Strongly Interacting Two-Dimensional Bose Gases (original) (raw)
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Critical Temperature of Interacting Bose Gases in Two and Three Dimensions
Physical Review Letters, 2008
The superfluid transition of a repulsive Bose gas in the presence of a sinusoidal potential which represents a simple-cubic optical lattice is investigate using quantum Monte Carlo simulations. At the average filling of one particle per well the critical temperature has a nonmonotonic dependence on the interaction strength, with an initial sharp increase and a rapid suppression at strong interactions in the vicinity of the Mott transition. In an optical lattice the positive shift of the transition is strongly enhanced compared to the homogenous gas. By varying the lattice filling we find a crossover from a regime where the optical lattice has the dominant effect to a regime where interactions dominate and the presence of the lattice potential becomes almost irrelevant.
Correlation effects in ultracold two-dimensional Bose gases
Physical Review A, 2008
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.
Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases
Annals of Physics, 2014
We derive a mean-field description for two-dimensional (2D) interacting Bose gases at arbitrary temperatures. We find that genuine Bose-Einstein condensation with long-range coherence only survives at zero temperature. At finite temperatures, many-body pairing effects included in our mean-field theory introduce a finite amplitude for the pairing density, which results in a finite superfluid density. We incorporate Berenzinskii-Kosterlitz-Thouless (BKT) physics into our model by considering the phase fluctuations of our pairing field. This then leads to the result that the superfluid phase is only stable below the BKT temperature due to these phase fluctuations. In the weakly interacting regime at low temperature we compare our theory to previous results from perturbative calculations, renormalization group calculations as well as Monte Carlo simulations. We present a finite-temperature phase diagram of 2D Bose gases. One signature of the finite amplitude of the pairing density field is a two-peak structure in the single-particle spectral function, resembling that of the pseudogap phase in 2D attractive Fermi gases.
arXiv preprint arXiv:1203.3254, 2012
Abstract: We develop a unified description for two-dimensional (2D) interacting Bose gases at arbitrary temperatures. The genuine Bose-Einstein condensation with long-range coherence only survives at zero temperature. At finite temperatures, many-body pairing effects introduce a finite amplitude of the pairing density, which results in a finite superfluid density. The superfluid phase is only stable below the Berenzinskii-Kosterlitz-Thouless (BKT) temperature due to phase fluctuations. We present a finite-temperature phase ...
Critical Point of a Weakly Interacting Two-Dimensional Bose Gas
Physical Review Letters, 2001
We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical |ψ| 4 -model on a lattice. The critical density and chemical potential are given by relations nc = (mT /2πh 2 ) ln(ξh 2 /mU ) and µc = (mT U/πh 2 ) ln(ξµh 2 /mU ), where T is the temperature, m is the mass, and U is the effective interaction. The dimensionless constant ξ = 380 ± 3 is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ξµ our result is ξµ = 13.2 ± 0.4. We also report the study of the quasi-condensate correlations at the critical point.
Two-dimensional weakly interacting Bose gas in the fluctuation region
Physical Review A, 2002
We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii-Kosterlitz-Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting |ψ| 4 models ) relations between thermodynamic parameters of the system, including superfluid and quasi-condensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical |ψ| 4 model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.
Superfluid Bose gas in two dimensions
2008
We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales (microphysics) to the characteristic extension of the probe l (macrophysics). In two dimensions the scale dependence of the dimensionless interaction strength λ is logarithmic. Furthermore, for large l the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for λ, and for large λ substantial deviations from the Bogoliubov results for the condensate depletion, the dispersion relation and the sound velocity. The melting of the condensate above the critical temperature Tc is associated to a phase transition of the Kosterlitz-Thouless type. The critical temperature in units of the density, Tc/n, vanishes for l → ∞ logarithmically.
Weakly interacting Bose gas in the vicinity of the critical point
2004
We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-superfluid phase transition point. We establish relations between basic thermodynamic functions: density, n(T,mu)n(T,\mu)n(T,mu), superfluid density ns(T,mu)n_s(T,\mu)ns(T,mu), and condensate density, nrmcnd(T,mu)n_{\rm cnd} (T,\mu)nrmcnd(T,mu). Being universal for all weakly interacting ∣psi∣4|\psi|^4∣psi∣4 systems, these relations are obtained from Monte Carlo simulations of the classical ∣psi∣4|\psi|^4∣psi∣4 model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean field theory.--This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a sign...
Coherence properties of a 2D trapped Bose gas around the superfluid transition
2011
We measure the momentum distribution of a 2D trapped Bose gas and observe the increase of the range of coherence around the Berezinskii-Kosterlitz-Thouless (BKT) transition. We quantitatively compare our observed profiles to both a Hartee-Fock mean-field theory and to quantum Monte-Carlo simulations. In the normal phase, we already observe a sharpening of the momentum distribution. This behavior is partially captured in a mean-field approach, in contrast to the physics of the BKT transition.
Collective and single-particle excitations in two-dimensional dipolar Bose gases
Physical Review A, 2012
The Berezinskii-Kosterlitz-Thouless transition in 2D dipolar systems has been studied recently by path integral Monte Carlo (PIMC) simulations [A. Filinov et al., PRL 105, 070401 (2010)]. Here, we complement this analysis and study temperature-coupling strength dependence of the density (particle-hole) and single-particle (SP) excitation spectra both in superfluid and normal phases. The dynamic structure factor, S(q, ω), of the longitudinal excitations is rigorously reconstructed with full information on damping. The SP spectral function, A(q, ω), is worked out from the one-particle Matsubara Green's function. A stochastic optimization method is applied for reconstruction from imaginary times. In the superfluid regime sharp energy resonances are observed both in the density and SP excitations. The involved hybridization of both spectra is discussed. In contrast, in the normal phase, when there is no coupling, the density modes, beyond acoustic phonons, are significantly damped. Our results generalize previous zero temperature analyses based on variational many-body wavefunctions [F. Mazzanti et al., PRL 102, 110405 (2009), D. Hufnagl et al., PRL 107, 065303 (2011, where the underlying physics of the excitation spectrum and the role of the condensate has not been addressed.