Abstract
Abstract We present new developments in nonadiabatic geometric phases along two lines for systems undergoing changes of quantum state in intense fields. We first present a geometric representation of the non-Hermitian Schrodinger equation and introduce the notion of a complex multiphoton Aharonov-Anandan (AA) phase associated with dissipative two-level systems driven by periodic fields. The concept is further extended to include field modulation effects. We then develop the AA phase for spin-j systems in periodic fields and find conditions for cyclic evolution for general multi-level systems. In both cases, generalizations of the Floquet formalism lead to general analytical expressions for geometric phases that can be tested by experiments.
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