Metrology withPT-Symmetric Cavities: Enhanced Sensitivity near thePT-Phase Transition

Abstract

We propose and analyze a new approach based on parity-time (PT ) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which 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-PT regimes. We believe that our results open a new direction for PT -symmetric physical systems and it may find use in ultra-high precision metrology and sensing.PACS numbers: 42.65. Yj, 06.30.Ft, 42.50.Wk Introduction.-The measurement of physical quantities with high precision is the subject of metrology. This has attracted much attention due to the increasing interest in, e.g., gravitational wave detection [1], sensing of nanostructures [2,3], as well as global positioning and navigation [4,5]. Developments in metrology over the past two decades have provided the necessary tools to determine the fundamental limits of measuring physical quantities and the resources required to achieve them [6,7].Among many different approaches, cavity-assisted metrology (CAM), where a high-quality (Q) factor cavity or resonator is coupled to a device under test (DUT), has emerged as a versatile and efficient experimental approach to achieve high-precision measurements. In CAM, the coupling between the resonator and the DUT manifests itself as a back-action-induced resonance frequency shift, resonance mode splitting, or a sideband in the output transmission spectrum [8]. Cavity-assisted metrology has been successfully applied for reading out the state of a qubit [9], measuring tiny mechanical motions [10,[12][13][14][15][16][17]42], and detecting nanoparticles with single-particle resolution [18,19].The readout signal (i.e., the transmission spectrum) of CAM is determined by the sum between the background spectrum of the cavity and the back-action spectrum of the DUT. The background spectrum is determined by the Q of the cavity whereas the back-action spectrum is determined by the strength of the cavity- * Electronic address: jing-zhang@mail.tsinghua.edu.cn † Electronic address: ozdemir@ese.wustl.edu DUT coupling (also dependent on Q) and the quantity to be measured. A broad background spectrum masks the back-action spectrum and decreases signal-to-noise ratio (SNR) [ Fig. 1(a)]. A higher coupling-strength between the cavity and the DUT and a higher Q of the cavity will be helpful to detect very weak signals and enable to resolve fine structures in the output spectra [ Fig. 1(b)]. A higher Q is also necessary to enhance the coupling strength between the cavity and the DUT. For example, for optomechanical resonators, the detection of tiny motions requires a strong optomechanical coupling, which is only possible with an high Q-factor. Therefore, CAM will benefit significantly from a narrower background spectrum which is fundamentally...

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