Magnetometry with entangled atomic samples

Abstract

We present a theory for the estimation of a scalar or a vector magnetic field by its influence on an ensemble of trapped spin polarized atoms. The atoms interact off-resonantly with a continuous laser field, and the measurement of the polarization rotation of the probe light, induced by the dispersive atom-light coupling, leads to spin-squeezing of the atomic sample which enables an estimate of the magnetic field which is more precise than that expected from standard counting statistics. For polarized light and polarized atoms, a description of the non-classical components of the collective spin angular momentum for the atoms and the collective Stokes vectors of the light-field in terms of effective gaussian position and momentum variables is practically exact. The gaussian formalism describes the dynamics of the system very effectively and accounts explicitly for the back-action on the atoms due to measurement and for the estimate of the magnetic field. Multi-component magnetic fields are estimated by the measurement of suitably chosen atomic observables and precision and efficiency is gained by dividing the atomic gas in two or more samples which are entangled by the dispersive atom-light interaction.

8 pages, 11 figures

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• Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement
• Bayesian parameter inference from continuously monitored quantum systems
• Tensor polarizability and dispersive quantum measurement of multilevel atoms
• Differential atom interferometry beyond the standard quantum limit
• Classification of Spin-Nematic Squeezing in Spin-1 Collective Atomic Systems
• Estimation of fluctuating magnetic fields by an atomic magnetometer
• Dissipation-assisted preparation of steady spin-squeezed states of SiV centers
• Gaussian State Description of Squeezed Light
• Phase variance of squeezed vacuum states
• Magnetic-field gradiometer based on ultracold collisions
• Quantum back-action in spinor condensate magnetometry
• Entanglement-Constrained Quantum Metrology: Rapid Low-Entanglement Gains, Tapered High-Level Growth
• Delta-kick Squeezing
• Study of the spin kitten states in a strongly coupled spin-oscillator system