Phase measurement with classical light

In this paper we investigate whether it is, in general, possible to substitute maximally path-entangled states, namely, NOON states, with classical light in Doppleron-type resonant multiphoton detection processes by studying adaptive phase measurement with classical light. We show that multiphoton detection probability using classical light coincides with that of NOON states and the multiphoton absorption rate is not hindered by the spatially unconstrained photons of the classical light in our scheme. We prove that the optimal phase variance with classical light can be achieved and scales the same as that using NOON states.

Figure 1

Measurement scheme for the unknown phase $\phi$ with the help of the NOON state $\left(\right|n,0\rangle +|0,n\rangle )/\sqrt{2}$.

Figure 2

Two-photon interference with classical light and the interaction of classical fields with the four-level atomic structure.

Figure 3

Two signal fields with frequencies ${\nu }_{+}$ and ${\nu }_{-}$ are shifted by the unknown phase $\phi$ and the controllable phase $\varphi$, respectively. The drive fields ${\omega }_{\pm }$ assist the directional resonance of $n$ photon absorption.