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Physics Letters A

Off-resonance effects in the adiabatic evolution of two-level systems with relaxation

David E. Rourke, John K. Saunders

Published Mar 1, 1996• 1 citation
Publisher
DOI
10.1016/0375-9601(96)00045-x

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Physical Review A•Jan 1, 1997•131 citations
We investigate the quantum dynamics of a two-level system driven by a bichromatic field, using a nonperturbative analysis.We make special emphasis in the case of two large frequencies, where the Magnus expansion can fail, and in the case of a large and a small frequency, where resonances can dominate.In the first case, we show that two large frequencies can be combined to produce an effective adiabatic evolution.In the second case, we show that high-frequency terms (which naturally arise as corrections to the adiabatic evolution obtained in the first case) can be used to produce a highly tunable adiabatic evolution over the whole Bloch sphere, controlled by multiphoton resonances.
We demonstrate that various properties of population transfer by delayed pulses in three-level systems on two-photon resonance can be deduced analytically and for general pulse shapes. We use the fact that the three-level system reduces to effective two-level problems at large intermediate-level detuning \ensuremath{\Delta}, on resonance (\ensuremath{\Delta}=0) and for completely overlapping pulses. Special attention is paid to the effect of the pulse order on the population transfer efficiency. We show that on resonance the transfer efficiency depends substantially on the pulse order, while at large \ensuremath{\Delta} it does not. We also find that under some natural restrictions on the symmetry of the problem, the population of the initial level does not depend on the pulse order at any \ensuremath{\Delta}. Furthermore, we demonstrate that the population transfer in the three-level system can be viewed as a level-crossing problem in an equivalent two-level system not only at large \ensuremath{\Delta} (which is known) but also on resonance, \ensuremath{\Delta}=0. The effective on-resonance two-level problem is interesting by itself as it shows that a level crossing and adiabatic evolution do not necessarily lead to complete population inversion. As examples throughout the paper, we present several analytically solvable models.