Bose-Einstein condensation in a two-dimensional, trapped, interacting gas

Abstract

We study Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to an harmonic oscillator type confining potential. The interaction among the 2D bosons is described by a delta-function in configuration space. Solving the Gross-Pitaevskii equation within the two-fluid model we calculate the condensate fraction, ground state energy, and specific heat of the system. Our results indicate that interacting bosons have similar behavior to those of an ideal system for weak interactions.PACS numbers: 03.75. Fi, 05.30Jp, 67.40Kh The observation of the Bose-Einstein condensation (BEC) phenomenon in dilute atomic gases [1][2][3][4] has caused a lot of attention, because it provides opportunities to study the thermodynamics of weakly interacting systems in a controlled way. The condensate clouds obtained in the experiments consist of a finite number of atoms (ranging from several thousands to several millions), and are confined in an externally applied confining potentials. The ground state properties of the condensed gases, including the finite size effects on the temperature dependence of the condensate fraction, are of primary interest. At zero temperature, the mean-field approximation provided by the Gross-Pitaevskii equation [5] describes the condensate rather well and at finite temperatures a self-consistent Hartree-Fock-Bogoliubov (HFB) approximation is developed.[6] Path Integral Monte Carlo (PIMC) simulations [7] on three-dimensional, interacting bosons appropriate to the current experimental conditions demonstrate the effectiveness of the meanfield type approaches. Various aspects of the mean-field theory, as well as detailed calculations corresponding to the available experimental conditions are discussed by Giorgini et al. [8] In this work, we examine the possibility of BEC in a two-dimensional (2D) interacting atomic gas, under a trap potential. Such a system may be realized by making one dimension of the trap very narrow so that the oscillator states are largely separated. Possible experimental configurations in spin polarized hydrogen and magnetic waveguides are currently under discussion.[9] The study of 2D systems is also interesting theoretically, since even though the homogeneous system of 2D bosons do not undergo BEC, [10] number of examples [11] have indicated such a possibility upon the inclusion of confining potentials. We employ the two-fluid, mean-field model developed by Minguzzi et al. [12] to study the 2D Bose gas. Similar approaches [13] are gaining attention because of their simple and intuitive content which also provide semi-analytical expressions for the density distribution of the condensate. Recently, Mullin [14] considered the self-consistent mean-field theory of 2D Bose particles interacting via a contact interaction within the Popov and semi-classical approximations. His conclusions were that a phase transition occurs for a 2D Bose system, in the thermodynamic limit, at some critical temperature, but not necessarily to a Bose-Einstein condensed ...

A Rigorous Derivation¶of the Gross–Pitaevskii Energy Functional¶for a Two-dimensional Bose Gas

“…The choice of g is an issue on which there has not been unanimous opinion in the recent papers [12,13,14,15,16,17,18] on this subject. We shall prove that a right choice is g = | ln(ρa 2 )| −1 wherē ρ is a mean density that will be defined more precisely below.…”

Harmonically Trapped Bosons on the Sierpiński Carpet

“…[4]. The results also correlate with the analysis of trapped weakly interacting bosons in two dimensions [21] and with the Hartree-Fock-Bogoliubov treatment of a quasi-two-dimensional trapped Bose system [22]. One should note that a harmonically trapped system in D dimensions effectively corresponds (in the semiclassical approach) to an ideal system in a 2D-dimensional rigid box, cf.…”

Collective excitations of a two-dimensional interacting Bose gas in external fields

“…They have concluded that two regimes can be realized: a true condensate and a quasicondensate with fluctuating phase. In the mean field approximation the properties of such a system have been studied by Bayindir and Tanatar [11]. They demonstrate the similarity in thermodynamic behavior of ideal 2D Bose systems in a harmonic trap and those with weak interactions and a finite number of the particles.…”