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  • Stochastic path-integral formalism for continuous quantum measurement

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    Accepted Manuscript (AM)
    Author(s)
    Chantasri, Areeya
    Jordan, Andrew N.
    Griffith University Author(s)
    Chantasri, Areeya
    Year published
    2015
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    Abstract
    We generalize and extend the stochastic path-integral formalism and action principle for continuous quantum measurement introduced in Chantasri, Dressel, and Jordan [Phys. Rev. A 88, 042110 (2013)], where the optimal dynamics, such as the most likely paths, is obtained by extremizing the action of the stochastic path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behavior of continuous quantum measurement. Examples are given for the qubit case. For qubit measurement with zero-qubit Hamiltonian, we find analytic solutions for average trajectories ...
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    We generalize and extend the stochastic path-integral formalism and action principle for continuous quantum measurement introduced in Chantasri, Dressel, and Jordan [Phys. Rev. A 88, 042110 (2013)], where the optimal dynamics, such as the most likely paths, is obtained by extremizing the action of the stochastic path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behavior of continuous quantum measurement. Examples are given for the qubit case. For qubit measurement with zero-qubit Hamiltonian, we find analytic solutions for average trajectories and their variances while conditioning on fixed initial and final states. For qubit measurement with unitary evolution, we use the perturbation method to compute expectation values, variances, and multi-time-correlation functions of qubit trajectories in the short-time regime. Moreover, we consider continuous qubit measurement with feedback control, using the action principle to investigate the global dynamics of its most likely paths, and finding that in an ideal case, qubit state stabilization at any desired pure state is possible with linear feedback. We also illustrate the power of the functional method by computing correlation functions for the qubit trajectories with a feedback loop to stabilize the qubit Rabi frequency.
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    Journal Title
    Physical Review A
    Volume
    92
    Issue
    3
    DOI
    https://doi.org/10.1103/PhysRevA.92.032125
    Copyright Statement
    © 2015 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Quantum Physics not elsewhere classified
    Publication URI
    http://hdl.handle.net/10072/347935
    Collection
    • Journal articles

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