Coherent feedback enhanced quantum-dense metrology in a lossy environment

Quantum dense metrology (QDM) performs high-precision measurements by a two-mode entangled state created by an optical parametric amplifier (PA), where one mode is a meter beam and the other is a reference beam. In practical applications, the photon losses of meter beam are unavoidable, resulting in a degradation of the sensitivity. Here, we employ coherent feedback that feeds the reference beam back into the PA by a beam splitter to enhance the sensitivity in a lossy environment. The results show that the sensitivity is enhanced significantly by adjusting the splitting ratio of the beam splitter. This method may find its potential applications in QDM. Furthermore, such a strategy that two non-commuting observables are simultaneous measurements could provide a new way to individually control the noise-induced random drift in phase or amplitude of the light field, which would be significant for stabilizing the system and long-term precision measurement.