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Bulletin of the American Physical Society

A Qubit-Coupled Nanomechanical Resonator Integrated with a Superconducting CPW Cavity

Y. L. Hao, Francisco P. M. Rouxinol, Seung‐Bo Shim, Matthew LaHaye

Published Mar 5, 2014• 0 citations
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Bulletin of the American Physical Society•Feb 29, 2012•0 citations
We theoretically study the transmission properties and the PT -symmetry in a hybrid quantum electromechanical system consisting of a coplanar-waveguide (CPW) microwave cavity, a nanomechanical resonator (NAMR) and a superconducting transmon qubit, where the qubit works in the large detuning condition with both the CPW microwave cavity and the NAMR. By adjusting the NAMR-qubit coupling, we find that the transmissivity and the phase shift of the input field passing through the system can be tuned effectively. We also find that the effective electromechanical coupling can be greatly enhanced by adjusting the NAMR-qubit coupling. Furthermore, with the effective electromechanical coupling, we can realize the transition from the broken PT -symmetry phase to the unbroken PT -symmetry phase when both the cavity loss and the mechanical gain are considered. This work presents an effective way to manipulate the propagation characteristics and to study the PT -symmetry in a hybrid quantum electromechanical system.
We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper (Armour A D and Blencowe M P 2008 New. J. Phys. 10 095004). The implementation is based on the circuit quantum electrodynamics (QED) set-up, with the addition of a mechanical degree of freedom formed out of a suspended, doubly-clamped segment of the superconducting loop of a dc SQUID located directly opposite the centre conductor of a coplanar waveguide (CPW). The relative merits of two SQUID based qubit realizations are addressed, in particular a capacitively coupled charge qubit and inductively coupled flux qubit. It is found that both realizations are equally promising, with comparable qubit–mechanical resonator mode as well as qubit–microwave resonator mode coupling strengths.
We study a tripartite quantum system consisting of a coplanar-waveguide (CPW) resonator and a nanomechanical resonator (NAMR) connected by a flux qubit, where the flux qubit has a large detuning from both resonators. By a unitary transformation and a second-order approximation, we obtain a strong and controllable (i.e., magnetic-field-dependent) effective coupling between the NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting can be observed from the voltage-fluctuation spectrum of the CPW resonator. We further study the properties of single-photon transport as inferred from the reflectance or equivalently the transmittance. We show that the reflectance and the corresponding phase-shift spectra both exhibit doublet of narrow spectral features due to vacuum Rabi splitting. By tuning the external magnetic field, the reflectance and the phase shift can be varied from 0 to 1 and $\ensuremath{-}\ensuremath{\pi}$ to $\ensuremath{\pi}$, respectively. The results indicate that this hybrid quantum system can act as a quantum router.