Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems

Abstract

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as “fermionization” and “superbunching”, can equivalently occur with attractive or repulsive interactions.

Localisation of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects

“…Beyond ultracold atoms, systems of ions 92 , superconducting devices (Circuit-QED) 93 , polariton systems 94,95 and the addition of high-Q cavities 96 offer opportunities to test our findings analogously via quantum simulation 97,98 . Moreover, the interplay of these effects in lattices with dissipation offer another venue of exploration 99,100 or measurement induced dynamics 101 . The findings of our work can aid in the development and characterise of transport properties in two dimensional systems for the development of new analog quantum technologies 102,103 .…”

Nonequilibrium photonic transport and phase transition in an array of optical cavities

“…In what follows, the coupling constant J will be used as an unit for all other model parameters, and will be assumed positive throughout. Very recently [27] it has been shown that the physics of driven-dissipative Bose-Hubbard model remains invariant under change of signs of the system parameters. Positive values of U are characteristic of the optical Kerr effect in resonant cavities, as discussed in [28].…”

Constructing k-local parent Lindbladians for matrix product density operators

“…These methods have been successfully used for the numerical investigation of various physical systems (see e.g. [58][59][60][61][62][63][64][65][66]). See e.g.…”