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Register a new userLearning the Fuzzy Phases of Small Photonic Condensates
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Phase transitions, being the ultimate manifestation of collective behaviour, are typically features of many-particle systems only. Here, we describe the experimental observation of collective behaviour in small photonic condensates made up of only a few photons. Moreover, a wide range of both equilibrium and non-equilibrium regimes, including Bose-Einstein condensation or laser-like 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 non-equilibrium physics at the few particle level.
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Weak measurement in tandem with real-time feedback control is a new route toward engineering novel non-equilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances -- spin-independent and spin-dependent -- but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful new tool for quantum engineering in cold-atom systems.
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Recently, stripe phases in spin-orbit coupled Bose-Einstein condensates (BECs) have attracted much attention since they are identified as supersolid phases. In this paper, we exploit experimentally reachable parameters and show theoretically that annular stripe phases with large stripe spacing and high stripe contrast can be achieved in spin-orbital-angular-momentum coupled (SOAMC) BECs. In addition to using Gross-Pitaevskii numerical simulations, we develop a variational ansatz that captures the essential interaction effects to first order, which are not present in the ansatz employed in previous literature. Our work should open the possibility toward directly observing stripe phases in SOAMC BECs in experiments.
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Controlled quantum systems such as ultracold atoms can provide powerful platforms to study non-equilibrium dynamics of closed many-body quantum systems, especially since a complete theoretical description is generally challenging. In this Letter, we present a detailed study of the rich out-of-equilibrium dynamics of an adjustable number $N$ of uncorrelated condensates after connecting them in a ring-shaped optical trap. We observe the formation of long-lived supercurrents and confirm the scaling of their winding number with $N$ in agreement with the geodesic rule. Moreover, we provide insight into the microscopic mechanism that underlies the smoothening of the phase profile.
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