Nonstandard Unitary Transformations of Quantum States

In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.