Low-dimensional trapped gases

Petrov, D. S.; Gangardt, D. M.; Shlyapnikov, G. V.

doi:10.1051/jp4:2004116001

Cited by 230 publications

(375 citation statements)

References 76 publications

(186 reference statements)

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“…However, the total density at the transition, n BKT , is not universal and depends on the strength of the interactions [1]. Interactions in a weakly interacting Bose gas trapped in a quasi-2D geometry (trap with tight confinement, at large frequency ω 0 , along one axis) are described by a dimensionless coupling constantg = √ 8πa/l 0 [14], where a is the 3D scattering length and l 0 = /M ω 0 the extent of the ground state along the tight direction. In the limit of weak interactions (ln(1/g) < 1), n BKT λ 2 ≈ ln(C/g) [15,16].…”

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“…For this phase, one expects a power law decay of the coherence mainly due to long wavelength phonons. The typical distance at which the coherence decreases by a factor of 2 is given by l = 2 1/α / √g n [14], where α is the coefficient of the power law decay whose value is 1/4 at the BKT transition. We calculate l ≈ 40 µm for our typical parameters at the BKT transition.…”

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Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

et al. 2009

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We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz and Thouless (BKT) transition temperature. By measuring the density profile, in situ and after time of flight, and the coherence length, we identify different states of the gas. In particular, we observe that the gas develops a bimodal distribution without long range order. In this state, the gas presents a longer coherence length than the thermal cloud; it is quasi-condensed but is not superfluid. Experimental evidence indicates that we observe the superfluid transition (BKT transition).PACS numbers: 03.75. Lm, 64.70.Tg One of the most fascinating aspects of a Bose gas in the degenerate regime is the role of dimensionality. A 2D interacting Bose gas is superfluid at low enough temperature [1,2]. However, by contrast to the 3D case, there is no long range coherence and the coherence decays as a power law [1,2]. At temperatures above the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, the gas is not superfluid. Due to proliferation of free vortices, the quasi-condensate (QC) is fractured into small regions of nearly uniform phase, whose size, which corresponds to the typical length of the exponential decay of the coherence, is larger than the thermal de Broglie wavelength (λ = 2π 2 /M k B T , where T is the temperature and M the atomic mass). For higher T, this size becomes smaller and approaches λ, as the gas crosses over to the thermal phase.Experiments on 2D bosonic systems, such as twodimensional 4 He films [3] and trapped Bose gases [4,5], are able to show signatures of the BKT transition. Other systems, such as the superconducting transition in arrays of Josephson junctions [6] and a two dimensional lattice of (3D) Bose-Einstein condensates [7], also exhibit a similar transition. Another interesting observation was in two dimensional spin polarized atomic hydrogen on liquid 4 He [8] where a reduction in three-body dipolar recombination (which is usually associated with condensation) was observed well above the BKT transition temperature. This observation results from a reduction of density fluctuations, which corresponds to quasi-condensation [9] [10].In this letter, we present evidence of transitions in a quasi-2D Bose gas from thermal (normal gas), to quasicondensate without superfluidity, to superfluid quasicondensate (BKT transition). We explicitly identify the theoretically expected non-superfluid quasi-condensate, a feature not clearly seen in other experiments on a 2D trapped Bose gases [4,5]. We use an interferometric method to study the coherence of the gas down to distances smaller than the thermal de Broglie wavelength. Our results can be understood using the local density approximation (LDA) on a model [11] of a homogeneous system. More recently, calculations for a trapped system have been carried out using classical-quantum field methods [12] and quantum Monte Carlo methods [13].The BKT transition occurs at a universal value of the superfluid density n s = 4/λ 2 . However, the ...

