Fluctuations of the hermitian phase operator of electromagnetic field for quantum phase superpositions of coherent states

ABSTRACT

Quantum-statistical properties of the phase of electromagnetic field in the case of phase superpositions of coherent states of the type $N_{\alpha ,\beta ,\xi }\left(\left|\sqrt{n}{e}^{i{\varphi }_{\alpha }}\right.⟩+e^{i\xi }\left|\sqrt{n}{e}^{i{\varphi }_{\beta }}\right.⟩\right)$ have been studied. Formulas for the average values and fluctuations (variances) of Hermitian phase operator ${\hat{\varphi }}_{\theta }$ of the electromagnetic field (so-called Pegg–Barnett optical phase operator) in the case of general superposition of coherent states are obtained and analysed. The states of phase superpositions of the ‘Schrödinger cat’ type $N_{\alpha ,-\alpha ,\xi }\left(|\alpha ⟩+e^{i\xi }|-\alpha ⟩\right),{\varphi }_{\beta }={\varphi }_{\alpha }+\pi$, and superpositions of coherent states of the type $N_{\alpha ,{\alpha }^{\ast },\xi }\left(|\alpha ⟩+e^{i\xi }|{\alpha }^{\ast }⟩\right),{\varphi }_{\beta }=-{\varphi }_{\alpha }$, are considered separately.

KEYWORDS:

• Hermitian phase operator
• coherent states superpositions
• quantum phase fluctuations