Monte Carlo study of few-bosons in a one-dimensional trap

Abstract

We consider a one-dimensional system of few-bosons in a harmonic trap that interact via a contact potential. In addition, we explore a system of non-interacting bosons in the presence of an impurity. The Variational Monte Carlo method is utilised to calculate an upper bound of the ground state energy. Furthermore, we numerically obtain the one-body density matrix, which allows us to determine the occupation numbers and the impurity density profile. The occupation numbers reveal that, in the absence of any impurity, the condensation diminishes as the repulsive interaction strength among bosons increases. Finally, in the presence of an impurity, we show the existence of two distinct regimes: a miscible regime and a non-miscible one.