NONADIABATIC TRANSITIONS IN A 2-LEVEL QUANTUM SYSTEM - PULSE-SHAPE DEPENDENCE OF THE TRANSITION-PROBABILITY FOR A 2-LEVEL ATOM DRIVEN BY A PULSED RADIATION-FIELD

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 dura tion is much greater than unity. Owing to the large atom-field detunin g, 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 differe nt pulse shapes: hyperbolic secant, Lorentzian, hyperbolic secant squa red, Lorentzian squared, and Gaussian. It is shown that the behavior o f the transition probability differs qualitatively for these pulses. A n explanation of this qualitative difference is given in terms of the Massey parameter. Numerical solutions are compared with asymptotic sol utions and several anomalies are noted. In the limit of large held str ength, 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 puls e can approach unity despite the fact that the pulse has an exponentia lly small Fourier amplitude at the atom-field detuning. This apparent violation of the energy-time uncertainty principle is explained in ter ms of the nonlinear atom-field interactions. [S1050-2947(98)01801-0].