Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature

Hepeng Yao (1) , David Clément (2) , Anna Minguzzi (3) , Patrizia Vignolo (4) , Laurent Sanchez-Palencia (1)

1 CPHT - Centre de Physique Théorique [Palaiseau]
2 Laboratoire Charles Fabry / Optique atomique
3 LPM2C - Laboratoire de physique et modélisation des milieux condensés
4 INLN - Institut Non Linéaire de Nice Sophia-Antipolis

The universal Tan relations connect a variety of microscopic features of many-body quantum systems with two-body contact interactions to a single quantity, called the contact. The latter has become pivotal in the description of quantum gases. We provide a complete characterization of the Tan contact of the harmonically trapped Lieb-Liniger gas for arbitrary interactions and temperature. Combining thermal Bethe ansatz, local-density approximation, and exact quantum Monte Carlo calculations, we show that the contact is a universal function of only two scaling parameters, and determine the scaling function. We find that the temperature dependence of the contact, or equivalently the interaction dependence of the entropy, displays a maximum. The presence of this maximum provides an unequivocal signature of the crossover to the fermionized regime and it is accessible in current experiments.

Domains: Quantum Gases [cond-mat.quant-gas]

Hepeng Yao, David Clément, Anna Minguzzi, Patrizia Vignolo, Laurent Sanchez-Palencia. Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature. Physical Review Letters, 2018, 121 (220402), ⟨10.1103/PhysRevLett.121.220402⟩. ⟨hal-01763698v2⟩