$s$-wave Contacts of Quantum Gases in Quasi-one and Quasi-two Dimensions

Abstract

In quasi-one- or quasi-two-dimensional traps with strong transverse confinements, quantum gases behave like strictly one- or two-dimensional systems at large length scales. However, at short distance, the two-body scattering intrinsically has three-dimensional characteristics such that an exact description of any universal thermodynamic relation requires three-dimensional contacts, no matter how strong the confinement is. A fundamental question arises as to whether one- or two-dimensional contacts, which were originally defined for strictly one or two dimensions, are capable of describing quantum gases in quasi-one- or quasi-two-dimensional traps. Here, we point out an exact relation between the three- and low-dimensional contacts in these highly anisotropic traps. Such relation allows us to directly connect physical quantities at different length scales, and to characterise the quasi-one- or quasi-two-dimensional traps using universal thermodynamic relations that were derived for strict one or two dimensions.

References in corpus (16)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Thermodynamics of the BCS-BEC crossover
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• Universal properties of Fermi gases in arbitrary dimensions
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• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
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• Width of the confinement-induced resonance in a quasi-one-dimensional trap with transverse anisotropy

Cited by in corpus (7)

• 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
• P-wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps
• Dynamical excitation processes and correlations of three-body two-dimensional mixtures
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Toward precision Fermi liquid theory in two dimensions