Dynamics of the Bose-Hubbard Model Induced by On-Site or Long-Range Two-Body Losses

TL;DR

This paper investigates how two-body losses, both on-site and long-range, affect the dissipative dynamics of the Bose-Hubbard model in one and two dimensions, revealing algebraic decay behaviors and dimensional differences.

Contribution

It provides a theoretical analysis of dissipative Bose-Hubbard dynamics with two-body losses, comparing analytical and numerical methods across different lattice geometries.

Findings

Intermediate-time density decay follows an interaction-dependent power law in 1D.

Long-range losses preserve algebraic decay, unlike on-site losses in 2D.

Results align well with tensor network simulations in 1D.

Abstract

We present a theoretical study of the dissipative dynamics of the Bose-Hubbard model induced by on-site or long-range two-body losses. We first consider the one-dimensional chain and the two-dimensional square lattice, and study the dynamics induced by the sudden switch-on of two-body losses on a weakly-interacting superfluid state. The time-dependent density is obtained in the spirit of the Bogolyubov approach by calculating theoretically the equations of motion associated to the relevant quadratic bosonic correlators. In the one-dimensional case, our results compare very well with quasi-exact numerical calculations based on the quantum jump method implemented using tensor networks. We find that the intermediate-time dynamics of the density displays an algebraic decay characterized by an interaction-dependent power-law exponent. The latter property still holds for long-range two-body loss processes but it is absent in the two-dimensional square lattice with on-site losses.