Adaptive Phase Measurements

Abstract

In this thesis I consider the general problem of how to make the best possible phase measurements using feedback. Both the optimum input state and optimum feedback are considered for both single-mode dyne measurements and two-mode interferometric measurements. I derive the optimum input states under general dyne measurements when the mean photon number is fixed, both for general states and squeezed states. I propose a new feedback scheme that introduces far less phase uncertainty than mark II feedback, and is very close to the theoretical limit. I also derive results for the phase variance when there is a time delay in the feedback loop, showing that there is a lower limit to the introduced phase variance, and this is approached quite accurately under some conditions. I derive the optimum input states for interferometry, showing that the phase uncertainty scales as 1/N for all the common measures of uncertainty. This is contrasted with the |j0>_z state, which does not scale as 1/N for all measures of phase uncertainty. I introduce an adaptive feedback scheme that is very close to optimum, and can give scaling very close to 1/N for the uncertainty. Lastly I consider the case of continuous measurements, for both the dyne and interferometric cases.

PhD thesis, 228 pages, 103 figures

References in corpus (8)

• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Quantum properties of classical Fisher information
• Adaptive Quantum Measurements of a Continuously Varying Phase
• Adaptive single-shot phase measurements: The full quantum theory
• Quantum Phase and Quantum Phase Operators: Some Physics and Some History
• Phase measurements at the theoretical limit
• Heterodyne and adaptive phase measurements on states of fixed mean photon number
• The effects of time delays in adaptive phase measurements