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Register a new userBose-Einstein condensation of atoms in a uniform potential
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We have observed Bose-Einstein condensation of an atomic gas in the (quasi-)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of our non-condensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.
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Bose-Einstein condensation is a unique phase transition in that it is not driven by inter-particle interactions, but can theoretically occur in an ideal gas, purely as a consequence of quantum statistics. This chapter addresses the question emph{`How is this ideal Bose gas condensation modified in the presence of interactions between the particles? } This seemingly simple question turns out to be surprisingly difficult to answer. Here we outline the theoretical background to this question and discuss some recent measurements on ultracold atomic Bose gases that have sought to provide some answers.
We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the forcing at high wave numbers, and study propagation of the turbulent spectrum toward the low wave numbers. Our primary goal is to compare the results for the evolving spectrum with the previous results obtained for the kinetic equation of weak wave turbulence. We demonstrate existence of a regime for which good agreement with the wave turbulence results is found in terms of the main features of the previously discussed self-similar solution. In particular, we find a reasonable agreement with the low-frequency and the high-frequency power-law asymptotics of the evolving solution, including the anomalous power-law exponent $x^* approx 1.24$ for the three-dimensional waveaction spectrum. We also study the regimes of very weak turbulence, when the evolution is affected by the discreteness of the Fourier space, and the strong turbulence regime when emerging condensate modifies the wave dynamics and leads to formation of strongly nonlinear filamentary vortices.
By quenching the strength of interactions in a partially condensed Bose gas we create a super-saturated vapor which has more thermal atoms than it can contain in equilibrium. Subsequently, the number of condensed atoms ($N_0$) grows even though the temperature ($T$) rises and the total atom number decays. We show that the non-equilibrium evolution of the system is isoenergetic and for small initial $N_0$ observe a clear separation between $T$ and $N_0$ dynamics, thus explicitly demonstrating the theoretically expected two-step picture of condensate growth. For increasing initial $N_0$ values we observe a crossover to classical relaxation dynamics. The size of the observed quench-induced effects can be explained using a simple equation of state for an interacting harmonically-trapped atomic gas.
A theory of Bose-Einstein condensation (BEC) of light in a dye microcavity is developed. The photon polarization degeneracy and the interaction between dye molecules and photons in all of the cavity modes are taken into account. The theory goes beyond the grand canonical approximation and allows one to determine the statistical properties of the photon gas for all numbers of dye molecules and photons at all temperatures, thus describing the microscopic, mesoscopic, and macroscopic light BEC from a general perspective. A universal relation between the degrees of second-order coherence for the photon condensate and the polarized photon condensate is obtained. The photon Bose-Einstein condensate can be used as a new source of nonclassical light.
A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.
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