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Metrology with $\mathcal{PT}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{PT}$-phase transition

We propose and analyze a new approach based on parity-time ($\mathcal{PT}$) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which $\mathcal{PT}$-symmetric microcavities allow to improve sensitivity beyond what is achievable in loss-only systems. We discuss its application to the detection of mechanical motion, and show that the sensitivity is significantly enhanced in the vicinity of the transition point from unbroken- to broken-$\mathcal{PT}$ regimes. We believe that our results open a new direction for $\mathcal{PT}$-symmetric physical systems and it may find use in ultra-high precision metrology and sensing.