Quasi-resonances for high-frequency perturbations

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Abstract
The authors study the quantum dynamics of a one-dimensional hydrogen atom perturbed by a high-frequency periodic electric field. They show that a time-dependent basis comprising states which diagonalise the compensated energy Hamiltonian provides a numerically efficient description of the wavefunction by explicitly allowing for the oscillatory motion of the bound electron due to the periodic field. They use this compensated energy representation to examine the behaviour of the system and show that for moderate strength fields which are slowly switched on and off only the relative few quasi-resonant states are significantly populated; this behaviour should be experimentally observable. They also show that a basis comprising only the few, typically between ten and twenty, compensated energy quasi-resonant states provides a remarkably good and efficient basis.