Sensitivity of Quantum-Enhanced Interferometers

Abstract

We review various schemes of quantum-enhanced optical interferometers, both linear (SU(2)) and non-linear (SU(1,1)) ones, as well as hybrid SU(2)/SU(1,1) options, using the unified modular approach based on the Quantum Cramèr–Rao bound (QCRB), and taking into account the practical limitations pertinent to all real-world highly-sensitive interferometers. We focus on three important cases defined by the interferometer symmetry: (i) the asymmetric single-arm interferometer; (ii) the symmetric two-arm interferometer with the antisymmetric phase shifts in the arms; and (iii) the symmetric two-arm interferometer with the symmetric phase shifts in the arms. We show that while the optimal regimes for these cases differ significantly, their QCRBs asymptotically correspond to the same squeezing-enhanced shot noise limit (2), which first appeared in the pioneering work by C. Caves in 1981.We show also that in all considered cases the QCRB can be asymptotically saturated by the standard (direct or homodyne) detection schemes.

Using Schrödinger cat quantum state for detection of a given phase shift

“…Following the review [2], we consider two practically important configurations of the Mach-Zehnder interferometer-the asymmetric one, see figure 1(a), and the antisymmetric one, see figure 1(b). In the conceptually simpler asymmetric case, the signal phase shift is introduced in the first arm, with the second one providing the reference beam.…”

“…On the fundamental level, the phase sensitivity of the interferometers is limited by quantum fluctuations of the probing light and, therefore, depends on its quantum state, see e.g. the review papers [1,2]. In the most basic case of coherent quantum states, generated by phase-stabilized lasers, the phase sensitivity corresponds to the shot noise limit (SNL):…”