https://hal-iogs.archives-ouvertes.fr/hal-03318184Bouchoule, I.I.BouchouleLaboratoire Charles Fabry / Gaz Quantiques - LCF - Laboratoire Charles Fabry - IOGS - Institut d'Optique Graduate School - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueDubail, J.J.DubailLPCT - Laboratoire de Physique et Chimie Théoriques - INC - Institut de Chimie du CNRS - UL - Université de Lorraine - CNRS - Centre National de la Recherche ScientifiqueBreakdown of Tan’s Relation in Lossy One-Dimensional Bose GasesHAL CCSD2021Quantum InformationGeneral PhysicsStatistical and Quantum Mechanics[PHYS.COND.GAS] Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas][PHYS.PHYS.PHYS-GEN-PH] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]Bouchoule, Isabelle2021-08-09 14:36:432023-03-24 14:53:222021-08-09 14:57:21enJournal articleshttps://hal-iogs.archives-ouvertes.fr/hal-03318184/document10.1103/PhysRevLett.126.160603application/pdf1In quantum gases with contact repulsion, the distribution of momenta of the atoms typically decays as ∼ 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.