The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

Abstract

We theoretically investigate the effect of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of KK-body losses (K=1,2,3,\dotsK=1,2,3,…) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion – where the gas behaves like an ideal Bose gas – and hard-core repulsion – where the gas is mapped to a non-interacting Fermi gas –, we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.

Relaxation of bosons in one dimension and the onset of dimensional crossover

“…In a first step, we have recently extended the applicability of GHD to the dimensional crossover regime [44] and tested it with the data at short to intermediate time scales. But still, many open questions remain, such as for example the many-body dephasing induced by non-trivial interactions [27], or the effect of atom losses [71]. We hope our investigations presented here will pave the way towards a more comprehensive understanding of the non-equilibrium quantum physics in the dimensional crossover regime and the influence of the effectively compactified dimensions.…”

Unbounded entanglement production via a dissipative impurity

“…Perturbative field-theoretical approaches are also available [17]. A promising direction is to extend the hydrodynamic framework to integrable systems subjected to dissipation [14,[18][19][20][21]. This is motivated by the tremendous success of Generalized Hydrodynamics (GHD) for integrable systems [22,23].…”

The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

“…From the theoretical viewpoint, a first important step in the description of the stronglycorrelated and lossy Bose gas has been presented in Refs. [34,35], focusing primarily on the limit of weak losses (the case of strong interactions and fermionisation is discussed only for one-body losses). Here, instead, we are interested in the case of strong two-body losses, and our goal is to characterise the simplest experimental observable, namely the dynamics of the total number of particles composing the gas.…”