Correlation Effects in Ultracold Two-Dimensional Bose Gases

Abstract

We study various properties of an ultracold two-dimensional (2D) Bose gas that are beyond a mean-field description. We first derive the effective interaction for such a system as realized in current experiments, which requires the use of an energy dependent $T$-matrix. Using this result, we then solve the mean-field equation of state of the modified Popov theory, and compare it with the usual Hartree-Fock theory. We show that even though the former theory does not suffer from infrared divergences in both the normal and superfluid phases, there is an unphysical density discontinuity close to the Berezinskii-Kosterlitz-Thouless transition. We then improve upon the mean-field description by using a renormalization group approach and show how the density discontinuity is resolved. The flow equations in two dimensions, in particular, of the symmetry-broken phase, already contain some unique features pertinent to the 2D XY model, even though vortices have not been included explicitly. We also compute various many-body correlators, and show that correlation effects beyond the Hartree-Fock theory are important already in the normal phase as criticality is approached. We finally extend our results to the inhomogeneous case of a trapped Bose gas using the local-density approximation and show that close to criticality, the renormalization group approach is required for the accurate determination of the density profile.

11 pages, 12 figures

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Cited by in corpus (11)

• The equilibrium state of a trapped two-dimensional Bose gas
• Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions
• Universal thermodynamics of a two-dimensional Bose gas
• The Influence of Remote Bands on Exciton Condensation in Double-Layer Graphene
• Universal correlations and coherence in quasi-two-dimensional trapped Bose gases
• Ab initio methods for finite temperature two-dimensional Bose gases
• Non-Universal Equation of State of the Two-Dimensional Bose Gas
• Pairing instabilities in quasi-two-dimensional Fermi gases
• Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations
• Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases
• Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action