Tan’s contact for one-dimensional Fermi gases

Talk

A universal decay power-law of the large-momentum tails of the momentum distribution, fixed by Tan’s contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. We derive the Tan’s contact of one-dimensional harmonically trapped gases, both in the case of a multicomponent Fermi gas and of a Bose gas. In the case of a multicomponent mixture, we find a direct correspondence between the value of the Tan’s contact and the symmetry of the state. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous gas is in excellent agreement with the results for the harmonically confined gas and predicts a scaling behavior of the Tan’s contact. This provides useful analytical expressions for the dependence on the number of particles, number of components and on interaction strength.

Back to list