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arXiv:1203.1811 · Journal of Physics Conference Series

Quasicondensation reexamined

Przemysław Bienias, Krzysztof Pawłowski, Mariusz Gajda, Kazimierz Rza̧żewski

Published Feb 8, 2013• 1 citation
arXivHTMLPDF

Abstract

We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions – exists in repulsive, attractive or in non-interacting Bose gas in some range of temperatures below characteristic temperature of the quantum degeneracy. Based on this observation we analyze the quasicondensation in terms of a ratio of the two largest eigenvalues of the single particle density matrix for the ideal gas. We show that in the thermodynamic limit in higher dimensions the second largest eigenvalue vanishes (as compared to the first one) with total number of particles as ≃ N −γ whereas goes to zero only logarithmically in one dimension. We also study the effect of quasicondensation for various geometries of the system: from quasi-1D elongated one, through spherically symmetric 3D case to quasi-2D pancake-like geometry.

DOI
10.1088/1742-6596/414/1/012031

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We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions – exists in repulsive, attractive or in non-interacting Bose gas in some range of temperatures below characteristic temperature of the quantum degeneracy. Based on this observation we analyze the quasicondensation in terms of a ratio of the two largest eigenvalues of the single particle density matrix for the ideal gas. We show that in the thermodynamic limit in higher dimensions the second largest eigenvalue vanishes (as compared to the first one) with total number of particles as ≃ N −γ whereas goes to zero only logarithmically in one dimension. We also study the effect of quasicondensation for various geometries of the system: from quasi-1D elongated one, through spherically symmetric 3D case to quasi-2D pancake-like geometry.
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasicondensate regime throughout the dimensional crossover from a purely one-dimensional (1D) to an almost three-dimensional (3D) gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasicondensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.
We present a detailed Monte Carlo study of correlations in an interacting two-dimensional Bose gas. The data for one-particle density matrix in coordinate representation are compared to the results for the local many-particle density correlators, which are responsible for the recombination rate in real experiments. We found that the appearance and growth of quasicondensate fluctuations changes local correlations between the particles well before the Kosterlitz-Thouless transition point. The amplitude of the 1/m!1/m!1/m!-effect is very sensitive even to a rather moderate interaction, and is considerably smaller than its limiting value.
This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas. We also perform measurements of the third moment of atom number fluctuations. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasi-condensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three body correlations in the system.
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.
We study, within the framework of the classical-field approximation, the density correlations of a weakly interacting expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We focus on elongated quasi-one-dimensional systems where there is a huge discrepancy between the existing theory and experimental results [A. Perrin et al., Nat. Phys. 8, 195 (2012)]. We find that the density correlation function is not reduced for temperatures below the critical one as it is predicted for the ideal gas or for a weakly interacting system within the Bogoliubov approximation. This behavior of the density correlations agrees with the above-mentioned experiment with the elongated system. Although the system was much larger than that studied here, we believe that the behavior of the density correlation function found there is quite generic. Our theoretical study indicates also large density fluctuations in the trap in the quasicondensate regime where only phase fluctuations were expected. We argue that the enhanced density fluctuations can originate in the presence of interactions in the system, or more precisely in the presence of spontaneous dark solitons in the elongated gas at thermal equilibrium.