Intensity product-based optical sensing to beat the diffraction limit

Classically defined optical phase sensitivity is known as the shot-noise limit (SNL) or standard quantum limit originating in the uncertainty principle of quantum mechanics. Based on SNL, the phase resolution (sensitivity) is inversely proportional to the square root N, where N is the number of interfering photons or individually measured events. Thus, using a high-power laser is advantageous due to the square root N gain in the signal-to-noise ratio. In an optical interferometer, however, the phase resolution remains in the N=1 case unless N probe photons are resolved in a detection process, resulting in the diffraction limit of classical optics. Here, a projective measurement is proposed for intensity product-based optical sensing to realize SNL in a typical interferometer commonly used for high-precision metrology. For this, one of the output ports of the interferometer is evenly divided into N ports and measured them for mth-intensity correlations (m is less than or equal to N), where the maximum N is given by the total number of photons of the input laser. The maximum temporal delay among N photons is constrained by the spectral bandwidth of the laser, which is the same as the effective coherence time of the photon ensemble used for coincidence detection-based quantum sensing.