Type of Document Dissertation Author Gao, Yang Author's Email Address email@example.com URN etd-07052010-071455 Title New Strategies for Phase Estimation in Quantum Optics Degree Doctor of Philosophy (Ph.D.) Department Physics & Astronomy Advisory Committee
Advisor Name Title Lee, Hwang Committee Chair Dowling, Jonathan Committee Co-Chair O'Connell, Robert Committee Member Sprunger, Phillip Committee Member Gunturk, Bahadir Dean's Representative Keywords
- Heisenberg limit
- shot-noise limit
- phase estimation
Date of Defense 2010-05-31 Availability unrestricted AbstractOne important problem in quantum optics is to resolve an extremely small change
of phase shift. The complementarity between photon number and phase sets an ultimate
limit, the so-called Heisenberg limit, on the phase measurement sensitivity. The precise
phase estimation has many technological applications, such as optical gyroscopes,
gravitational wave detection, quantum imaging and sensing.
In this thesis I show that the utilization of the parity measurement in the optical
interferometry is actually applicable to a wide range of quantum entangled input states.
Comparison of the performance of the various quantum states then can be made within
such a unified output measurement scheme. Based on such a universal detection scheme,
we present a comparison of the phase sensitivity reduction for various quantum states of
light in the presence of photon loss.
I also provide a simple condition that could be used to check whether an arbitrary
state can achieve the Heisenberg limit independently of the detection scheme. It implies
that the fidelity between the two output states with zero phase and minimal detectable
phase applied respectively should significantly different from unity as the minimal phase
shift scaling as 1/N, whereas the average number of input photons N goes to infinity.
Next I give several measures to characterize the which-way information in the
interference experiment. We define a new distinguishability associated with the fidelity
between two density matrices to measure the which-way information. We demonstrate
that the changes of mutual entropy as well as the entanglement of formation of the whole
system, i.e. the physical system plus the which-way detector can also be used to describe
the which-way information. With such quantities, we show that as the fringe visibility of
the interference pattern gets larger, the less which-way information is obtained.
Finally, I show that coherent light coupled with photon number resolving detectors
can provide a super-resolution much below the Rayleigh diffraction limit, with sensitivity
no worse than shot-noise in terms of the detected photon power. This scheme would have
applications to laser radar, given the difficulty in making entangled states of light, as well
as their susceptibility to atmospheric absorption.
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