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Register a new userTheory of Critical Temperature Adiabatic Change for Ideal Gas Bose-Einstein Condensation in Optical Lattices
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We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that the width of the lowest energy band appears as the main parameter determining the critical temperature of condensation. Is obtained a very simple, proportional to 1/3 degree, regularity for this dependence. The fundamental role of tunneling in physics of condensate establishment is underscored.
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We find universal structure and scaling of BEC statistics and thermodynamics for mesoscopic canonical-ensemble ideal gas in a trap for any parameters, including critical region. We identify universal constraint-cut-off mechanism that makes BEC fluctuations non-Gaussian and is responsible for critical phenomena. Main result is analytical solution to problem of critical phenomena. It is derived by calculating universal distribution of noncondensate occupation (Landau function) and then universal functions for physical quantities. We find asymptotics of that solution and its approximations which describe universal structure of critical region in terms of parabolic cylinder or confluent hypergeometric functions. Results for order parameter, statistics, and thermodynamics match known asymptotics outside critical region. We suggest 2-level and 3-level trap models and find their exact solutions in terms of cut-off negative binomial distribution (that tends to cut-off gamma distribution in continuous limit) and confluent hypergeometric distribution. We introduce a regular refinement scheme for condensate statistics approximations on the basis of infrared universality of higher-order cumulants and method of superposition and show how to model BEC statistics in actual traps. We find that 3-level trap model with matching the first 4 or 5 cumulants is enough to yield remarkably accurate results in whole critical region. We derive exact multinomial expansion for noncondensate occupation distribution and find its high temperature asymptotics (Poisson distribution). We demonstrate that critical exponents and a few known terms of Taylor expansion of universal functions, calculated previously from fitting finite-size simulations within renorm-group theory, can be obtained from presented solutions.
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.
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.
In this article, we present theoretical as well as experimental results on resonantly enhanced tunneling of Bose-Einstein condensates in optical lattices both in the linear case and for small nonlinearities. Our results demonstrate the usefulness of condensates in optical lattices for simulating Hamiltonians originally used for describing solid state phenomena.
Paper is published in J. Phys. A: Math. Theor. 43 (2010) 225001, doi:10.1088/1751-8113/43/22/225001. Exact analytical solution for the universal probability distribution of the order parameter fluctuations as well as for the universal statistical and thermodynamic functions of an ideal gas in the whole critical region of Bose-Einstein condensation is obtained. A universal constraint nonlinearity is found that is responsible for all nontrivial critical phenomena of the BEC phase transition. Simple analytical approximations, which describe the universal structure of the critical region in terms of confluent hypergeometric or parabolic cylinder functions, as well as asymptotics of the exact solution are derived. The results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities, including specific heat, perfectly match the known asymptotics outside critical region as well as the phenomenological renormalization-group ansatz with known critical exponents in the close vicinity of the critical point. Thus, a full analytical solution to a long-standing problem of finding a universal structure of the lambda-point for BEC in an ideal gas is found.
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