Geometric phase kickback in a mesoscopic qubit-oscillator system

Source: arXiv


We illustrate a reverse Von Neumann measurement scheme in which a geometric
phase induced on a quantum harmonic oscillator is measured using a microscopic
qubit as a probe. We show how such a phase, generated by a cyclic evolution in
the phase space of the harmonic oscillator, can be kicked back on the qubit,
which plays the role of a quantum interferometer. We also extend our study to
finite-temperature dissipative Markovian dynamics and discuss potential
implementations in micro and nano-mechanical devices coupled to an effective
two-level system.

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    • "One may show more generally that the area of an arbitrary closed circuit will appear in this exponential. The proof (also discussed in [5]) goes as follows: consider an arbitrary closed curve in phase space made by a sequence of optomechanical interactions. One may break this sequence into a series of small but finite phase space displacements and then write the overall unitary operator as a product of each displacement. "
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    ABSTRACT: We demonstrate that a geometric phase, generated via a sequence of four optomechanical interactions, can be used to increase, or generate nonlinearities in the unitary evolution of a mechanical resonator. Interactions of this form lead to new mechanisms for preparing mechanical squeezed states, and preparation of non-classical states with significant Wigner negativity.
    Full-text · Article · Oct 2012 · New Journal of Physics