Nonclassical vibrational states in a quantized trap

The quantized center-of-mass (c.m.) motions of a single two-level atom or ion confined into a one-dimensional harmonic potential and interacting with a single-mode classical traveling-wave laser field are examined. We demonstrate that trap quantum states with remarkable nonclassical properties such as quadrature and amplitude-squared squeezing and sub-Poissonian statistics can be generated in this simple trap model when the c.m. motion is initially in certain coherent trap states. Our analyses also indicate that there exist some time regions where the production of nonclassical vibrational states is possible even if squeezing or sub-Poissonian statistics do not appear.