Tan's contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions
1 Université Grenoble-Alpes, LPMMC, F-38000 Grenoble, France and CNRS, LPMMC, 38000 Grenoble, France
2 Université Côte d'Azur, CNRS, Institut Non Linéaire de Nice, 1361 route des Lucioles, 06560 Valbonne, France
a e-mail: email@example.com
Received: 25 October 2016
Revised: 27 December 2016
Published online: 25 May 2017
We study Tan's contact, i.e. the coefficient of the high-momentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion. Our results are relevant for ongoing experiments with ultracold atomic gases.
© The Author(s) 2017
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