Hamiltonian engineering via invariants and dynamical algebra
- 14 April 2014
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 89 (4)
Abstract
We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations as slow, adiabatic ones. As application examples, we design families of shortcut Hamiltonians that drive two- and three-level systems between initial and final configurations, imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.Keywords
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This publication has 61 references indexed in Scilit:
- Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errorsPhysical Review A, 2013
- Quest for absolute zero in the presence of external noisePhysical Review E, 2013
- Shortcuts to adiabaticity in a time-dependent boxScientific Reports, 2012
- Optimal control of number squeezing in trapped Bose-Einstein condensatesPhysical Review A, 2009
- High-fidelity fast quantum transport with imperfect controlsPhysical Review A, 2009
- Optimal transport of ultracold atoms in the non-adiabatic regimeEurophysics Letters, 2008
- Assisted Adiabatic Passage RevisitedThe Journal of Physical Chemistry B, 2005
- Adiabatic Population Transfer with Control FieldsThe Journal of Physical Chemistry A, 2003
- Dynamical algebraic approach and invariants for time-dependent Hamiltonian systems in two dimensionsJournal of Mathematical Physics, 1993
- Dynamical Noether invariants for time-dependent nonlinear systemsJournal of Mathematical Physics, 1981