Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings

Abstract

Dissipative preparation of a pure steady state usually involves a commutative action of a coherent and a dissipative dynamics on the target state. Namely, the target pure state is an eigenstate of both the coherent and dissipative parts of the dynamics. We show that working in the Zeno regime, i.e. for infinitely large dissipative coupling, one can generate a pure state by a non commutative action, in the above sense, of the coherent and dissipative dynamics. A corresponding Zeno regime pureness criterion is derived. We illustrate the approach, looking at both its theoretical and applicative aspects, in the example case of an open $XXZ$ spin-$1/2$ chain, driven out of equilibrium by boundary reservoirs targeting different spin orientations. Using our criterion, we find two families of pure nonequilibrium steady states, in the Zeno regime, and calculate the dissipative strengths effectively needed to generate steady states which are almost indistinguishable from the target pure states.

8 pages, 6 figures

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• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Winding up quantum spin helices: How avoided level crossings exile classical topological protection
• Targeting pure quantum states by strong noncommutative dissipation
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• Boundary driven $XYZ$ chain: Exact inhomogeneous triangular matrix product ansatz
• Dissipative generation of pure steady states and a gambler's ruin problem
• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Transition between dissipatively stabilized helical states
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation
• Switching pure states of the dissipative Heisenberg XXZ chain by local magnetic fields