IS THERE A UNIQUE OPERATOR FOR THE PHASE DIFFERENCE OF 2 QUANTUM-FIELDS

The recent operational approach to the phase operator of a quantized e lectromagnetic field is applied to the problem of determining the phas e difference between two weak coherent fields in two different ways. T he phase difference is determined directly, and indirectly by measurin g each field in turn against the field of a strong local oscillator. W e show by measurements with an eight-port interferometer that these tw o different schemes lead to quite different outcomes for the probabili ty distribution of the phase difference, in agreement with our theory, but in disagreement with most other theoretical approaches.