Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as Delta phi alpha 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 (1 > 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 Delta phi alpha 1/(N-2 - 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. (C) 2018 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.