Correlated input-port, matter-wave interferometer: Quantum-noise limits to the atom-laser gyroscope

I derive the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input ports. I show that if the incident particles are entangled and correlated properly, then the phase sensitivity scales asymptotically like the Heisenberg-limited $\Delta \phi =O(1/N),$ for large $N,$ where $N$ is the number of particles incident per unit time. (In a one-input-port device, the sensitivity can be at best $\Delta \phi =1/\sqrt{N}.$) My calculation applies to bosons or fermions of arbitrary integer or half-integer spin. Applications to optical, atom-beam, and atom-laser gyroscopes are discussed—in particular, an atom-laser can be used to obtain the required entanglements for achieving this Heisenberg-limited sensitivity with atomic matter waves.