The authors demonstrate that an extended Bose condensate can be stable in a random potential for a suitable weak-repulsive limit of a dense Bose gas, even though the non-interacting case is pathological. The condensate exists primarily because the interactions allow screening of the random potential. This may happen even when the chemical potential is in the Lifshitz tails of the single-particle case. Indeed, the authors argue that there are no Lifshitz tail states in their dense but weakly-interacting system. Using a number-phase representation, they calculate the increase in the depletion of the condensate with increasing randomness (at fixed density) which indicates the eventual destruction of the condensed phase-perhaps to a localized phase. The physical picture discussed should be relevant to the understanding of helium thin films.
In this study, we reveal nontrivial quantum physics in an infinite-temperature system. By performing an unbiased quantum Monte Carlo simulation, we study a hybrid model composed of hard-core bosons, whose hopping amplitude is mediated by the density of another type of soft-core bond bosons that can absorb entropy indefinitely. It is shown that the Bose-Einstein condensate can persist in three dimensions even when the temperature approaches the infinite-temperature limit. In contrast, in two dimensions, the quasi-superfluid is depleted by the fluctuations of the bond bosons, which, on the other hand, enhance the conductivity of the hard-core bosons in the normal phase. A generalization to the fermionic model has also been discussed.
We investigate the properties of hard-core bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body density matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the ``natural'' single-particle orbitals and their occupation, including the condensate fraction. At low boson density, ${\mathrm{na}}^{3}<{10}^{\ensuremath{-}5},$ where
n=N/V and a is the hard-core diameter, the condensate is localized at the center of the trap. As
na3 increases, the condensate moves to the edges of the trap. At high density, it is localized at the edges of the trap. At ${\mathrm{na}}^{3}<~{10}^{\ensuremath{-}4},$ the Gross-Pitaevskii theory of the condensate describes the whole system within
1 At ${\mathrm{na}}^{3}\ensuremath{\approx}{10}^{\ensuremath{-}3},$ corrections are
3 to the Grass-Pitaevskii energy but
30 to the Bogoliubov prediction of the condensate depletion. At ${\mathrm{na}}^{3}\ensuremath{\gtrsim}{10}^{\ensuremath{-}2},$ mean-field theory fails. At ${\mathrm{na}}^{3}\ensuremath{\gtrsim}0.1,$ the bosons behave more like a liquid
4He droplet than a trapped boson gas.
We consider the Bose-Einstein condensation of atoms in a trap where the density of particles is so high that the low-density approach of Gross [J. Math. Phys. (N.Y.) 4, 195 (1963)] and Pitaevskii
(V. L. Ginsburg and L. P. Pitaevskii, Zh. \'Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 1858 (1958)]
) will not be applicable. For this purpose we use the slave boson representation which is valid for hard-core bosons at any density. This description leads to the same results as the Gross-Pitaevskii approach in the low-density limit, but for higher densities, it predicts the depletion of the condensate in the regions where the density of the atomic cloud is high.
We study the low-temperature states of a system of spinless bosons trapped in a broad spherical shell. In our virtual (path-integral Monte Carlo) experiments, we specifically examine how the equilibrium structure and overall superfluidity of the system are affected by a change of the interparticle-potential core from hard to increasingly soft. In this manner we bridge the gap between the behaviors of two species of bosons: Helium-like atoms, which self-assemble into ordinary crystalline solids, and Rydberg-dressed atoms, which in simulation form cluster (super)solids. We also vary the particle mass, i.e., the quantumness of the system, so as to modify the relative stability of ``solid'' and fluid states. We thus find a whole spectrum of (finite-size) phases with a curved structure, including multilayer and cluster phases, as well as superfluids and single layer supersolids. In particular, we confirm that supersolids only occur in the presence of clusters. By considering three system sizes (from 60 to 180 particles), but rescaling the trap radius so that the density stays fixed, we verify that supersolid states only exist in the same range of particle masses. Our model serves as a platform to test how emergent properties are modified, in spherical geometry, in the crossover from atoms to dressed atoms.
We study the correlation properties of the ground states of few ultracold bosons, trapped in double wells of varying barrier height in one dimension. Extending previous results on the signature of the transition from a Bose-condensed state via fragmentation to the hard-core limit, we provide a deeper understanding of that transition by relating it to the loss of coherence in the one-body density matrix and to the emerging long-range tail in the momentum spectrum. These are accounted for in detail by discussing the natural orbitals and their occupations. Our discussion is complemented by an analysis of the two-body correlation function.