Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

Delfino, Francesco; Vicari, Ettore

doi:10.1103/physreva.96.043623

Cited by 10 publications

(13 citation statements)

References 127 publications

(232 reference statements)

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“…[11][12][13] In this manuscript, we study layered systems with an O(2)-symmetric order parameter using a quasi-2D quantum O(2) model which can be seen as a quantum generalization of the Lawrence-Doniach model. 27,28 This model captures quantum fluctuations at low temperatures but describes otherwise qualitatively the same physics as the (classical) layered 3D XY model. Our approach is based on the nonperturbative renormalization-group approach (NPRG) and, contrary to most previous works, does not introduce vortices explicitly.…”

Section: Introductionmentioning

confidence: 94%

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

Rançon

Dupuis

2017

Phys. Rev. B

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We study the quasi-two-dimensional quantum O(2) model, a quantum generalization of the Lawrence-Doniach model, within the nonperturbative renormalization-group approach and propose a generic phase diagram for layered three-dimensional systems with an O(2)-symmetric order parameter. Below the transition temperature we identify a wide region of the phase diagram where the renormalization-group flow is quasi-two-dimensional for length scales smaller than a Josephson length lJ , leading to signatures of Kosterlitz-Thouless physics in the temperature dependence of physical observables. In particular the order parameter varies as a power law of the interplane coupling with an exponent which depends on the anomalous dimension (itself related to the stiffness) of the strictly two-dimensional low-temperature Kosterlitz-Thouless phase. arXiv:1710.01000v2 [cond-mat.stat-mech]

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Section: Introductionmentioning

confidence: 94%

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

Rançon

Dupuis

2017

Phys. Rev. B

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“…G(x, 0) = δ(x), (10) summing ( 9) over all times finally yields the steady-state Green's function (8). Evaluating the remaining Schwinger integral in equation ( 8) leads to a modified Bessel function of the second kind K 0 [27, (3.471.9)]:…”

Section: Elimination Of Temperature Differencementioning

confidence: 99%

Photon BEC with thermo-optic interaction at dimensional crossover

Stein

Pelster²

2022

New J. Phys.

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Since the advent of experiments with photon Bose-Einstein condensates in dye-filled microcavities in 2010, many investigations have focused upon the emerging effective photon-photon interaction. Despite its smallness, it can be identified to stem from two physically distinct mechanisms. On the one hand, a Kerr nonlinearity of the dye medium yields a photon-photon contact interaction. On the other hand, a heating of the dye medium leads to an additional thermo-optic interaction, which is both delayed and non-local. The latter turns out to represent the leading contribution to the effective interaction for the current 2D experiments. Here we analyse theoretically how the effective photon-photon interaction increases when the system dimension is reduced from 2D to 1D. To this end, we consider an anisotropic harmonic trapping potential and determine via a variational approach how the properties of the photon Bose-Einstein condensate in general, and both aforementioned interaction mechanisms in particular, change with increasing anisotropy. We find that the thermo-optic interaction strength increases at first linearly with the trap aspect ratio and lateron saturates at a certain value of the trap aspect ratio. Furthermore, in the strong 1D limit the roles of both interactions get reversed as the thermo-optic interaction remains saturated and the contact Kerr interaction becomes the leading interaction mechanism. Finally, we discuss how the predicted effects can be measured experimentally.

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“…for 1 ψ > 2, providing a relation between the quantities x ′ and σ ′ , which is necessary to evaluate the excess free energy via Eq. (24). Focusing now on the case 1 ψ ∈ (1, 2) we note that the last term on the RHS of Eq.…”

Section: Walls Perpendicular To Kmentioning

confidence: 97%

“…In the most standard setup, the dimensional crossover is realized by confining the system in one or more directions and manipulating the thermodynamic parameters so that the characteristic length scale becomes larger (or smaller) than the confining parameter [see e.g. [23][24][25][26][27], Here we analyze a natural alternative avenue, already outlined in Sec. II, where the dimensional crossover between distinct effective dimensionalities is tuned by manipulating the hopping parameters.…”

Section: Dimensional Crossovermentioning

confidence: 99%

Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices

Łebek,

Jakubczyk

2020

Preprint

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We consider the Bose gas on a d-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature T . We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this phenomenon. Subsequently we study the thermodynamic Casimir effect occurring in this system. We compute the exact profile of the scaling function for the Casimir energy. As an effect of strongly anisotropic scale invariance, the Casimir force below or at the critical temperature T c may be repulsive even for periodic boundary conditions. The corresponding Casimir amplitude is universal only in a restricted sense, and the power law governing the decay of the Casimir interaction becomes modified. We also demonstrate that, under certain circumstances, the scaling function is constant for sufficiently large values of the scaling variable, and in consequence is not an analytical function. At T > T c the Casimir-like interactions reflect the structure of the correlation function, and, for certain orientations of the confining walls, show exponentially damped oscillatory behavior so that the corresponding force is attractive or repulsive depending on the distance.

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Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

Cited by 10 publications

References 127 publications

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

Photon BEC with thermo-optic interaction at dimensional crossover

Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices

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