Dissipation-induced topological insulators: A no-go theorem and a recipe
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...
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| Format: | Article |
| Language: | English |
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SciPost
2019-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.7.5.067 |
| _version_ | 1819081817204981760 |
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| author | Moshe Goldstein |
| author_facet | Moshe Goldstein |
| author_sort | Moshe Goldstein |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T20:06:48Z |
| format | Article |
| id | doaj.art-9b728455857a4af197f6982ffa62217b |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-21T20:06:48Z |
| publishDate | 2019-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-9b728455857a4af197f6982ffa62217b2022-12-21T18:51:49ZengSciPostSciPost Physics2542-46532019-11-017506710.21468/SciPostPhys.7.5.067Dissipation-induced topological insulators: A no-go theorem and a recipeMoshe GoldsteinNonequilibrium 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.https://scipost.org/SciPostPhys.7.5.067 |
| spellingShingle | Moshe Goldstein Dissipation-induced topological insulators: A no-go theorem and a recipe SciPost Physics |
| title | Dissipation-induced topological insulators: A no-go theorem and a recipe |
| title_full | Dissipation-induced topological insulators: A no-go theorem and a recipe |
| title_fullStr | Dissipation-induced topological insulators: A no-go theorem and a recipe |
| title_full_unstemmed | Dissipation-induced topological insulators: A no-go theorem and a recipe |
| title_short | Dissipation-induced topological insulators: A no-go theorem and a recipe |
| title_sort | dissipation induced topological insulators a no go theorem and a recipe |
| url | https://scipost.org/SciPostPhys.7.5.067 |
| work_keys_str_mv | AT moshegoldstein dissipationinducedtopologicalinsulatorsanogotheoremandarecipe |