Measurements of the Phase Difference between Two Fields: Is There a Universal Phase Operator?
The problem of identifying the appropriate dynamical variable to represent the phase of a quantum field continues to occupy research workers. Our operational approach, based on what is usually measured, leads to the conclusion that there is not one universal phase operator, but that different measurement schemes correspond to different operators.1,2 This approach has resulted in very good agreement between theory and experiment in all cases so far.3,4 As a further argument in favor of a non-unique phase, we now point out that, according to our formalism, direct measurement of the phase difference between two weak fields (mean photon number ≪ 1) should result in a different answer than does indirect measurement of each weak field against a strong local oscillator. This prediction is readily testable by experiment.
KeywordsPhase Difference Operational Approach Indirect Measurement Dynamical Variable Space Representation