Harnessing Quantum Metrological Power through Nonclassicality of Optical Probes

Abstract

Quantum optical systems exhibiting nonclassical features are essential for the practical implementation of quantum technologies, including quantum metrology, quantum sens ing, quantum information and quantum computation protocols. In quantum metrology and quantum sensing, employing nonclassical light as probe states is key to harness ing the quantum advantage. It has been shown that the nonclassicality of a quantum optical field is a quantifiable resource for these applications. Therefore, detecting and quantifying the nonclassicality of a bosonic mode in a resource theoretic framework is a significant yet challenging task in quantum optics. The nonclassicality of a quantum optical state is usually described by Glauber Su darshan P distribution, which is often impractical to measure directly because it is not a genuine classical probability distribution. Instead, the nonclassicality is characterized using indirect measures such as Mandel Q parameter, second order correlation func tion, amplitude and quadrature squeezing and various entropy-based measures. Despite many rigorous efforts, establishing a unified measure of nonclassicality for single-mode quantum optical states remains an open and challenging problem. In this thesis we present the notion of metrological power as a measure of nonclassicality, which has an operational significance in terms of measurement-precision sensitivity exceeding the classical limit. Since it does not increase under linear optical elements, this measure establishes the resource theory of nonclassicality and is based on the quantum Fisher information of the generator of the unknown parameter to be estimated. We examine a broad class of continuous-variable light states as initial probe states for selected quantum metrology tasks. First, we analyze their nonclassicality using traditional measures such as the Mandel Q parameter, quadrature squeezing and the negativity of the Wigner function. Then, we harness the metrological power by calcu lating the quantum Fisher information of the initial probe states undergoing unitary evolution governed by the generators related to parameters such as phase and displace ment. We demonstrate that our selected optical probes can be described by generalized coherent states of quantum optical fields based on su(1,1) Lie algebra. This broad class of su(1,1) coherent states includes a wide range of squeezed and superposition states, including squeezed vacuum and Schrödinger cat states. Moreover, we demonstrate that the metrological power of certain states can be significantly enhanced through multiphoton excitation. These findings highlight various crucial properties of nonclas sical probes, constituting resource for quantum metrology and quantum sensing. The results in this thesis will be helpful in preparing and utilizing nonclassical states for precision-sensing applications, such as quadrature sensing and phase sensing in optical interferometery.