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@ARTICLE{Zeuch:887651,
      author       = {Zeuch, Daniel and Hassler, Fabian and Slim, Jesse J. and
                      DiVincenzo, David P.},
      title        = {{E}xact rotating wave approximation},
      journal      = {Annals of physics},
      volume       = {423},
      issn         = {0003-4916},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier},
      reportid     = {FZJ-2020-04313},
      pages        = {168327 -},
      year         = {2020},
      abstract     = {The 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.},
      cin          = {PGI-11},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-11-20170113},
      pnm          = {144 - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000596612200002},
      doi          = {10.1016/j.aop.2020.168327},
      url          = {https://juser.fz-juelich.de/record/887651},
}