Operator formalism for the Wigner phase distribution

Abstract

The probability distribution for finding a state of the radiation field in a particular phase is described by a multitude of theoretical formalisms; the phase-sensitivity of the Wigner quasiprobability distribution being one of them. We construct a hermitian phase operator for this Wigner phase. We show that this operator is complete and also elucidate a set of complete but non-orthogonal states that seems to be naturally associated with such an operator. Further we show that our operator satisfies a weak equivalence relation with the Pegg-Barnett operator, thus showing that the essential phase information furnished by both formalisms are the same. It is also shown that this operator gives results which are in correct agreement with the expected uniform phase distribution of a Fock state.

Atomic and entanglement dynamics in the mixed squeezed coherent state version of the Jaynes-Cummings interaction

“…If we increase N s further, the peak of the PCD comes down and the oscillatory behaviour becomes very significant. This oscillatory behaviour of the PCD is manifested in the atomic inversion and in the entanglement dynamics [3].…”

“…This oscillatory behaviour of the PCD explains the ringing revivals effect in the atomic inversion [4]. It also affects the entanglement dynamics [3]. Earlier, Satyanarayana et al, have used the J-C model to study the atom-field interaction, where the field is in a superposition of thermal and coherent states [4].…”

“…In the present study, we have used the Jaynes-Cummings model (J-C model), which is a paradigm model of interaction in quantum optics [1,2]. Using this model, Subeesh et al, have studied the dynamics of atom-field interaction, where they took the radiation field to be in a pure squeezed coherent state (PSCS) and the atom as a two-level system, and they have studied the photon counting distribution (PCD), the atomic inversion (W (t)) and the entanglement dynamics [3]. They observed that the addition of squeezed photons has a drastic effect on the PCD.…”

Comment on ‘Operator formalism for the Wigner phase distribution’

“…Using it as a basis to define the operatorρ W (θ) to represent phase is therefore without appropriate justification. This leaves the merits of the operatorρ W (θ) introduced in [3] open to question.…”

“…As such, it cannot be taken to represent physical properties in the way that probability distributions represent the statistical properties of the things they describe. So it comes as something of a surprise to find the same function being used as a basis for describing the phase observable of a single mode radiation field, as Subeesh and Sudhir have recently done [3]. They derive an operatorρ W (θ),…”