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arXiv:2502.09008

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

Julien Despres, Leonardo Mazza, Marco Schirò

Published Feb 13, 2025• 0 citations
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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.

DOI
10.48550/arxiv.2502.09008

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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.
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We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a periodic chain and with spatially homogeneous one-body loss and pump within the Markovian approximation. The steady state is non-thermal and is formally equivalent to an infinite-temperature state with finite chemical potential set by the dissipative parameters. While there is no effect of interactions on the steady state, we observe a nontrivial behaviour of the space-time two-point correlation function, obtained by exact diagonalisation. In particular, we find that the decay width of the propagator is not only renormalised at increasing interactions, as it is the case of a single non-linear resonator, but also at increasing hopping strength. Furthermore, we numerically predict at large interactions a plateau value of the decay rate which goes beyond perturbative results in the interaction strength. We then compute the full spectral function, finding that it contains both a dispersive free-particle like dispersion at low energy and a doublon branch at energy corresponding to the on-site interactions. We compare with the corresponding calculation for the ground state of a closed quantum system and show that the driven-dissipative nature – determining both the steady state and the dynamical evolution – changes the low-lying part of the spectrum, where noticeably, the dispersion is quadratic instead of linear at small wavevectors. Finally, we compare to a high temperature grand-canonical equilibrium state and show the difference with respect to the open system stemming from the additional degree of freedom of the dissipation that allows one to vary the width of the dispersion lines.
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