Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas

Abstract

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 $N_B\sim \mathcal{O}(10^6)$ atoms is brought into a $\mathcal{O}(1)$ $\mu \text{m}$ proximity of the flux qubit in an experimentally realistic geometry, we demonstrate the appearance of a two- to five-fold amplification of $\mathcal{M}$ over the bare value without the BEC, by calculating the instantion 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 Cramér-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.

10 pages, 2 figures

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Cited by in corpus (1)

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