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arXiv:1506.01801 · Physical Review A

Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit

Wei Xiong, Da-Yu Jin, Jun Jing, Chi‐Hang Lam, J. Q. You

Published Sep 21, 2015• 30 citations

Abstract

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.

DOI: 10.1103/physreva.92.032318

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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.

We have experimentally studied a superconducting flux qubit strongly coupled to a single mode of a high-quality transmission-type coplanar-waveguide resonator. The qubit-resonator coupling is revealed in the resonator transmission spectrum as a vacuum Rabi splitting. In the dispersive regime the qubit energy levels are spectroscopically probed. We observe a shift in the qubit transition frequency that linearly depends on the number of photons in the resonator, which is attributed to the ac-Zeeman shift. The observations are in agreement with the theoretical predictions.

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 investigate the hybrid quantum system of a superconducting flux qubit, a single electronic spin associated with a negatively charged nitrogen vacancy (NV) center in diamond, and a high-quality magnetized nanomechanical resonator (NAMR). It is shown that the quantized motion of the NAMR can strongly couple to both the NV spin and the flux qubit. We estimate that the coupling strength of the NAMR to both the NV spin and the flux qubit can be about 2 π × 100 kHz, which is one order of magnitude larger than direct spin–qubit coupling. This enables the quantum state transfer to be faster and more robust against decoherence. The present work may provide an appealing way for quantum information processing based on hybrid solid-state quantum systems.

We have fabricated and characterized systems consisting of superconducting quantum bits (qubits) of the transmon type, coupled to a tunable transmission line resonator. The resonator consists of a superconducting quarter wavelength coplanar waveguide (CPW) resonator that is made tunable by terminating the transmission line to ground through a superconducting quantum interference device (SQUID). Here we present measurements on two devices where we observe Rabi oscillations as we drive the qubit, and vacuum Rabi splitting both as we tune the qubits into resonance with the resonator and as we tune the resonator into resonance with the qubits. We also observe coherent interaction between two resonant qubits. In addition, we demonstrate that we can calculate the response very accurately using a multilevel Hamiltonian.

We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generalized situations where the superconducting Josephson junction system is a multi-level system. We also address the practical issues concerning experimental realization.

We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.