Abstract
The uncertainty relations for the phase-difference operators of two electromagnetic fields, which have been proposed earlier in [10], are obtained and analyzed. The uncertainty relations for the phase-difference cosine and sine operators, as well as for the operators of the sum of the photon number and phase-difference operators for two fields, are investigated. The Fock and coherent quantum states of the fields, as well as general states of quantum superpositions of coherent field states and states of the Schrödinger’s cat of the fields, are considered. The rigorous uncertainty relation (Cauchy–Schwartz inequality) and the Heisenberg uncertainty relation for these operators and quantum field states are analyzed. The differences between the rigorous uncertainty relations and the Heisenberg uncertainty relations for the trigonometric phase-difference operators are demonstrated using examples of considered field states. It is shown that the rigorous uncertainty relations and the Heisenberg uncertainty relations are qualitatively different for coherent states as well as the states of quantum superpositions, but coincide in the case of the Fock states of the fields.
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Kozlovskii, A. Uncertainty Relation for Trigonometrical Phase-Difference Operators of Quantum Electromagnetic Fields. J. Exp. Theor. Phys. 133, 658–668 (2021). https://doi.org/10.1134/S1063776121110108
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DOI: https://doi.org/10.1134/S1063776121110108