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 internal degree 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 show 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 detected by driving the hybridized-mode with mean-occupancy well below one photon. By tuning qubit away from the cavity, electromechanical coupling can be enhanced to 40 kHz. In this limit, a small coherent drive on the mechanical resonator results in the splitting of qubit spectrum, and we observe interference signature arising from the Landau-Zener-Stückelberg effect. With improvements in qubit coherence, this system offers a platform to realize rich interactions and could potentially provide full control over the quantum motional states.

At low temperatures, microwave cavities are often preferred for the readout and control of a variety of systems. In this paper, we present design and measurements on an optomechanical device based on a 3-dimensional rectangular waveguide cavity. We show that by suitably modifying the electromagnetic field corresponding to the fundamental mode of the cavity, the equivalent circuit capacitance can be reduced to 29 fF. By coupling a mechanical resonator to the modified electromagnetic mode of the cavity, we achieved a capacitance participation ratio of 43 %. We demonstrate an optomechanical cooperativity, C ∼ 40, characterized by performing measurements in the optomechanically-induced absorption (OMIA) limit. In addition, due to a low-impedance environment between the two-halves of the cavity, our design has the flexibility of incorporating a DC bias across the mechanical resonator, often a desired feature in tunable optomechanical devices.

Sodium ion batteries are considered as a potential alternative to existing Li‐ion batteries. Layered transition metal oxides are found to be suitable cathode candidates for Na‐ion batteries. In this study, solid state synthesis of P2‐Na0.7Ni0.45Mn0.55O2 with different Mg substitutions is reported. The synthesized materials are characterized thoroughly using X‐ray diffraction (XRD), field‐emission scanning electron microscopy (FE‐SEM), energy dispersive spectroscopy (EDS), inductively coupled plasma atomic emission spectroscopy (ICP‐AES), and x‐ray photoemission spectroscopy (XPS) analysis. SEM analysis reveals the morphology of synthesized materials to layered structure with a particle size in the range of 5–50 µm. Powder XRD shows all synthesized materials of P2 structure irrespective of Mg substitution. A spurious P3 phase is observed in 0% and 5% of Mg substituted samples which are absent in 10% and 15% of Mg substituted materials. Electrochemical performance analysis shows specific capacity reduces with Mg substitution whereas mid‐voltage reaches maximum up to 3.5 V with 10% substitution. 10% Mg substituted NMO shows a specific capacity 105 mA h g−1 in the voltage ranges of 2–4.3 V versus Na/Na+ with excellent cycling stability and rate capability.

With artificially engineered systems, it is now possible to realize the coherent interaction rate, which can become comparable to the mode frequencies, a regime known as ultrastrong coupling (USC). We experimentally realize a cavity-electromechanical device using a superconducting waveguide cavity and a mechanical resonator. In the presence of a strong pump, the mechanical-polaritons splitting can nearly reach 81% of the mechanical frequency, overwhelming all the dissipation rates. Approaching the USC limit, the steady-state response becomes unstable. We systematically measure the boundary of the unstable response while varying the pump parameters. The unstable dynamics display rich phases, such as selfinduced oscillations, period-doubling bifurcation, and period-tripling oscillations, ultimately leading to the chaotic behavior. The experimental results and their theoretical modeling suggest the importance of residual nonlinear interaction terms in the weak-dissipative regime.