Transitionless quantum driving

For a general quantum system driven by a slowly time-dependent Hamiltonian, transitions between instantaneous eigenstates are exponentially weak. But a nearby Hamiltonian exists for which the transition amplitudes between any eigenstates of the original Hamiltonian are exactly zero for all values of...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 42; no. 36; pp. 365303 - 365303 (9)
Main Author Berry, M V
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 11.09.2009
IOP
Subjects
Exact sciences and technology
Physics
Eigenstates
Transition amplitudes
Quantum system
Degeneration
Magnetic fields
Hamiltonians
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Summary:For a general quantum system driven by a slowly time-dependent Hamiltonian, transitions between instantaneous eigenstates are exponentially weak. But a nearby Hamiltonian exists for which the transition amplitudes between any eigenstates of the original Hamiltonian are exactly zero for all values of slowness. The general theory is illustrated by spins driven by changing magnetic fields, and implies that any spin expectation history, including those where the spin never precesses, can be generated by infinitely many driving fields, here displayed explicitly. Asymptotically, the absence of transitions is explained by continuation to complex time, where the complex degeneracies in the transitionless driving fields have a nongeneric structure for which there is no Stokes phenomenon; this is analogous to the explanation of reflectionless potentials.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/36/365303