Title page for ETD etd-07052010-071455

Type of Document Dissertation
Author Gao, Yang
Author's Email Address ygao1@tigers.lsu.edu
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
  • Heisenberg limit
  • shot-noise limit
  • phase estimation
  • parity
Date of Defense 2010-05-31
Availability unrestricted
One 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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