Strongly interacting Bose gas: Nozières and Schmitt-Rink theory and beyond (original) (raw)

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.

Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas

Physical Review Letters, 2011

We measure the zero-temperature equation of state of a homogeneous Bose gas of Li7 atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).PHRVAO0031-899X10.1103/PhysRev.106.1135]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant ξ>0.44(8) that would characterize the universal Bose gas at the unitary limit.

Behavior of trapped ultracold dilute Bose gases at large scattering length near a Feshbach resonance

Physical Review A, 2014

We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.

Bose gases near resonance: Renormalized interactions in a condensate

Annals of Physics, 2013

Bose gases at large scattering lengths or beyond the usual dilute limit for long have been one of the most challenging problems in many-body physics. In this article, we investigate the fundamental properties of a near-resonance Bose gas and illustrate that three-dimensional Bose gases become nearly fermionized near resonance when the chemical potential as a function of scattering lengths reaches a maximum and the atomic condensates lose meta-stability. The maximum and accompanied instability are shown to be a precursor of the sign change of g2, the renormalized two-body interaction between condensed atoms. That is g2 changes from effectively repulsive to attractive when approaching resonance from the molecular side, even though the scattering length is still positive. This occurs when dimers, under the influence of condensates, emerge at zero energy in the atomic gases at a finite positive scattering length. We investigate the properties of near-resonance Bose gases via applying a self-consistent renormalization group equation which is further subject to a thermodynamic boundary condition. We also comment on the relation between the approach here and the diagrammatic calculation in an early article [Phys. Rev. A 85, 023620(2012)].

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

2004

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)] that has recently observed this crossover temperature.

Bose-Einstein condensation in interacting gases

The European Physical Journal B, 1999

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a marked change of the velocity profile just above the transition: low velocities are more populated than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres.

Effects of Interactions on the Critical Temperature of a Trapped Bose Gas

Physical Review Letters, 2011

We perform high-precision measurements of the condensation temperature of a harmonically-trapped atomic Bose gas with widely-tuneable interactions. For weak interactions we observe a negative shift of the critical temperature in excellent agreement with mean-field theory. However for sufficiently strong interactions we clearly observe an additional positive shift, characteristic of beyond-mean-field critical correlations. We also discuss non-equilibrium effects on the apparent critical temperature for both very weak and very strong interactions.

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...

Critical Temperature Shift in Weakly Interacting Bose Gas

Physical Review Letters, 2001

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional |ψ| 4 -theory (which includes quantum Bose gas). In terms of critical density, nc, mass, m, interaction, U , and temperature, T , this shift is universal: ∆nc(T ) = −Cm 3 T 2 U , the constant C found to be equal to 0.0140 ± 0.0005. For quantum Bose gas with the scattering length a this implies ∆Tc/Tc = C0an 1/3 , with C0 = 1.29 ± 0.05.