Generating Fock states and two-Fock states superposition from circular states, in a trapped ion

Abstract

We propose three schemes to engineer 2^M and M+1 circular states for the motion of the center of mass of a trapped ion, $M$ being the number of laser pulses. Since the ion is subjected to several laser pulses, we analyze the necessary duration of each one for generating the circular states, and from these, the Fock states and superposition of two-Fock states. We also calculate the probability for obtaining the required states.