  A method for gaining information about the phonon-number moments and the
generalized nonlinear and linear quadratures in the motion of trapped ions (in
particular, position and momentum) is proposed, valid inside and outside the
Lamb-Dicke regime. It is based on the measurement of first time derivatives of
electronic populations, evaluated at the motion-probe interaction time t=0. In
contrast to other state-reconstruction proposals, based on measuring Rabi
oscillations or dispersive interactions, the present scheme can be performed
resonantly at infinitesimal short motion-probe interaction times, remaining
thus insensitive to decoherence processes.
