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 $ {{\cal 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.

© 2020 Optical Society of America

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