A theory of the relative phase and number difference of two quantized harmonic oscillators

• We present a comprehensive and self-consistent theory of relative-phase measurements and the associated Hermitian relative-phase operator of two harmonic oscillators. We find that since Nature does not favor any particular initial condition of the two oscillators, the relative-phase operator is not unique. We show that the relative-phase eigenstates; are maximally entangled. Therefore. most relative-phase operators lack a classical correspondence, even in the high-excitation limit. Furthermore, we find that the relative phase and the excitation number difference are noncommuting, noncanonical observables and we derive a commutation relation.

Nyckelord

bohrs correspondence principle

minimum-uncertainty states

2 quantum-fields

operational approach

hilbert-space

optical-phase

operator

breakdown

distributions

superposition

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