François Riggio | Searcharxiv

arXiv2024

Effects of atom losses on a one-dimensional lattice gas of hardcore bosons

Atom losses occur naturally during cold atoms experiments. Since this phenomenon is unavoidable, it is important to understand its effect on the remaining atoms. Here we study a gas of hard-core bosons on a lattice subject to $K$-body losses (where $K=1,2,3,\dots$ is the number of atoms lost in each loss event), and in particular we investigate the effect of losses on the rapidity distribution $ρ(k)$ of the atoms. Under the assumption that losses are weak enough so that the system relaxes between two loss events, we are able to determine the loss functional $F[ρ](k)$ encoding the loss process for $K$-body losses. We derive closed expressions for the cases of one- and two-body losses, and show their effects on the evolution of the total number of particles. Then we add a harmonic trapping potential and study the evolution of the position-dependent rapidity distribution of this system by solving numerically the evolution equation for one-, two- and three-body losses.

cond-mat.quant-gas↗

arXiv2022

Gradient corrections to the local density approximation in the one-dimensional Bose gas

The local density approximation (LDA) is the central technical tool in the modeling of quantum gases in trapping potentials. It consists in treating the gas as an assembly of independent mesoscopic fluid cells at equilibrium with a local chemical potential, and it is justified when the correlation length is larger than the size of the cells. The LDA is often regarded as a crude approximation, particularly in the ground state of the one-dimensional (1D) Bose gas, { where the correlation length is "therefore said to be" infinite (in the sense that correlation functions decay as a power law).} Here we take another look at the LDA. The local density $ρ(x)$ is viewed as a functional of the trapping potential $V(x)$, to which one applies a gradient expansion. The zeroth order in that expansion is the LDA. The first-order correction in the gradient expansion vanishes due to reflection symmetry. At second order, there are two corrections proportional to $d^2V/dx^2$ and $(dV/dx)^2$, and we propose a method to determine the corresponding coefficients by a perturbative calculation in the Lieb-Liniger model. This leads to an expression for the coefficients in terms of matrix elements of the density operator, which can in principle be evaluated numerically for an arbitrary coupling constant; here we show how to efficiently evaluate the coefficient associated to the curvature of the potential $d^2V/dx^2$, which dominates the deviation to LDA near local minima or maxima of the trapping potential. Both coefficients are evaluated analytically in the limits of infinite repulsion (hard-core bosons) and small repulsion (quasi-condensate).} The corrected LDA density profiles are compared to DMRG calculations, with significant improvement compared to zeroth-order LDA.

cond-mat.quant-gas↗