Hybrid devices based on the superconducting qubits have emerged as a promising platform for controlling the quantum states of macroscopic resonators. The nonlinearity added by a qubitcan be a valuable resource for such control. Here we study a hybrid system consisting of a mechanical resonator longitudinally coupled to a transmon qubit. The qubit readout can be done by coupling to a readout mode like in c-QED setup. The coupling between the mechanical resonator and transmon qubit can be implemented by modulation of the SQUID inductance. In such a tri-partite system, we analyze the steady-state occupation of the mechanical mode when all three modes are dispersively coupled. We use the quantum-noise and the Lindblad formalism to show that the sideband cooling of the mechanical mode to its ground state is achievable. We further experimentally demonstrate that measurements of the thermomechanical motion is possible in the dispersive limit, while maintaining a large coupling between qubit and mechanical mode. Our theoretical calculations suggest that single-photon strong coupling is within the experimental reach in such hybrid devices.
Superconducting qubits utilize the strong non-linearity of the Josephson junctions. Control over the Josephson nonlinearity, either by a current bias or by the magnetic flux, can bea valuable resource that brings tunability in the hybrid system consisting of superconducting qubits. To enable such a control, here we incorporate a fast-flux line for a frequency tunable transmon qubit in 3D cavity architecture. We investigate the flux-dependent dynamic range, relaxation from unconfined states, and the bandwidth of the flux-line. Using time-domain measurements, we probe transmon’s relaxation from higher energy levels after populating the cavity with ≈2.1×104 photons. For the device used in the experiment, we find a resurgence time corresponding to the recovery of coherence to be 4.8~μs. We use a fast-flux line to tune the qubit frequency and demonstrate the swap of a single excitation between cavity and qubit mode. By measuring the deviation in the transferred population from the theoretical prediction, we estimate the bandwidth of the flux line to be ≈~100~MHz, limited by the parasitic effect in the design. These results suggest that the approach taken here to implement a fast-flux line in a 3D cavity could be helpful for the hybrid devices based on the superconducting qubit.
Control over the quantum states of a massive oscillator is important for several technological applications and to test the fundamental limits of quantum mechanics. Addition of an internaldegree of freedom to the oscillator could be a valuable resource for such control. Recently, hybrid electromechanical systems using superconducting qubits, based on electric-charge mediated coupling, have been quite successful. Here, we realize a hybrid device, consisting of a superconducting transmon qubit and a mechanical resonator coupled using the magnetic-flux. The coupling stems from the quantum interference of the superconducting phase across the tunnel junctions. We demonstrate a vacuum electromechanical coupling rate up to 4 kHz by making the transmon qubit resonant with the readout cavity. Consequently, thermal-motion of the mechanical resonator is detectable by driving the dressed-mode with mean-occupancy well below one photon. By tuning the qubit away from the cavity, electromechanical coupling between qubit and mechanical mode can be further enhanced to 40 kHz. In this limit, a small coherent drive of the mechanical resonator results into the splitting of qubit spectrum and we observe interference signature arising from the Landau-Zener-Stuckelberg effect. With further improvements in the qubit coherence, this system offers a novel platform to realize rich interactions and could potentially provide full control over the quantum motional states.