## Experimental demonstration of nonlinear quantum metrology with optimal quantum state

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• ReceivedDec 27, 2017
• AcceptedMar 9, 2018
• PublishedMar 20, 2018
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### Abstract

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as $\mathrm{\Delta }\varphi \propto 1/{N}^{2}$ under quadratic phase accumulation, which is $1/N$ times smaller than the linear counterpart, where N is probe number. Here, we experimentally demonstrate the nonlinear quantum metrology by using a spin-I ($I>1/2$) nuclear magnetic resonance (NMR) ensemble that can be mapped into a system of $N=2I$ spin-1/2 particles and the quadratic interaction can be utilized for the quadratic phase accumulation. Our experimental results show that the phase uncertainty can scale as $\mathrm{\Delta }\varphi \propto 1/\left({N}^{2}-1\right)$ by optimizing the input states, when N is an odd number. In addition, the interferometric measurement with quadratic interaction provides a new way for estimating the quadrupolar coupling strength in an NMR system. Our system may be further extended to exotic nonlinear quantum metrology with higher order many-body interactions.

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