Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative dynamics could be used as a resource. By proper engineering of the reservoirs and their couplings to a system, one may drive the system towards desired quantum-correlated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium many-particle phases are those which are distinguished by topology rather than by symmetry. A natural question thus arises: which of these topological states can be achieved as the result of dissipative Lindblad-type (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologically-nontrivial states in quantum simulators, especially ultracold atomic gases. Here I give a general answer for Gaussian states and quadratic Lindblad evolution, mostly concentrating on 2D Chern insulator states. I prove a no-go theorem stating that a finite-range Lindbladian cannot induce finite-rate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentially-local dynamics, or a mixed state arbitrarily close to the desired pure one via finite-range dynamics. I also address the cold-atom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.
Cited by 7
Simon Lieu et al., Tenfold Way for Quadratic Lindbladians
Phys. Rev. Lett. 124, 040401 (2020) [Crossref]
F. Tonielli et al., Topological Field Theory Far from Equilibrium
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Daniel Azses et al., Identification of Symmetry-Protected Topological States on Noisy Quantum Computers
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Tsuneya Yoshida et al., Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian
Phys. Rev. Research 2, 033428 (2020) [Crossref]
Gal Shavit et al., Topology by dissipation: Transport properties
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Chun-Hui Liu et al., Helical damping and dynamical critical skin effect in open quantum systems
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Souvik Bandyopadhyay et al., Dissipative preparation of many-body Floquet Chern insulators
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- German-Israeli Foundation for Scientific Research and Development [GIF]
- Israel Science Foundation [ISF]
- Ministry of Science and Technology, Israel
- United States - Israel Binational Science Foundation (through Organization: United States-Israel Binational Science Foundation [BSF])