Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas
Tyler J. Volkoff, Uwe R. Fischer · Physical Review A · 2016
We calculate a measure of superposition macroscopicity $\mathcal{M}$ for a superposition of screening current states in a superconducting flux qubit (SFQ), by relating $\mathcal{M}$ to the action of an instanton trajectory connecting the potential wells of the flux qubit. When a magnetized Bose-Einstein condensed (BEC) gas containing ${N}_{B}\ensuremath{\sim}O({10}^{6})$ atoms is brought into a $O(1) \ensuremath{\mu}\text{m}$ proximity of the flux qubit in an experimentally realistic geometry, we demonstrate the appearance of a twofold to fivefold amplification of $\mathcal{M}$ over the bare value without the BEC, by calculating the instanton trajectory action from the microscopically derived effective flux Lagrangian of a hybrid quantum system composed of the flux qubit and a spin-$F$ atomic Bose gas. Exploiting the connection between $\mathcal{M}$ and the maximal metrological usefulness of a multimode superposition state, we show that amplification of $\mathcal{M}$ in the ground state of the hybrid system is equivalent to a decrease in the quantum Cram\'er-Rao bound for estimation of an externally applied flux. Our result therefore demonstrates the increased usefulness of the BEC-SFQ hybrid system as a sensor of ultraweak magnetic fields below the standard quantum limit.