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

Contact and universal thermodynamic relations provide physicists a unique and powerful tool to bridge few- and many-body physics in dilute quantum systems and have been extensively studied in different dimensions separately in the past decade. In quasi-one- or quasi-two-dimensional traps with strong transverse confinements, quantum gases behave as strictly one- or two-dimensional systems at large length scales, while the two-body scattering intrinsically has three-dimensional characteristics at short distance such that an exact description of any universal thermodynamic relation requires three-dimensional contacts. 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. In this talk, I will show an exact relation between the three- and low-dimensional contacts in these highly anisotropic traps. Such relation allows one to directly connect physical quantities at different length or momentum scales, and to characterize the quasi-one- or quasi-two-dimensional traps using universal thermodynamic relations that were derived for strict one or two dimensions.