Bose-Einstein Condensation and Supersolids (original) (raw)
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Bose-Einstein Condensation and Quasicrystals
Armenian Journal of Physics, 2021
We consider interacting Bose particles in an external local potential. It is shown that large class of external quasicrystal potentials cannot sustain any type of Bose-Einstein condensates. Accordingly, at spatial dimensions D ≤ 2 in such quasicrystal potentials a supersolid is not possible via Bose-Einstein condensates at finite temperatures. The latter also hold true for the two-dimensional Fibonacci tiling. However, supersolids do arise at D ≤ 2 via Bose-Einstein condensates from infinitely long-range, nonlocal interparticle potentials.
Supersolids in one-dimensional Bose-Fermi mixtures
Physical Review B, 2008
Using quantum Monte Carlo simulations, we study a mixture of bosons and fermions loaded on an optical lattice. With simple on-site repulsive interactions, this system can be driven into a solid phase. We dope this phase and, in analogy with pure bosonic systems, identify the conditions under which the bosons enter a supersolid phase, i.e., exhibiting at the same time charge density wave and superfluid order. We perform finite size scaling analysis to confirm the presence of a supersolid phase and discuss its properties, showing that it is a collective phase that also involve phase coherence of the fermions.
Bose–Einstein condensation in a decorated lattice: an application to the problem of supersolid He
Low Temperature Physics, 2008
The Bose-Einstein condensation of vacancies in a three-dimensional decorated lattice is considered. The model describes possible scenario of superfluidity of solid helium, caused by the presence of zero-point vacancies in a dislocation network. It is shown that the temperature of Bose-Einstein condensation decreases under increase of the length of the network segments, and the law of decrease depends essentially on the properties of the vertices of the network. If the vertices correspond to barriers with a small transparency, the critical temperature varies inversely as the square of the length of the segment. On the contrary, if the vertices correspond to traps for the vacancies ͑it is energetically preferable for the vacancies to be localized at the vertices͒, an exponential lowering of the temperature of transition takes place. The highest temperature of Bose-Einstein condensation is reached in the intermediate case of vertices with large transparency, but in the absence of tendency of localization at them. In the latter case the critical temperature is inversely as the length of the segment.
Supersolid behavior in one-dimensional self-trapped Bose-Einstein condensate
2020
Supersolid is an exotic state of matter, showing crystalline order with a superfluid background, observed recently in dipolar Bose-Einstein condensate (BEC) in a trap. Here, we present exact solutions of the desired Bloch form in the self-trapped free-floating quantum fluid. Our general solutions of the amended nonlinear Schrödinger equation, governing the mean-field and beyond mean-field dynamics, are obtained through a Möbius transform, connecting a wide class of supersolid solutions to the ubiquitous cnoidal waves. The solutions yield the constant condensate, supersolid behavior and the self-trapped droplet in different parameter domains. The lowest residual condensate is found to be exactly one-third of the constant background.
Possible Existence of Bose-Einstein Condensation in One and Two Dimensions
Physical Review A, 1971
The proof of Jasnow and Fisher that no spontaneous ordering can occur in oneand twodimensional systems with continuous symmetry is shown to fail for nonlocal potentials of sufficiently long range. The occurrence of Bose-Einstein condensation for finite temperature (in the infinite-volume limit) is, therefore, not forbidden for such potentials. This result also follows from the postulate of the completeness of the noninteracting equilibrium states. Thus, the completeness postulate represents a weaker assumption on the nature of an interacting equilibrium state (or, equivalently, on the basic interactions between particles) than is usually found in the literature.
Creating a supersolid in one-dimensional Bose mixtures
Physical Review A, 2009
We identify a one-dimensional supersolid phase in a binary mixture of near-hardcore bosons with weak, local interspecies repulsion. We find realistic conditions under which such a phase, defined here as the coexistence of quasi-superfluidity and quasi-charge density wave order, can be produced and observed in finite ultra-cold atom systems in a harmonic trap. Our analysis is based on Luttinger liquid theory supported with numerical calculations using the time-evolving block decimation method. Clear experimental signatures of these two orders can be found, respectively, in time-of-flight interference patterns, and the structure factor S(k) derived from density correlations.
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.
Bose-Einstein condensation in real space
Arxiv preprint cond-mat/0304286, 2003
We illustrate how Bose-Einstein condensation occurs not only in momentum space but also in coordinate (or real) space. Analogies between the isotherms of a van der Waals gas of extended (or finite-diameter) identical atoms and the point (or zero-diameter) particles of an ideal Bose gas allow one to conclude that, in contrast to the van der Waals case, the volume per particle can go to zero in the pure Bose condensate phase precisely because the particle diameter is zero.
arXiv (Cornell University), 2007
In a one dimensional shallow optical lattice, in the presence of both cubic and quintic nonlinearity, a superfluid density wave, is identified in Bose-Einstein condensate. Interestingly, it ceases to exist, when only one of these interaction is operative. We predict the loss of superfluidity through a classical dynamical phase transition, where modulational instability leads to the loss of phase coherence. In certain parameter domain, the competition between lattice potential and the interactions, is shown to give rise to a stripe phase, where atoms are confined in finite domains. In pure two-body case, apart from the known superfluid and insulating phases, a density wave insulating phase is found to exist, possessing two frequency modulations commensurate with the lattice potential.