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

TL;DR

This paper demonstrates that placing a magnetized Bose-Einstein condensate near a superconducting flux qubit significantly amplifies its superposition macroscopicity, enhancing its potential as a sensitive magnetic field sensor beyond quantum limits.

Contribution

The study introduces a microscopic calculation showing how a magnetized BEC amplifies the superposition macroscopicity of a flux qubit, improving quantum sensing capabilities.

Findings

Amplification of superposition macroscopicity by 2- to 5-fold with BEC proximity.

Enhanced quantum metrological usefulness for ultraweak magnetic field detection.

Decreased quantum Cramér-Rao bound indicating improved measurement precision.

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 Cram\'{e}r-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.