Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Xinfang Nie, Jiahao Huang, Zhaokai Li, Wenqiang Zheng, Chaohong Lee, Xinhua Peng, Jiangfeng Du

Index: 10.1016/j.scib.2018.03.007

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Abstract

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as Δϕ∝1/N2Δϕ∝1/N2 under quadratic phase accumulation, which is 1/N1/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>1/2I>1/2) nuclear magnetic resonance (NMR) ensemble that can be mapped into a system of N=2IN=2I spin-1/21/2 particles and the quadratic interaction can be utilized for the quadratic phase accumulation. Our experimental results show that the phase uncertainty can scale as Δϕ∝1/(N2-1)Δϕ∝1/(N2-1) 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.