Coherent and Squeezed States

G. E. Drăgănescu, A. Messina, Anna Napoli

In this work we study different types of coherent and squeezed states for the Charlier, Kravchuk and Meixner oscillators. We calculate the average values of different observables corresponding to the coherent states. We found that the coherent and squeezed states of the Kravchuk oscillator are unstable. There are also coherent and squeezed states that are similar to the coherent and squeezed states of the harmonic oscillator. We have introduced a discrete variable model for the biophoton coherent radiation, and the coherent thermal and squeezed thermal states.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

G. M. Saxena

In this paper, we define the eigenvalue equation of the squeezed coherent state using recently introduced inverse annihilation and creation operators. The salient feature of the eigenvalue equation of the squeezed coherent state is that it consistently yields the eigenvalue equation of the squeezed vacuum when the coherent amplitude is reduced to zero. The squeezed coherent state defined by others, without using the inverse operators, cannot be reduced to the squeezed vacuum state. The time evolution of the squeezed states is also discussed. The squeezed states have phase-dependent quantum noise. The phase operators have an important role in the squeezing experiments. We show that the inverse operators are also useful in defining the phase operators. We also discuss the eigenvalue equation of the squeezed coherent state defined by Yuen vis-à-vis that is introduced in this paper using inverse annihilation and creation operators for bosons.

Ae‐Ran Kim

Kanwarpreet S. Grewal

Several recent studies on the subject of environment induced decoherence have suggested that the predictability sieve selects coherent states over squeezed states. Most of such studies have considered a system consisting of an oscillator linearly coupled to a bath of harmonic oscillators. In this paper, we consider an environment consisting of squeezed oscillators. We derive the master equation for an oscillator coupled to such an environment. We solve this master equation for the case of the oscillator being in a coherent state and for the oscillator in a squeezed state. We then compare the stability of coherent states and squeezed states in the general squeezed environment. Our aim is to find if coherent states are more stable than squeezed states in a squeezed environment as well or is this fact true only in an environment of coherent oscillator states? We argue that unless we show that coherent states are preferred in a nonclassical environment as well, we cannot assume that coherent states form most environments and therefore the study of the stability of states only in an environment of coherent oscillator states is not a general case.