Control Schemes of Quantum-Based Pico-Newton Force Measurement

We propose control-measurement schemes for flux-quantum-based pico-newton force metrology. A micron-sized superconducting ring placed in magnetic field gradients can serve as a pico-newton force gauge. Constant-force steps can be realized by controlling the flux quanta in the superconductor ring. Two different schemes are proposed to control and measure the number of flux quanta in the ring. They are the fixed bias-flux mode and the fixed bias-current mode. In the fixed bias-flux (bias-current) mode, external bias-flux (transport bias-current) is fixed just below the resistive transition and entry of the flux quanta is monitored by counting the voltage bumps with increasing the bias current (the external flux). At the targeted number of flux quanta, bias current and flux are reset to zero. The number of flux quanta trapped in the ring can be confirmed by counting the voltage bumps with increasing the bias current up to the maximum critical current of the ring. Simultaneous flux control and force measurement is made by measuring force steps in field gradient with counting the number of flux quanta exciting the ring with increasing the bias current.