Quantum Enhanced Metrology For Simultaneous Multi-parameter Estimation

Quantum enhanced metrology concerns the study for precise measurements of phys-ical parameters based on the principles of quantum mechanics.It plays an important role in fundamental science and technology.This thesis focuses on estimating multiple pa-rameters simultaneously in quantum systems,with illustrative applications including im-proving the precision for Lorentz-symmetry violation in standard model extension with entangled atoms.First,to address the estimation of multiple phases associated with multiple modes,we propose a multi-mode interferometer using unentangled particles.We obtain the optimal probe state and the corresponding quantum Cramér-Rao bound depending on a given set of parameters.We conclude that estimating multiple parameters simultaneously will gen-erally outperform the precisions from estimating them individually.When the operators of generating multiple phases are mutually commuting,the measurement saturating the quantum Cramér-Rao bound exists theoretically.We prove that if(but not iff)the multi-mode splitting process₁is orthogonal,the combining process satisfying time reversal U₂=U₁^?followed by particle number detection afterwards provides the best precision allowed by the quantum Cramér-Rao bound for small phase shifts.We further present a scheme that estimate two parameters generated by joint non-commuting operators.Spin-nematic squeezed state,which exhibits squeezing in two sep-arate SU(2)subspaces,can be prepared in=1 spinor condensate.To take advantage of the metrological gain provided by spin-nematic squeezing in both subspaces,one needs to transfer part of the atoms to the auxillary F=2 state,leading to effective detection noise proportional to the total atomic number in a linear interferometric scheme.We propose to circumvent this difficulty by implementing nonlinear readout,based on an effective time reversal evolution.In addition,we also discuss the use of spin-echo pulses to counteract against the decoherence caused by ambient fluctuating magnetic field.Finally,we propose to test Lorentz-symmetry violation within the framework of standard-model extension with entanglement enhanced precision.For an atomic system with fixed5),the Lorentz-symmetry violation dynamics is analogous to a quadratic Zee-man shift,which can be estimated by an atomic interferometer.We present two types of symmetric entangled states of spin-1 atoms,the maximally entangled state and the bal-anced spin-1 Dicke state.The latter of which is readily available in deterministic fashion,while both can achieve precision beyond standard quantum limit theoretically.This offers additional incentives for pursuing practical applications of many-atom entangled states.