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 3
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
Phys. Rev. Lett. 124, 240404 (2020) [Crossref]
Gal Shavit et al., Topology by dissipation: Transport properties
Phys. Rev. B 101, 125412 (2020) [Crossref]
Ontology / TopicsSee full Ontology or Topics database.
Author / Affiliation: mappings to Contributors and OrganizationsSee all Organizations.
- 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])