Nonadiabatic Transitions in a Two State Quantum System: Two-Level Atom + Radiation Pulse

N. A. Chigir

P. R. Berman, Lixin Yan, Keng-Hwee Chiam +1 more

The problem of a two-level atom interacting with a radiation pulse is studied in the limit that the atom-field detuning times the pulse duration is much greater than unity. Owing to the large atom-field detuning, transitions result from nonadiabatic coupling of the states by the field. The transition probability for the atom to be excited following the pulse is studied as a function of field strength for five different pulse shapes: hyperbolic secant, Lorentzian, hyperbolic secant squared, Lorentzian squared, and Gaussian. It is shown that the behavior of the transition probability differs qualitatively for these pulses. An explanation of this qualitative difference is given in terms of the Massey parameter. Numerical solutions are compared with asymptotic solutions and several anomalies are noted. In the limit of large field strength, a universal expression for the transition probability is found. An interesting feature of the solutions is that, in the limit of very large field strengths, the transition probability for a Gaussian pulse can approach unity despite the fact that the pulse has an exponentially small Fourier amplitude at the atom-field detuning. This apparent violation of the energy-time uncertainty principle is explained in terms of the nonlinear atom-field interactions.

H.S. Zivi, ALFRED BAUDER, Hs. H. Günthard

Vladimir V. Likhanskii

Expressions are obtained for the probability of a nonadiabatic transition between two degenerate levels under the action of laser radiation with a continuously variable resonance frequency. It is shown that this problem reduces to the solution of the Landau–Zener problem for eigenvectors of the matrix of a transition between two degenerate levels.

T. A. Vartanyan, Sergey G. Przhibel'skii, N. A. Chigir

Tianshi Lü, X. Miao, H. Metcalf

To apply the adiabatic rapid passage process repetitively [T. Lu, X. Miao, and H. Metcalf, Phys. Rev. A 71, 061405(R) (2005)], the nonadiabatic transition probability of a two-level atom subject to chirped light pulses over a finite period of time needs to be calculated. Using a unitary first-order perturbation method in the rotating adiabatic frame, an approximate formula has been derived for such transition probabilities in the entire parameter space of the pulses.