000887651 001__ 887651 000887651 005__ 20210130010613.0 000887651 0247_ $$2doi$$a10.1016/j.aop.2020.168327 000887651 0247_ $$2ISSN$$a0003-4916 000887651 0247_ $$2ISSN$$a1096-035X 000887651 0247_ $$2Handle$$a2128/26085 000887651 0247_ $$2WOS$$aWOS:000596612200002 000887651 0247_ $$2altmetric$$aaltmetric:44748140 000887651 037__ $$aFZJ-2020-04313 000887651 082__ $$a530 000887651 1001_ $$0P:(DE-Juel1)170090$$aZeuch, Daniel$$b0$$eCorresponding author$$ufzj 000887651 245__ $$aExact rotating wave approximation 000887651 260__ $$aAmsterdam [u.a.]$$bElsevier$$c2020 000887651 3367_ $$2DRIVER$$aarticle 000887651 3367_ $$2DataCite$$aOutput Types/Journal article 000887651 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1604928672_19101 000887651 3367_ $$2BibTeX$$aARTICLE 000887651 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000887651 3367_ $$00$$2EndNote$$aJournal Article 000887651 520__ $$aThe Hamiltonian of a linearly driven two-level system, or qubit, in the standard rotating frame contains non-commuting terms that oscillate at twice the drive frequency, , rendering the task of analytically finding the qubit’s time evolution nontrivial. The application of the rotating wave approximation (RWA), which is suitable only for drives whose amplitude, or envelope, , is small compared to and varies slowly on the time scale of , yields a simple Hamiltonian that can be integrated relatively easily. We present a series of corrections to the RWA Hamiltonian in , resulting in an effective Hamiltonian whose time evolution is accurate also for time-dependent drive envelopes in the regime of strong driving, i.e., for . By extending the Magnus expansion with the use of a Taylor series we introduce a method that we call the Magnus–Taylor expansion, which we use to derive a recurrence relation for computing the effective Hamiltonian. We then employ the same method to derive kick operators, which complete our theory for non-smooth drives. The time evolution generated by our kick operators and effective Hamiltonian, both of which depend explicitly on the envelope and its time derivatives, agrees with the exact time evolution at periodic points in time. For the leading Hamiltonian correction we obtain a term proportional to the first derivative of the envelope, which competes with the Bloch–Siegert shift. 000887651 536__ $$0G:(DE-HGF)POF3-144$$a144 - Controlling Collective States (POF3-144)$$cPOF3-144$$fPOF III$$x0 000887651 588__ $$aDataset connected to CrossRef 000887651 7001_ $$0P:(DE-HGF)0$$aHassler, Fabian$$b1 000887651 7001_ $$0P:(DE-HGF)0$$aSlim, Jesse J.$$b2 000887651 7001_ $$0P:(DE-Juel1)143759$$aDiVincenzo, David P.$$b3$$ufzj 000887651 773__ $$0PERI:(DE-600)1461336-0$$a10.1016/j.aop.2020.168327$$gVol. 423, p. 168327 -$$p168327 -$$tAnnals of physics$$v423$$x0003-4916$$y2020 000887651 8564_ $$uhttps://juser.fz-juelich.de/record/887651/files/1807.02858.pdf$$yOpenAccess 000887651 909CO $$ooai:juser.fz-juelich.de:887651$$pdnbdelivery$$pdriver$$pVDB$$popen_access$$popenaire 000887651 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)170090$$aForschungszentrum Jülich$$b0$$kFZJ 000887651 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)143759$$aForschungszentrum Jülich$$b3$$kFZJ 000887651 9131_ $$0G:(DE-HGF)POF3-144$$1G:(DE-HGF)POF3-140$$2G:(DE-HGF)POF3-100$$3G:(DE-HGF)POF3$$4G:(DE-HGF)POF$$aDE-HGF$$bEnergie$$lFuture Information Technology - Fundamentals, Novel Concepts and Energy Efficiency (FIT)$$vControlling Collective States$$x0 000887651 9141_ $$y2020 000887651 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0600$$2StatID$$aDBCoverage$$bEbsco Academic Search$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)1150$$2StatID$$aDBCoverage$$bCurrent Contents - Physical, Chemical and Earth Sciences$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0113$$2StatID$$aWoS$$bScience Citation Index Expanded$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)9900$$2StatID$$aIF < 5$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000887651 915__ $$0StatID:(DE-HGF)0030$$2StatID$$aPeer Review$$bASC$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0100$$2StatID$$aJCR$$bANN PHYS-NEW YORK : 2018$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0160$$2StatID$$aDBCoverage$$bEssential Science Indicators$$d2020-09-08 000887651 915__ $$0StatID:(DE-HGF)0420$$2StatID$$aNationallizenz$$d2020-09-08$$wger 000887651 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2020-09-08 000887651 920__ $$lyes 000887651 9201_ $$0I:(DE-Juel1)PGI-11-20170113$$kPGI-11$$lJARA Institut Quanteninformation$$x0 000887651 980__ $$ajournal 000887651 980__ $$aVDB 000887651 980__ $$aUNRESTRICTED 000887651 980__ $$aI:(DE-Juel1)PGI-11-20170113 000887651 9801_ $$aFullTexts