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arXiv:1601.04374

Interferometric Phase Estimation Though Quantum Filtering in Coherent States

John Edward Gough

Published Jan 18, 2016• 2 citations
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Abstract

We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.

DOI
10.48550/arxiv.1601.04374

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We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.
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We propose and experimentally demonstrate nondestructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors, i.e., vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on-off detection, phase stabilized, and phase randomized homodyne detection. We find that on-off detection, optimal in the ideal theoretical setting, is superior to the homodyne strategy also in a practical setting.
Quantum optical metrology deals with estimation of an unknown parameter by exploiting the non-classical properties of the light. The unknown parameter that we are trying to estimate is the optical phase. Precise optical phase measurement has been a well-known problem and has many applications, most notably the gravitational wave detection. In this thesis we investigate the interferometric measurement schemes. We consider the parity detection for a class of input states that have been shown to exhibit sub-shot noise limited phase estimate with their respective detection schemes. Our results indicate that the parity detection applies to all these strategies with various input states and thus acts as a unified detection scheme towards the goal of interferometric phase estimates beyond the shot-noise limit. We also consider the performance of the so-called optimal state with the canonical phase measurement scheme that was proposed by Sanders and Milburn [Phys. Rev. Lett. 75, 2944 (1995)] in presence of photon loss. The model for photon loss is a generic fictitious beam splitter and the analytical treatment requires density matrix approach rather than the state-vector formalism. We present full density-matrix calculations. Our results indicate that, for a given amount of loss, the phase estimate saturates but does not diverge as one would expect with increasing the loss. Finally, we study the continuous measurement and feedback scheme with optical homodyne detection for a single optical qubit. We found a protocol that speeds up the rate of increase of the average purity of the system and generates a deterministic evolution for the purity in the limit of strong feedback.