Lewis-Riesenfeld invariants and transitionless quantum driving

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dc.contributor.author Chen, Xi
dc.contributor.author Torrontegui Muñoz, Erik
dc.contributor.author Muga, Juan Gonzalo
dc.date.accessioned 2021-03-18T11:33:55Z
dc.date.available 2021-03-18T11:33:55Z
dc.date.issued 2011-06
dc.identifier.bibliographicCitation Chen, X., Torrontegui, E., Muga, J. G. (2011). Lewis-Riesenfeld invariants and transitionless quantum driving. Physical Review A, 83(6).
dc.identifier.issn 1050-2947
dc.identifier.uri http://hdl.handle.net/10016/32182
dc.description.abstract Different methods have been recently put forward and implemented experimentally to inverse engineer the time-dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via nonadiabatic shortcuts. In the "transitionless quantum driving" proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on first designing a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian that connects these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are, in fact, strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study, as explicit examples, expansions of time-dependent harmonic traps and the state preparation of two-level systems.
dc.description.sponsorship We thank M. Berry for commenting on the manuscript. This work was supported by the Basque Government (Grant No. IT 472-10), Ministerio de Ciencia e Innovación(Grant No. FIS2009-12773-C02-01), Juan de la Cierva Programme, the National Natural Science Foundation of China (Grant No. 60806041), and the Shanghai Leading Academic Discipline Program (Grant No. S30105). E.T. acknowledges support from the Basque Government (Grant No. BFI08.151).
dc.format.extent 8
dc.language.iso eng
dc.publisher American Physical Society
dc.rights ©2011 American Physical Society
dc.title Lewis-Riesenfeld invariants and transitionless quantum driving
dc.type article
dc.subject.eciencia Física
dc.identifier.doi http://dx.doi.org/10.1103/PhysRevA.83.062116
dc.rights.accessRights openAccess
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 062116-1
dc.identifier.publicationissue 6
dc.identifier.publicationlastpage 062116-8
dc.identifier.publicationtitle Physical Review A
dc.identifier.publicationvolume 83
dc.identifier.uxxi AR/0000026572
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