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 Δφ=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 Δφ=1/√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.