Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions

Abstract

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.

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• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Universal Tan relations for quantum gases in one dimension
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Tan's contact in a cigar-shaped dilute Bose gas
• Tan's contact as an indicator of completeness and self-consistency of a theory
• High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance
• Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential
• Symmetries and Correlations in Strongly Interacting One-dimensional Quantum Gases
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter