Motivated by the experimental search for Bose condensation of quasiparticles in semiconductors, the response functions of a weakly interacting Bose gas, with isotropic but nonquadratic dispersion, are considered. Nonquadratic dispersion modifies the definition of particle current, and leads to modified sum rules for the current-current response function. The effect of these modifications on the Berezhinski-Kosterlitz-Thouless transition is discussed.
Motivated by the experimental search for Bose condensation of quasiparticles in semiconductors, the response functions of a weakly interacting Bose gas, with isotropic but nonquadratic dispersion, are considered. Nonquadratic dispersion modifies the definition of particle current, and leads to modified sum rules for the current-current response function. The effect of these modifications on the Berezhinski-Kosterlitz-Thouless transition is discussed.
Abstract In the work the problem of phenomenon of superfluidity is considered within the framework of Bose-Einshtein condensation, theoretically. We discuss the main features of the excitation spectrum in a weakly interacting Bose gas. Our analysis will show that the healing length, which determines the length scale below which collective phenomena are physically more relevant than free-particle-like ones. Since the weakly interacting gas of Bose particles has been mapped onto a gas of noninteracting quasiparticles, we are able to analyze the thermodynamics of the system and find how temperature affect the depletion of the condensate.
We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-fluid--superfluid phase transition point. We establish relations between basic thermodynamic functions: density $n(T,\ensuremath{\mu})$, superfluid density ${n}_{s}(T,\ensuremath{\mu})$, and condensate density ${n}_{\text{cnd}}(T,\ensuremath{\mu})$. Being universal for all weakly interacting ${\ensuremath{\mid}\ensuremath{\psi}\ensuremath{\mid}}^{4}$ systems, these relations are obtained from Monte Carlo simulations of the classical ${\ensuremath{\mid}\ensuremath{\psi}\ensuremath{\mid}}^{4}$ 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 significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.
In a Bose fluid having a condensate, the density response has two components. One is associated with exciting single quasiparticles out of the condensate and the second is the usual two-body density response involving states above the condensate appearing in any fluid. We derive the contribution of each component to the f-sum rule. The single quasiparticle contribution is proportional to the condensate function n0(T) at all wave vectors Q. This simple sum rule is analogous to the Ambegaokar, Conway, and Baym sum rule giving the one-phonon contribution to the f-sum rule in solids. It is very useful in interpreting neutron scattering measurements of superfluid 4He.
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,μ), superfluid density ns(T,μ), and condensate density, ncnd(T,μ). Being universal for all weakly interacting ∣ψ∣4 systems, these relations are obtained from Monte Carlo simulations of the classical ∣ψ∣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 significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.
Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of band structure can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jim\'enez-Garcia, and I. B. Spielman, Nature (London) 471, 83 (2011)], in the regime where the lower-band dispersion has the form ${\ensuremath{\varepsilon}}_{\mathbit{k}}\ensuremath{\sim}{k}_{x}^{4}/4+{k}_{y}^{2}+...$, or using the shaken lattice scheme of Parker et al. [C. V. Parker, L.-C. Ha, and C. Chin, Nat. Phys. 9, 769 (2013)]. We numerically compare the ground-state energies of the mean-field Bose-Einstein condensate (BEC) and various trial wave functions, where bosons avoid each other at short distances. We discover that, at low densities, several types of strongly correlated states have an energy per particle ($\ensuremath{\epsilon}$), which scales with density (n) as $\ensuremath{\epsilon}\ensuremath{\sim}{n}^{4/3}$, in contrast to $\ensuremath{\epsilon}\ensuremath{\sim}n$ for the weakly interacting Bose gas. These competing states include a Wigner crystal, quasicondensates described in terms of properly symmetrized fermionic states, and variational wave functions of Jastrow type. We find that one of the latter has the lowest energy among the states we consider. This Jastrow-type state has a strongly reduced, but finite, condensate fraction, and true off-diagonal long-range order, which suggests that the ground state of interacting bosons with quartic dispersion is a strongly correlated condensate reminiscent of superfluid helium-4. Our results show that even for weakly interacting bosons in higher dimensions, one can explore the crossover from a weakly coupled BEC to a strongly correlated condensate by simply tuning the single-particle dispersion or density.
We study the superfluid transition of weakly interacting Bose gases, classical fields and related systems in two dimensions, where it is a Berezinskii-Kosterlitz-Thouless transition, and in three dimensions, where it is a U(1) transition accompanied by the onset of Bose-Einstein condensation. We show that for small interaction strength U, these systems can be described by a :Ψ:4 model based on classical complex fields and we establish universal behavior among systems of different microscopical details, such as classical and quantum, continuous and lattice. By numerical simulations of the classical lattice field, using Worm Algorithm, we solve all relevant thermodynamical functions of this system, which are density, condensate density (in 3D), superfluid density and quasi-condensate. Through universality considerations, we can translate these results to all systems which can be described by a :Ψ:4 model based on a classical complex field. Our results cover the fluctuation region and extend into mean field and critical region, where we connect them to results of mean field theory and renormalization group theory respectively. We also establish that the quasicondensate, which exists in two and three dimensions, is a basis for a more accurate mean field theory treatment than the condensate, which exists only in three dimensions.