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.
