Metrologically useful states of spin-1 Bose condensates with macroscopic magnetization

Abstract

We study theoretically the usefulness of spin-1 Bose condensates with macroscopic magnetization in a homogeneous magnetic field for quantum metrology. We demonstrate Heisenberg scaling of the quantum Fisher information for states in thermal equilibrium. The scaling applies to both antiferromagnetic and ferromagnetic interactions. The effect preserves as long as fluctuations of magnetization are sufficiently small. Scaling of the quantum Fisher information with the total particle number is derived within the mean-field approach in the zero temperature limit and exactly in the high magnetic field limit for any temperature. The precision gain is intuitively explained owing to subtle features of the quasi-distribution function in phase space.

9 pages, 5 figures

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• Optimal atomic interferometry robust to detection noise using spin-1 atomic condensates
• Rapid production of many-body entanglement in spin-1 atoms via cavity output photon counting
• Efficient two-mode interferometers with spinor Bose-Einstein condensates
• Exploring the thermodynamics of spin-1 ${}^{87}$Rb Bose Gases with synthetic magnetization