We propose a procedure that allows one to create arbitrary, discrete superpositions of coherent states of the quantized center-of-mass motion of a trapped ion along a line in phase space. In view of the overcompleteness of the coherent states, such a method can be used for the engineering of motional quantum states.
We proposed a scheme for generating arbitrary, discrete superpositions of motional coherent and squeezed coherent states of the quantized center of mass along a straight line in phase space for N trapped ions. We also show that such a method can be used for the engineering of motional quantum states. Furthermore, these states should help to examine the dynamics behavior of various systems and might be used for applications in quantum information processing.
We propose a scheme to generate a superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment. Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.