Abstract
We study the minimum uncertainty relation obeyed by the phase operator [Formula: see text] in two-mode coherent state. The operator is suitable for Shapiro–Wagner heterodyne phase measurement scheme. It is due to the |ξ> representation (see Eq. (4)) that the difficulty brought by nonlinear square root operation in [Formula: see text] can be avoided in calculating miscellaneous expectation values. Just as the single-mode coherent state | z1> makes uncertainty relation, satisfied by S–G phase operator, minimum for large |z1|2, we show that |z1,z2> makes uncertainty relation obeyed by [Formula: see text] minimum when |z1|=|z2| is large enough. Some figures are plotted to support our conclusion.
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