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arXiv:1110.0123 · Physical Review A

Behavior of the anomalous correlation function in a uniform two-dimensional Bose gas

Abdelâali Boudjemâa

Published Oct 9, 2012• 30 citations
arXivHTMLPDF

Abstract

We investigate the behavior of the anomalous correlation function in two-dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify, in particular, the chemical potential, the ground-state energy, the depletion, and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the noncondensed one at zero temperature. The single-particle anomalous correlation function is expressed in two-dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature, while it does not exist at finite temperature.

DOI
10.1103/physreva.86.043608

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We present a systematic study of dilute three-dimensional dipolar Bose gas employing a finite temperature perturbation theory (beyond the mean field). We analyze in particular the behavior of the anomalous density, we find that this quantity has a finite value in the limit of weak interactions at both zero and finite temperatures. We show that the presence of the dipole–dipole interaction enhances fluctuations, the second order correlation function and thermodynamic quantities such as the chemical potential, the ground state energy, the compressibility and the superfluid fraction. We identify the validity criterion of the small parameter of the theory for Bose-condensed dipolar gases.
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Abstract We study the impact of a weak random potential with a Gaussian correlation function on the thermodynamics of a two-dimensional dipolar bosonic gas. Analytical expressions for the quantum depletion, anomalous density, the ground state energy, the equation of state and the sound velocity are derived in the roton regime within the framework of the Bogoliubov theory. Surprisingly, we find that the condensate depletion and the anomalous density are comparable. The structure factor and the superfluid fraction are also obtained analytically and numerically. We show that these quantities acquire dramatically modified profiles when the roton is close to zero yielding the transition to an unusual quantum state.
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The physical properties of a homogeneous system at the thermodynamic equilibrium are strongly constrained by its dimensionality. In this respect, the two dimensional Bose gas constitutes a particularly interesting system: while it is impossible to observe a long range order at non-zero temperatures, there exists nevertheless a phase transition to a superfluid state at low temperatures. Furthermore, owing to the reduced dimensionality, the equation of state of the weakly interacting two-dimensional Bose gas is scale invariant. In this thesis, we present an experimental study of the two-dimensional Bose gas. We measure its equation of state with two different methods, and find a good agreement with analytic and numerical predictions. These results confirm as well the scale invariance of the system. Furthermore, one of the methods allows for a determination of the equation of state with a single adjustable parameter. We then characterize the superfluid response of the system., by showing evidence for a dissipationless response of the system to a moving perturbation. Finally, we analyze the fluctuations dynamics of the 2D Bose gas, which confirms both the suppression of density fluctuations in the superfluid phase, and the dominating contribution of phonons to the phase fluctuations.
Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.