Generation of motional SU(1,1) intelligent states of a trapped ion

We propose a scheme for generating SU(1,1) intelligent states for the quantized vibrational motion of a napped ion. The SU(1,1) intelligent states are those states satisfying the equalized SU(I,1) uncertainty relation. The relevant operators can be realized for one or two vibrational modes (the states for the latter having strong intermode correlations) and we consider both cases. In the single-mode case, three codirectional laser beams are used to excite the trapped ion, while for the two-mode case, five laser beams along different directions in the X-Y plane of the ion trap are required. Our desired states are obtained as the steady-state solutions, indicated by the extinction of the fluorescence by the ion, of the master equation containing dissipative terms due to spontaneous emission with appropriately chosen initial states. The system is also studied numerically using a Monte Carlo state-vector method.