Nonlinear Interferometry Using Atomic Spinor Bose-einstein Condensates

Quantum metrology employs entanglement to improve measurement signal-to-noise ratio.The conventional approach based on reducing quantum noise with squeezed states demands low-noise detection.An alternative route magnifies signal instead by using non-linear interferometry with nonlinear‘path'splitter and recombiner,and is capable of en-hancing the robustness to detection noise.In this thesis,we focus on the design and im-plementation of nonlinear interferometer with atomic spinor Bose-Einstein condensates.Previous nonlinear interferometer requires the nonlinear‘path'recombining as the time reversal of splitting,which is difficult to realize in a general many-body system.To circumvent this challenge,in the first study,we present an idea for implementing nonlin-ear interferometry without invoking time reversal.Instead of time-reversed evolution,we time the system's return to the immediate vicinity of the initial state due to cyclic quan-tum dynamics.Utilizing the quasi-periodic spin mixing dynamics in a⁸⁷Rb atom spinor condensate as an example,we implement the first three-mode nonlinear interferometer and achieve a metrological gain of 3.87_-0⁺⁰..⁹9¹5decibels over the classical limit for a total of26500 atoms.The high precision we observe is attributed to the entangled non-Gaussian state generated by the long-term spin dynamics in the‘path'splitting.Therefore,this work also demonstrates,for the first time,the power of nonlinear interferometry in utiliz-ing non-Gaussian states for precision measurement.In the second work,we theoretically investigate the spin-nematic interferometer based on the spin-nematic squeezed state generated during the initial‘path'splitting stage of spin mixing dynamics.Such an interferometer works in the‘undepleted-pump'regime,where time reversal is realized by imprinting a phase of?/2 on the pump mode.Thanks to the large quantum Fisher information of spin-nematic squeezed state,and the short non-linear evolution time for deep squeezing,the nonlinear spin-nematic interferometer can provide the highest theoretical metrological gain of 18 d B at a total particle number of26500,and is significantly less sensitive to atom loss or detection noise in experiment.We hope it can be utilized to realize a high-precision atomic magnetometer in the future.