Losses are always present in cold atoms experiments. However in presence of correlations between atoms, evaluating their effect is a difficult theoretical problem which is largely unexplored. This is illustrated by our recent work on the effect of losses on a gas with contact interactions: if one makes the usual assumption that the environment involved in the loss process has a vanishing correlation time, which is the assumption that leads to the famous Lindblad equation used so far to describe losses in the context of cold atoms, then we show that the energy increase rate in the gas diverges in dimensions larger than 1. The description of losses requires either taking into account the finite correlation time of the reservoir, or taking into account the finite interaction range between atoms.
In dimension 1, such a divergence is absent and for short enough correlation time of the reservoir, losses are well described by the Lindblad equation, even in the presence of contact interactions. We have investigated the effect of losses in the Lieb-Liniger model of 1D bosons with contact interaction. We assume slow losses so that the gas has time to relax at any time. In contrast to chaotic systems which relax towards a thermal state parameterized by 2 quantities, the particle density and the energy density, the local properties of the Lieb-Liniger model after relaxation are parameterized by a whole function, the rapidity distribution. We have computed the evolution of the rapidity distribution in presence losses, thus characterizing entirely the effect of slow losses. We observe that losses bring the system to a non-thermal state, and we show that a manifestation of the non-thermal nature of the state is the breakdown of the popular Tan's relation.
In the particular case when the gas lies into the quasi-condensate regime, the effect of losses can be computed within the Bogoliubov framework. Experimentally, our measurements, which concern long wave-length collective modes, are in agreement with those theoretical predictions.