenomena in a driven and dissipative array of superconducting microwave resonators. Specifically, we show that by using an appropriately designed coupling of microwave photons to superconducting qubits, an effective dissipative mechanism can be engineered, which scatters photons towards low-momentum states while conserving their number. This mimics a tunable coupling of bosons to a low temperature bath, and leads to the formation of a stationary photon condensate in the presence of losses and under continuous-driving conditions. Here we propose a realistic experimental setup to observe this effect in two or multiple coupled cavities, and study the characteristics of such an out-of-equilibrium condensate, which arise from the competition between pumping and dissipation processes

Advances in small lasers

M.T.H was supported by an Australian Research council Future Fellowship research grant for this work. M.C.G. is grateful to the Scottish Funding Council (via SUPA) for financial support.Small lasers have dimensions or modes sizes close to or smaller than the wavelength of emitted light. In recent years there has been significant progress towards reducing the size and improving the characteristics of these devices. This work has been led primarily by the innovative use of new materials and cavity designs. This Review summarizes some of the latest developments, particularly in metallic and plasmonic lasers, improvements in small dielectric lasers, and the emerging area of small bio-compatible or bio-derived lasers. We examine the different approaches employed to reduce size and how they result in significant differences in the final device, particularly between metal- and dielectric-cavity lasers. We also present potential applications for the various forms of small lasers, and indicate where further developments are required.PostprintPeer reviewe

Thermalisation of a two-dimensional photonic gas in a 'white-wall' photon box

Bose-Einstein condensation, the macroscopic accumulation of bosonic particles in the energetic ground state below a critical temperature, has been demonstrated in several physical systems. The perhaps best known example of a bosonic gas, blackbody radiation, however exhibits no Bose-Einstein condensation at low temperatures. Instead of collectively occupying the lowest energy mode, the photons disappear in the cavity walls when the temperature is lowered - corresponding to a vanishing chemical potential. Here we report on evidence for a thermalised two-dimensional photon gas with freely adjustable chemical potential. Our experiment is based on a dye filled optical microresonator, acting as a 'white-wall' box for photons. Thermalisation is achieved in a photon number-conserving way by photon scattering off the dye-molecules, and the cavity mirrors both provide an effective photon mass and a confining potential - key prerequisites for the Bose-Einstein condensation of photons. As a striking example for the unusual system properties, we demonstrate a yet unobserved light concentration effect into the centre of the confining potential, an effect with prospects for increasing the efficiency of diffuse solar light collection.Comment: 15 pages, 3 figure