Breakdown of Tan's relation in lossy one-dimensional Bose gases

TL;DR

This paper demonstrates that Tan's relation, linking momentum distribution tails to interaction parameters, breaks down in certain stationary states of the 1D Bose gas with contact repulsion, especially those induced by atom losses.

Contribution

It reveals the breakdown of Tan's relation in specific stationary states of the 1D Bose gas and explains how atom losses lead to these states with altered momentum distributions.

Findings

Tan's relation fails in certain stationary states of the 1D Bose gas.

Atom losses can induce states with modified rapidity distributions.

Exact calculations support the phenomena in both strong and weak interaction regimes.

Abstract

In quantum gases with contact repulsion, the distribution of momenta of the atoms typically decays as $\sim 1/|p|^4$ at large momentum $p$. Tan's relation connects the amplitude of that $1/|p|^4$ tail to the adiabatic derivative of the energy with respect to the gas' coupling constant or scattering length. Here it is shown that the relation breaks down in the one-dimensional Bose gas with contact repulsion, for a peculiar class of stationary states. These states exist thanks to the infinite number of conserved quantities in the system, and they are characterized by a rapidity distribution which itself decreases as $1/|p|^4$. In the momentum distribution, that rapidity tail adds to the usual Tan contact term. Remarkably, atom losses, which are ubiquitous in experiments, do produce such peculiar states. The development of the tail of the rapidity distribution originates from the ghost singularity of the wavefunction immediately after each loss event. This phenomenon is discussed for arbitrary interaction strengths, and it is supported by exact calculations in the two asymptotic regimes of infinite and weak repulsion.