Squeezed vibrational states in a quantized trap

The quantized center of mass (c.m.) motion of a single two-level atom or ion confined in a one-dimensional harmonic potential and interacting with a single-mode classical traveling laser field, is investigated. We show that both quadrature and amplitude-squared squeezed vibrational states can be generated in this simple trap model when c.m. motion is initially in a certain coherent trap state.