Optical enhanced interferometry with two-mode squeezed twin-Fock states and parity detection

We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach-Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ=0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramér-Rao bound can be approached with the parity detection.