Phase-difference between two quantized harmonic oscillators

Gunnar G. Bjork, Jonas Söderholm, Alexei S. Trifonov +1 more

Sixia Yu

A quantum description for the phase difference between two harmonic oscillators is proposed. Being represented by a Hermitian operator, phase difference displays two striking quantum features. First, its eigenvalues form a new type of quantized value which is countable and dense in a $2\ensuremath{\pi}$ window. Second, because quantized phase difference cannot be defined as a difference of phases, it obeys a quantum addition rule which may not be commutative.

R. Shepard Scott

G. Björk, Jonas S derholm, Alexei S. Trifonov +1 more

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.

Daniel Rohrlich

H. Dekker