Pegg–Barnett coherent states

Abstract

In this paper, we show that the Pegg–Barnett formalism accepts coherent states constructed as eigenstates of the annihilation operator, considering both the number and the phase. These operators are defined within a ( s + 1 ) -dimensional Hilbert space H s and with periodic conditions. The coherent states that we find are determined by the eigenvalue of the annihilation operator, which leads to a discrete spectrum. This approach allows calculation of the discrete-finite counterpart of the Wigner function in a phase space defined by the variables of number and phase.

Formal relation between Pegg-Barnett and Paul quantum phase frameworks

“…A significant interest was devoted especially to the Pegg-Barnett formalism, in which the obstacles standing in the way of a well-defined quantum phase operator are overcome by reducing the problem to a finite dimension. After its discovery, the formalism quickly gave rise to an alternative derivation [11] and extension [12], among others [13][14][15][16]. Nowadays, the Pegg-Barnett formalism is used, e.g., to investigate phase properties of various non-classical phenomena, including photon antibunching in the case of photon addition and subtraction [17,18], phase-number squeezing in atom field interactions [19] and nonlinear squeezed states [20].…”