Supersensitive phase estimation by thermal light in a Kerr-nonlinear interferometric setup

Estimation of the phase delay between interferometer arms is the core of transmission phase microscopy. Such phase estimation may exhibit an error below the standard quantum (shot-noise) limit, if the input is an entangled two-mode state, e.g., a N00N state. We show, by contrast, that such supersensitive phase estimation (SSPE) is achievable by incoherent, e.g., thermal, light that is injected into a Mach-Zehnder interferometer via a Kerr-nonlinear two-mode coupler. Phase error is shown to be reduced below 1/n¯, n¯ being the mean photon number, by thermal input in such interferometric setups, even for small nonlinear phase shifts per photon pair or for significant photon loss. Remarkably, the phase accuracy achievable in such setups by thermal input surpasses that of coherent light with the same n¯. Available mode couplers with giant Kerr nonlinearity that stem either from dipole-dipole interactions of Rydberg polaritons in a cold atomic gas, or from cavity-enhanced dispersive atom-field interactions, may exploit such effects to substantially advance interferometric phase microscopy using incoherent, faint light sources.