Mapping repulsive to attractive interaction in driven–dissipative quantum systems

Abstract

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven–dissipative quantum systems. For the example of a photonic Bose–Hubbard dimer, we establish a one-to-one mapping relating cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with a time-reversal-invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and those in a non-frustrated partner lattice.

Keywords

• driven–dissipative photonic systems
• nonequilibrium many-body physics
• Bose–Hubbard dimer
• time-reversal symmetry