Geometric-phase backaction in a mesoscopic qubit-oscillator system

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 nanomechanical devices coupled to an effective two-level system.

Figure 1

The oscillator's conditional dynamics pictured in phase space. (a) The oscillator is displaced along a square whose area is proportional to the phase $\theta$. (b) The oscillator is displaced while undergoing a dissipative process. Here ${\widehat{\mathcal{U}}}_{\delta t}^{\varphi }$ and ${\widehat{\mathcal{D}}}_{\delta t}$ are the superoperators describing the unitary and dissipative evolution of duration $\delta t$, respectively.

Figure 2

(a) Probabilities ${\mathcal{P}}_{+}$ and ${\mathcal{P}}_{-}$ versus the displacement ${\alpha }_0$ and the parameter V for $\eta /\gamma =0.05$ and $\gamma T_1=20$. (b) The same probabilities versus $V$ for ${\alpha }_0=0$ and the same parameters as in (a).