Tan's contact in a cigar-shaped dilute Bose gas

Decamp, Jean; Albert, Mathias; Vignolo, Patrizia

doi:10.1103/physreva.97.033611

Cited by 11 publications

(11 citation statements)

References 31 publications

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“…18,19 and references therein). Its generalization to low-dimensional gases has also been widely discussed 13,[20][21][22][23][24][25][26][27][28] . For the Bose gas case of interest here, experimental determinations of two-and three-body contacts are much more scarce, and concentrated so far on either the quasi-pure BEC regime 29,30 or the thermal one 29,31 .…”

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confidence: 99%

Tan’s two-body contact across the superfluid transition of a planar Bose gas

et al. 2021

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Tan’s contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e., the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings.

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confidence: 99%

Tan’s two-body contact across the superfluid transition of a planar Bose gas

et al. 2021

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“…As a consequence the 2D and the 1D contacts are linked via a geometric factor √ π and the harmonic oscillator length of the strongly confined direction. Note that the three-dimensional contact is also related to the lower dimensional ones through specific geometric factors and the oscillator lengths in the tightly confined directions [15,29,30]. In what follows, we shall explore D(α, E) rescaled by the factor 1/l y (or √ α in harmonic oscillator units) in order to expose the connection between the contacts in 1D and 2D, and subsequently showcase the saturation of the D 2D for large values of α towards the value of the 1D contact.…”

Section: Tan Contactsmentioning

confidence: 99%

“…Corrections to the mean energy of weakly interacting Bose gases, have also been reported in box potentials, at the crossover from three to lower dimensions for contact [27] as well as dipolar interactions [28]. Moreover, it has been showcased that the two-body Tan contact in three-dimensions (3D) and in 2D, 1D are proportional by factors depending on the dimension [15,29,30]. Additionally, next-to-leading order terms of the two-body momentum distribution for large momenta have been calculated and found to depend on three-body physics and the spatial dimension [31].…”

Section: Introductionmentioning

confidence: 99%

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

Bougas,

Mistakidis,

Alshalan

et al. 2020

Preprint

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We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two and the one dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wavefunction, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions while for fixed anisotropy quenches towards the non-interacting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher-lying excited states.

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“…In such strong-coupling regimes, universal relations exist among microscopic and thermodynamic quantities, which are connected by a set of key parameters called the contacts. First derived by Tan for a three-dimensional Fermi gas near an s-wave Feshbach resonance (FR) [1][2][3], contacts and the corresponding universal relations have been experimentally confirmed [4][5][6] and have been generalized to various situations such as quantum gases in low dimensions [7][8][9][10][11][12][13][14][15][16][17], systems with higher or mixed partial-wave scatterings [18][19][20][21][22][23][24][25], bosonic gases [26][27][28][29][30][31], and Fermi gases under synthetic gauge field [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance

Qin

Jie

et al. 2018

Phys. Rev. A

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In a recent proposal [Jie and Zhang, Phys. Rev. A 95, 060701(R) (2017)], it has been shown that center-of-mass-momentum-dependent two-body interactions can be generated and tuned by Raman coupling the closed-channel bound states in a magnetic Feshbach resonance. Here we investigate the universal relations in a three-dimensional Fermi gas near such a laser modulated s-wave Feshbach resonance. Using the operator-product expansion approach, we find that, to fully describe the high-momentum tail of the density distribution up to q −6 (q is the relative momentum), four center-of-mass-momentum-dependent parameters are required, which we identify as contacts. These contacts appear in various universal relations connecting microscopic and thermodynamic properties. One contact is related to the variation of energy with respect to the inverse scattering length and determines the leading q −4 tail of the high-momentum distribution. Another vector contact appears in the subleading q −5 tail, which is related to the velocity of closed-channel molecules. The other two contacts emerge in the q −6 tail and are respectively related to the variation of energy with respect to the range parameter and to the kinetic energy of closed-channel molecules. Particularly, we find that the q −5 tail and part of the q −6 tail of the momentum distribution show anisotropic features. We derive the universal relations and, as a concrete example, estimate the contacts for the zero-temperature superfluid ground state of the system using a mean-field approach. arXiv:1801.07448v5 [cond-mat.quant-gas]

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Tan's contact in a cigar-shaped dilute Bose gas

Cited by 11 publications

References 31 publications

Tan’s two-body contact across the superfluid transition of a planar Bose gas

Tan’s two-body contact across the superfluid transition of a planar Bose gas

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance

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