Towards a micromechanical qubit based on quantized oscillations in superfluid helium

Superconducting circuits can exhibit quantized energy levels and long coherence times. Harnessing the anharmonicity offered by Josephson junctions, such circuits have been successfully employed as qubits, quantum limited amplifiers and sensors. Here, we consider superfluidity as the charge-neutral analogue of superconductivity. Both dissipationless mass flow and Josephson tunneling have been demonstrated in superfluid helium. We propose a quantum device, consisting of a superfluid weak link and a mechanical element. The superfluid motion in this device is quantized. The resulting discrete energy levels are resolvable at millikelvin temperatures essential to maintaining the superfluid state. Appropriate device engineering can yield the necessary nonlinearity to realize qubit functionality. Hence, this device can potentially operate as a charge-neutral, superfluid quantum bit with micron-sized dimensions and millisecond scale coherence time. We show that this quantum regime is within reach for a range of device designs.