Exact solutions of boundary driven dissipative quantum spin chains with disorder

Nonequilibrium steady states (NESS) of driven-dissipative quantum spin chains have unique and often surprising properties arising from the interplay of lattice dynamics, driving, and dissipation. Exact solutions are especially valuable to understanding this interplay and the resulting NESS. Here, we derive an exact solution for the steady state of an XX-coupled N-qubit spin chain, with possibly non-uniform couplings, that is subject to a boundary Rabi drive and boundary loss on one end [1]. This model maps to an interacting fermionic model and is thus not amenable to standard techniques to solve for its NESS; however, the model is solvable by exploiting a “hidden” time reversal symmetry in the dissipative dynamics, which allows the model to be solved by creating a doubled version of the system that relaxes into a pure steady state [2]. The model is solvable for a wide range of parameters, including arbitrary non-uniform XX couplings. We show that the non-equilibrium steady state exhibits surprising correlation effects, including an emergent real-space pairing of hole excitations that arises from dynamically constrained hopping. Furthermore, the doubled system is itself is a nontrivial, physically realizable spin chain model whose pure steady state is highly entangled between the two chains. Thus, it provides a means for stabilizing remote multi-qubit entanglement without the use of squeezed light. We outline how this system could be experimentally implemented in e.g., circuit QED or trapped ions. Finally, we discuss extensions of this model.

[1] A. Lingenfelter, et al, arXiv:2307.09482

[2] D. Roberts, et al, PRX Quantum (2021)