Nonlinear motional effects in the spectroscopy of a trapped and laser-driven atom

The interaction of a cold trapped ion with a strong laser field is studied in a configuration in which quasienergetic levels become important but heat ing of the system is unessential. Absorption spectroscopy of the quasienerg etic states of a strongly confined and laser-driven trapped ion is analyzed by probing vibrational transitions. Calculations are carried out analytica lly by using the master equation in quasienergetic state representation. We consider a V-level scheme for the ion with a resonant strong pump field an d a weak probe field. The steady-state and time-evolution behavior of the s ystem is discussed and the probe-field absorption spectrum for various init ial population distributions of the motional state is calculated. It is fou nd that the absorption spectrum displays vibrational sidebands with multipe ak splitting due to the nonlinear dependence of the Rabi frequencies on bot h the Lamb-Dicke parameter and the trap occupation number. This multipeak s plitting has interesting consequences and can be useful for the measurement of the initial trap number population distribution. [S1050-2947(98)01812-5 ].