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Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

et al. 2009

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“…At the CIR a Tonks gas with additional DDI would lead to a super-Tonks gas, with Luttinger parameter K < 1 [26]. For small values of |g 1D |, and although strictly condensation is prevented in 1D, a finite-size system at a sufficiently low temperature allows for a quasi-condensate [27]. This quasi-1D dipolar BEC may present a remarkable physics, as it becomes clear from an analysis of the dispersion law E(k) for axial excitations of momentum k on top of an homogeneous quasi-1D BEC:…”

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Cold Dipolar Gases in Quasi-One-Dimensional Geometries

2007

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We analyze the physics of cold dipolar gases in quasi one-dimensional geometries, showing that the confinement-induced scattering resonances produced by the transversal trapping are crucially affected by the dipole-dipole interaction. As a consequence, the dipolar interaction may drastically change the properties of quasi-1D dipolar condensates, even for situations in which the dipolar interaction would be completely overwhelmed by the short-range interactions in a 3D environment.Low-dimensional ultra cold gases have recently attracted a major attention. One and two-dimensional gases are created in sufficiently strong optical lattices [1], or by means of magnetic wires [2]. Low-dimensionality leads to a very rich physics, highlighted by the recently observed Berezinskii-Kosterlitz-Thouless transition in 2D gases [3], the enhanced role of thermal and quantum phase fluctuations in elongated gases [4], and the realization of the Tonks-Girardeau regime of 1D bosons [5].The properties of quantum gases are crucially determined by the interparticle interactions. Current experiments typically involve particles at very low energies interacting via a short-range isotropic potential characterized by an s-wave scattering length a. The latter may be modified by means of scattering resonances induced by magnetic fields (Feshbach resonance) or by properly detuned lasers [6]. Interestingly, the scattering properties in quasi-1D (also in 2D [7]) may be crucially affected by the contrained geometry. In particular the transversal confinement can induce a novel resonance known as confinement-induced resonance (CIR) [8] To a very good approximation the combined effects of the short-range interactions and the DDI can be understood by means of a pseudopotential theory, which includes a contact interaction, characterized by a scattering length a, and the DDI itself [13,20]. However, the correct value of a is in general not that in absence of DDI, but the result of the scattering problem including both the short-range and the DDI potentials. Hence the DDI may affect the value of a, even very severely in the vicinity of the so-called shape resonances [13,20,21]. In addition, the combination of the DDI and the dressing of rotational excitations with static and microwave fields may allow for the engineering of novel types of interaction potentials for polar molecules in 2D geometries [22].In this Letter, we analyze the scattering properties of dipolar gases in quasi-1D geometries. By solving the corresponding scattering problem, including the short-range interaction, the DDI, and the trap potential, we obtain an effective 1D pseudopotential consisting of a contact interaction with an effective 1D coupling constant and a regularized dipolar potential. Similar as for the case without DDI we observe the appearance of a CIR, however the position of the CIR is crucially modified by the DDI. In particular, even for large values of a for which in a 3D environment the short-range interaction fully dominates the DDI, the latter can dramatically mod...

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“…2. The statistical properties of the polariton gas are then governed by its dimensionality (see, e.g., [19]). In particular, in the case of resonance coupling the low branch polariton mass can be found from (21):…”

Section: Quantum Degeneracy Of a 1d Polariton Gasmentioning

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Excitation of coherent polaritons in a two-dimensional atomic lattice

Barinov¹,

Alodjants²,

Аракелян³

2009

Quantum Electron.

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We describe a new type of spatially periodic structure (lattice models): a polaritonic crystal (PolC) formed by a two-dimensional lattice of trapped two-level atoms interacting with quantised electromagnetic field in a cavity (or in a one-dimensional array of tunnelling-coupled microcavities), which allows polaritons to be fully localised. Using a one-dimensional polaritonic crystal as an example, we analyse conditions for quantum degeneracy of a low-branch polariton gas and those for quantum optical information recording and storage.

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Low-dimensional trapped gases

Cited by 230 publications

References 76 publications

Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

Cold Dipolar Gases in Quasi-One-Dimensional Geometries

Excitation of coherent polaritons in a two-dimensional atomic lattice

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