Scale-invariant spin dynamics and the quantum limits of field sensing

Abstract

We describe quantum limits to field sensing that relate noise, geometry and measurement duration to fundamental constants, with no reference to particle number. We cast the Tesche and Clarke (TC) bound on dc-SQUID sensitivity as such a limit, and find analogous limits for volumetric spin-precession magnetometers. We describe how randomly-arrayed spins, coupled to an external magnetic field of interest and to each other by the magnetic dipole-dipole interaction, execute a spin dynamics that depolarizes the spin ensemble even in the absence of coupling to an external reservoir. We show the resulting spin dynamics are scale invariant, with a depolarization rate proportional to spin number density and thus a number-independent quantum limit on the energy resolution per bandwidth $E_R$. Numerically, we find $E_R\ge \alpha \hslash$, $\alpha \sim 1$, in agreement with the TC limit, for paradigmatic spin-based measurements of static and oscillating magnetic fields.

arXiv comment14 pages, 4 figures, 56 references

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Cited by in corpus (5)

• Quantum limits to the energy resolution of magnetic field sensors
• Quantum Sensing in Tweezer Arrays: Optical Magnetometry on an Individual-Atom Sensor Grid
• Surpassing the Energy Resolution Limit with ferromagnetic torque sensors
• Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below $\hslash$
• Optically Pumped Magnetometer with High Spatial Resolution Magnetic Guide for the Detection of Magnetic Droplets in a Microfluidic Channel