Interatomic collisions in a tightly confined Bose gas

Петров, Д. С.; Shlyapnikov, G. V.

doi:10.1103/physreva.64.012706

Cited by 440 publications

(606 citation statements)

References 29 publications

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“…This result was first obtained by Petrov et al [15,16] by considering the 2D scattering problem. We will present a detailed study of interactions in the 2D Bose condensed system elsewhere [17].…”

Section: Formalism a Mean-field Theory And Hfb-popov Equationssupporting

confidence: 62%

Coherence properties of the two-dimensional Bose-Einstein condensate

Gies

Hutchinson

2004

Phys. Rev. A

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We present a detailed finite-temperature Hartree-Fock-Bogoliubov (HFB) treatment of the twodimensional trapped Bose gas. We highlight the numerical methods required to obtain solutions to the HFB equations within the Popov approximation, the derivation of which we outline. This method has previously been applied successfully to the three-dimensional case and we focus on the unique features of the system which are due to its reduced dimensionality. These can be found in the spectrum of low-lying excitations and in the coherence properties. We calculate the Bragg response and the coherence length within the condensate in analogy with experiments performed in the quasione-dimensional regime [Richard et al., Phys. Rev. Lett. 91, 010405 (2003)] and compare to results calculated for the one-dimensional case. We then make predictions for the experimental observation of the quasicondensate phase via Bragg spectroscopy in the quasi-two-dimensional regime.

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Section: Formalism a Mean-field Theory And Hfb-popov Equationssupporting

confidence: 62%

Coherence properties of the two-dimensional Bose-Einstein condensate

Gies

Hutchinson

2004

Phys. Rev. A

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“…A direct generalization of Olshanii's theory to anisotropic transverse confinement shows that there is only one harmonic CIR (HCIR) resonance, no matter how large the transverse anisotropy [19]. For large anisotropy, this theory crosses over smoothly to the case of a quasi-2D trap, where a single HCIR occurs with a negative S-wave scattering length, a 3D < 0 [20][21][22].…”

Section: Introductionmentioning

confidence: 98%

Confinement-induced resonances in anharmonic waveguides

Peng

Liu

et al. 2011

Phys. Rev. A

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We develop the theory of anharmonic confinement-induced resonances (ACIR). These are caused by anharmonic excitation of the transverse motion of the center of mass (COM) of two bound atoms in a waveguide. As the transverse confinement becomes anisotropic, we find that the COM resonant solutions split for a quasi-1D system, in agreement with recent experiments. This is not found in harmonic confinement theories. A new resonance appears for repulsive couplings (a3D > 0) for a quasi-2D system, which is also not seen with harmonic confinement. After inclusion of anharmonic energy corrections within perturbation theory, we find that these ACIR resonances agree extremely well with anomalous 1D and 2D confinement induced resonance positions observed in recent experiments. Multiple even and odd order transverse ACIR resonances are identified in experimental data, including up to N = 4 transverse COM quantum numbers.

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“…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].…”

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confidence: 99%

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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Interatomic collisions in a tightly confined Bose gas

Cited by 440 publications

References 29 publications

Coherence properties of the two-dimensional Bose-Einstein condensate

Coherence properties of the two-dimensional Bose-Einstein condensate

Confinement-induced resonances in anharmonic waveguides

Cold Dipolar Gases in Quasi-One-Dimensional Geometries

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