Power narrowing in coherent atomic excitation by smoothly shaped pulsed fields

When atoms are excited by laser radiation the conventional wisdom dictates that the spectral excitation profile – the excited-state population vs the detuning – broadens as the radiation intensity increases. This common expectation has been shown to be incorrect in the fluorescence signal following two-photon excitation of xenon atoms by a Gaussian laser pulse, which showed almost no power broadening [T. Halfmann, T. Rickes, N.V. Vitanov, K. Bergmann, Optics Communications, 220 (2003) 353] Here we go a step further and show that for a class of pulse shapes, the falling edges of which vanish as inverse powers of time, ∝t−n∝t−n (with n>1n>1), the spectral excitation profile must exhibit power narrowing, i.e. the spectral linewidth scales as Ω0−1/(n−1), where Ω0Ω0 is the Rabi frequency of the transition. We provide a simple physical explanation based upon the notions of adiabatic evolution and coherent population return and discuss important experimental applications.