Abstract
Quantum-mechanical operators of phase difference between two electromagnetic fields are proposed and their properties are analyzed. The Hermitian phase-difference operators are determined using the operators of interference of the two fields, which appears upon their mixing on a beam splitter. The results of calculations for the measured mean values and dispersions (fluctuations) of the trigonometric functions of the phase-difference operators, which follow from the Pegg–Barnett theory, are compared with the corresponding values for the proposed operators. Calculations and comparison are carried out for the Fock, coherent, and squeezed quantum states of electromagnetic fields. Analysis is performed for quantum microscopic fields with mean values $$\hat {n}$$ ~ 1 of the number of photons, which are currently used in quantum technologies. The quantitative agreement between two different theories is demonstrated for the Fock and squeezed states of the fields; in the case of coherent states, an appreciable quantitative difference in the predictions of the theories is observed.
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