Dissipative generation of pure steady states and a gambler's ruin problem

Abstract

We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open XXZ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.

arXiv comment7 pages

References in corpus (23)

• Repulsively bound atom pairs in an optical lattice
• Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
• Topology by dissipation
• Quantum Zeno effect by general measurements
• Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
• Experimental realization of quantum zeno dynamics
• Continuous and Pulsed Quantum Zeno Effect
• Quantum Control by Imaging : The Zeno effect in an ultracold lattice gas
• Confined quantum Zeno dynamics of a watched atomic arrow
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• Measurement quantum mechanics and experiments on quantum Zeno effect
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement
• Dissipative Universal Lindbladian Simulation
• Initialization of quantum simulators by sympathetic cooling
• Geometry, robustness, and emerging unitarity in dissipation-projected dynamics
• Effective quantum Zeno dynamics in dissipative quantum systems
• Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice
• Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings
• Modular Quantum Information Processing by Dissipation
• Targeting pure quantum states by strong noncommutative dissipation
• Spin-helix states in the $XXZ$ spin chain with strong dissipation
• Transition between dissipatively stabilized helical states

Cited by in corpus (8)

• Triviality of quantum trajectories close to a directed percolation transition
• Long-Range Coherence and Multiple Steady States in a Lossy Qubit Array
• Full spectrum of the Liouvillian of open dissipative quantum systems in the Zeno limit
• Out-of-equilibrium steady states of a locally driven lossy qubit array
• Time periodicity from randomness in quantum systems
• Quantum spin helices more stable than the ground state: onset of helical protection
• Signatures of quantum phases in a dissipative system
• Dissipative cooling towards phantom Bethe states in boundary driven XXZ spin chain