Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Area of Science:

• Quantum physics
• Metrology
• Nuclear Magnetic Resonance (NMR)

Background:

• Nonlinear quantum metrology offers potential for superior precision scaling compared to linear approaches.
• Phase estimation uncertainty can scale as Δϕ∝1/N², a significant improvement over the linear Δϕ∝1/N scaling.

Purpose of the Study:

• To experimentally demonstrate nonlinear quantum metrology using a spin-I nuclear magnetic resonance (NMR) ensemble.
• To achieve and verify the predicted precision scaling for phase estimation in a nonlinear regime.

Main Methods:

• Utilized a spin-I (I>1/2) NMR ensemble, effectively mapping to N=2I spin-1/2 particles.
• Implemented quadratic phase accumulation through engineered interactions within the NMR system.
• Optimized input states to achieve the desired scaling.

Main Results:

• Experimental demonstration of nonlinear quantum metrology with phase uncertainty scaling as Δϕ∝1/(N²-1) for odd N.
• Successful application of interferometric measurement with quadratic interaction for estimating quadrupolar coupling strength in NMR.

Conclusions:

• The study validates the enhanced precision of nonlinear quantum metrology in an experimental NMR setting.
• The developed method offers a novel approach for quadrupolar coupling strength estimation.
• The system provides a foundation for exploring advanced nonlinear quantum metrology with higher-order interactions.