Schrodinger Cat States and their Metrological Power

Abstract

Schrodinger Cat States, which in quantum optics refer to a superposition of distinct co herent states, have acquired pedestal due to their application in quantum technologies. Despite the challenges involved, efforts are underway to generate large size cat states in the laboratories. Their importance in quantum metrology, in enhancing precision mea surement is monumental. This thesis explores the power these states hold in enhancing metrology for phase and displacement sensing. We begin by exploring the nonclassicality of cat states through Wigner function, then continue towards analyzing their photon statistics. We analyti cally studied as to whether Mandel Q parameter can serve as an indicator for relative strength of cat states, with coherent states as benchmark, for precisely measuring phase and displacement. Our results demonstrate that Q is not sufficient in dictating the metro logical advantage of the cat states across different parameters. The study was extended to include various probe states with similar construction as Schr¨ odinger cat states called as multiheaded cats. Next, we explore the impact of single photon addition on metro logical power of all the states considered. Through graphical analysis, we elucidate that this manipulation of cat states result in further enhancing their metrological potential, as photon addition is a non-local operation and can add to the operational nonclassicality of a state. Our findings underscore the significance of Schr¨odinger cat states and highlight the ad vantage of manipulation of photon number in enhancing quantum metrology.