ABSTRACT
In this work, we use focused ion beam (FIB) milling to generate custom mirror shapes for quantum simulation in optical microcavities. In the paraxial limit, light in multimode optical microcavities follows an equation of motion which is equivalent to Schrödinger's equation, with the surface topography of the mirrors playing the role of the potential energy landscape. FIB milling allows us to engineer a wide variety of trapping potentials for microcavity light, through exquisite control over the mirror topography, including 2D box, 1D waveguide, and Mexican hat potentials. The 2D box potentials are sufficiently flat over tens of microns, that the optical modes of the cavity, found by solving Schrödinger's equation on the measured cavity topography, are standing-wave modes of the box, rather than localised to deviations. The predicted scattering loss due to surface roughness measured using atomic force microscopy is found to be 177 parts per million, which corresponds to a cavity finesse of 2.2 × 104 once other losses have been taken into account. Spectra from dye-filled microcavities formed using these features show thermalised light in flat 2D potentials close to dye resonance, and spectrally-resolved cavity modes at the predicted frequencies for elliptical potentials. These results also represent a first step towards realising superfluid light and quantum simulation in arbitrary-shaped optical microcavities using FIB milling.
ABSTRACT
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.
ABSTRACT
While equilibrium phase transitions are easily described by order parameters and free-energy landscapes, for their non-stationary counterparts these quantities are usually ill-defined. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity. We quench the system to a far-from-equilibrium state and find delayed condensation close to a critical excitation energy, a transient equivalent of critical slowing down. Besides number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit timing jitter in the condensate formation. This jitter is a manifestation of the randomness associated with spontaneous emission, showing that condensation is a stochastic, rather than deterministic process. Despite the non-equilibrium character of this phase transition, we construct an effective free-energy landscape that describes the formation jitter and allows, in principle, its generalization to a wider class of processes.
ABSTRACT
We investigate the response of a photonic gas interacting with a reservoir of pumped dye molecules to quenches in the pump power. In addition to the expected dramatic critical slowing down of the equilibration time around phase transitions, we find extremely slow equilibration even far away from phase transitions. This noncritical slowing down can be accounted for quantitatively by fierce competition among cavity modes for access to the molecular environment, and we provide a quantitative explanation for this noncritical slowing down.
