Appearance of classical coherent oscillator states under environment-induced decoherence

The existence of well-defined quasiprobabilities has long been known to be the signature of a classical state. Recent studies on environment induced decoherence have suggested the use of the Wigner function to illustrate the destruction of coherence on interaction with the environment. Due to the overcompleteness of coherent states, any state can be represented as a mixture of coherent states with a relative weight $P(v).$ This is known as the P representation of the state. In this paper we use the P representation of a state to see how its classical form emerges on interaction with the environment. We also use the concept of ``depth of classicality'' introduced recently to see how classicality is increased on interaction with the environment. We use the example of superposition of Gaussian wave packets for all the calculations. We also attempt to implement the predictability sieve using the P representation of a state. We use this definition of the predictability sieve to show that coherent states are more robust to environment-induced decoherence than squeezed states.