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

Abstract

We calculate a measure of superposition macroscopicity M for a superposition of screening current states in a superconducting flux qubit (SFQ), by relating 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 similar to O (10(6)) atoms is brought into a O(1) mu m proximity of the flux qubit in an experimentally realistic geometry, we demonstrate the appearance of a twofold to fivefold amplification of 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 M and the maximal metrological usefulness of a multimode superposition state, we show that amplification of M in the ground state of the hybrid system is equivalent to a decrease in the quantum Cramer-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.