Critical temperature of a Bose gas in an optical lattice

Baillie, D.; Blakie, P. B.

doi:10.1103/physreva.80.031603

Cited by 17 publications

(24 citation statements)

References 23 publications

(36 reference statements)

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“…Previous approximate theoretical studies addressed the onset of superfluidity in weak unidirectional optical lattices [39], and the meanfield suppression of T c in combined harmonic plus opticallattice potentials [40]. The determination of T c in extended systems is a highly nonperturbative problem that can be rigorously solved only using unbiased quantum many-body techniques such as the PIMC method employed in this work.…”

Section: Fig 1 (Color Onlinementioning

confidence: 99%

Critical Temperature of Interacting Bose Gases in Periodic Potentials

et al. 2014

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The superfluid transition of a repulsive Bose gas in the presence of a sinusoidal potential which represents a simple-cubic optical lattice is investigated 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. The combined effect of interparticle interactions and external potentials plays a fundamental role in determining the quantum-coherence properties of several many-body systems, including He in Vycor or on substrates, paired electrons in superconductors and in Josephson junction arrays, neutrons in the crust of neutron stars [1], and ultracold atoms in optical potentials. However, even the (apparently) simple problem of calculating the superfluid transition temperature T c of a dilute homogeneous Bose gas has challenged theoreticians for decades [2]. Many techniques have been employed, obtaining contradicting results, differing even in the functional dependence of T c on the interaction parameter (the two-body scattering length a) and in the sign of the shift with respect to the ideal gas transition temperature T 0 c (for a review see Ref.[3]). In the weakly interacting limit, the shift of the critical temperature 4,5], where n is the density and the coefficient c ¼ 1.29ð5Þ was determined using Monte Carlo simulations of a classical-field model defined on a discrete lattice [6,7]. Continuous-space quantum Monte Carlo simulations of Bose gases with short-range repulsive interactions have shown that this linear form is valid only in the regime n 1=3 a ≲ 0.01, while at stronger interaction T c reaches a maximum where ΔT c =T 0 c ≃ 6.5% and then decreases for n 1=3 a ≳ 0.2 [8]. This suppression of T c occurs in a regime where universality in terms of the scattering length is lost and other details of the interaction potential become relevant [8][9][10]. In recent years ultracold atomic gases have emerged as the ideal experimental test bed for many-body theories [11]. However, the direct measurement of interactions effects on T c has been hindered by the presence of the harmonic trap. In the presence of confinement the main interactions effect can be predicted by mean-field theory and is due to the broadening of the density profile [12], leading to a suppression of T c . Deviations from the mean-field prediction and effects due to critical correlations have been measured in Refs. [13,14]. A major breakthrough has been achieved recently with the realization of Bose-Einstein condensation in quasiuniform trapping potentials [15]. This setup allows a more ...

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Section: Fig 1 (Color Onlinementioning

confidence: 99%

Critical Temperature of Interacting Bose Gases in Periodic Potentials

et al. 2014

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“…Although this is the current trend in the field, experimental and theoretical studies on non-interacting many-body systems [10,14] are still being considered due to the possibility of tuning off the strength of interactions between particles in experimental situations.…”

Section: Introductionmentioning

confidence: 99%

“…These systems with planar symmetry have been described in [8,9] and several periodic potentials have been used such as the sinusoidal [10] and the biparabolic [11] with good results only in the low particle energy limit, or in the tight-binding approximation [12]. However, to analyze structural effects like particle trapping between the planes or quasi-2D behavior when plane separation is of the order of half the thermal wavelength, it is necessary to consider a much wider temperature region in which a large number of energy bands needs to be included in the calculation of the system thermodynamic properties.…”

Section: Introductionmentioning

confidence: 99%

Dimensional crossover of a boson gas in multilayers

et al. 2010

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We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability P 0 between layers. The BEC critical temperature Tc coincides with the ideal gas BEC critical temperature T0 when P = 0 and rapidly goes to zero as P increases to infinity for any finite interlayer separation. The specific heat CV vs T for finite P and plane separation a exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than Tc which highlights the effects due to particle confinement. Then we discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of P . For T < Tc the crossover is revealed by the change in the slope of log CV (T ) and when T > Tc, it is evidenced by a broad minimum in CV (T ).

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“…The requirements of this type of loading can be understood from the entropy considerations [16,20]. For the rotating condensate in an optical lattice, the normalized entropy per particle is given by [29] …”

Section: Entropy Of the Systemmentioning

confidence: 99%

“…A good semiclassical approximate [22,23,24,25,26] is provided. The advantage of the semiclassical approach lies in its simplicity, in comparison to the quantum-mechanical calculations (Bose Hubbard model) [27,28], and its generality allows the treatment of the finite temperature regime [29,30]. Our approach can be summarized as follow: a conventional method of quantum mechanics is used to calculate the localized spectrum of this system [31,32,33,34], in which the classical analogy approach first used by Fetter [35] is employed.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic loading of rotating bosons into 1D optical lattice

Soliman¹,

Elsharkawy²

2015

Turk J Phys

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Abstract:In this paper, the entropy-temperature curves are investigated for rotating boson gases in a 1D optical lattice with transverse harmonic confinement. Regimes at which the atomic sample can be significantly heated or cooled by adiabatically changing the lattice depth and the rotation rate are demonstrated. The suggested approach, which is the semiclassical approximation, includes the correction due to the finite size effect. The obtained results show that the entropy-temperature curves have a monotonically increasing nature for this system, in agreement with the standard thermodynamic arguments. For fixed temperature, entropy always increases with the increasing of the rotation rate or optical potential depth.

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Critical temperature of a Bose gas in an optical lattice

Cited by 17 publications

References 23 publications

Critical Temperature of Interacting Bose Gases in Periodic Potentials

Critical Temperature of Interacting Bose Gases in Periodic Potentials

Dimensional crossover of a boson gas in multilayers

Adiabatic loading of rotating bosons into 1D optical lattice

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