A phase operator for photons
Abstract
We define a unitary phase operator for photons in a single momentum mode. The operator acts on a Hilbert space with basis consisting of all number states in both polarizations. The Susskind Glogower operator, ${\hat{E}} = e^{i \hat{\phi}}$, thus defined is unitary and acts as a true ladder operator over all the states. It satisfies the commutation relation $[{\hat{E}}, {\hat{n}}] = {\hat{E}}$; consequently, the phase $\hat{\phi}$ satisfies the canonical commutation relation $[{\hat{n}}, {\hat{\phi}}] = i$. The eigenstates of the Susskind Glogower operator are found. Our model is able to directly account for phase measurements when polarization changes cannot be neglected and at the same time gives a well defined phase operator.
 Publication:

arXiv eprints
 Pub Date:
 May 2011
 DOI:
 10.48550/arXiv.1105.2750
 arXiv:
 arXiv:1105.2750
 Bibcode:
 2011arXiv1105.2750P
 Keywords:

 Quantum Physics;
 Physics  Optics