Quantum-state manipulation via quantum nondemolition measurements in a two-dimensional trapped ion - art. no. 043419

The quantum nondemolition measurement is applied to a two-dimensional (2D) trapped-ion model in which two laser beams drive the corresponding vibratio nal motions and are carrier resonant with the two-level system of the ion. The information about the ionic vibrational energy can be detected by the o ccupation probability of the internal electronic level. The substantial dif ference of the 2D model from the one-dimensional one is that two orthogonal beams have a fixed phase shift instead of statistical independence. As a r esult, the atomic Rabi oscillation is involved in the coherent superpositio n of two sub-Rabi oscillations induced by the corresponding driving beams. This means that, in the bidimensional case, the phase difference between th e two laser beams plays the role of an adjustable external parameter which allows us to optimize the measurement scheme itself, in terms of precision and sensitivity. As in the one-dimensional case, our proposal leads to inte resting applications as, for example, the cooling and preparation of arbitr ary bimodal Fock states. The model can be considered as a cooling method fo r the trapped ion from the vibrational thermal state to the vacuum state. D ue to the coherent superposition of two sub-Rabi oscillations, the Rabi fre quency degeneration and offset may occur in this model. This provides the p ossibility of generating various entangled superposition of Fock states, th e pair coherent state, and entangled pair coherent states.