Interaction-based nonlinear quantum metrology with a cold atomic ensemble

摘要: In this manuscript we present an experimental and theoretical investigation of quantum-noise-limited measurement by nonlinear interferometry, or from another perspective, interaction-based measurement. The work is performed using a polarization-based quantum interface between propagating light pulses cold rubidium-87 atoms trapped in optical dipole trap. We first review the theory metrology estimation theory, describe proposals for as developed group Carlton M. Caves University New Mexico. then our proposal, made 2010, to implement group's ideas interactions atomic ensemble spin To evaluate proposal develop two approaches, extension collective variables approach, often employed interfaces ensembles, processes. This results effective Hamiltonian containing terms form described group, demonstrates qualitative equivalence schemes. second approach uses Maxwell-Bloch equations propagation through ensemble, including inhomogeneities relaxation effects. latter method makes quantitative predictions about rotation signals under realistic conditions. We implementation light-atom interface. We existing trapping probing system, focusing on characteristics that make it suitable shot-noise-limited projection-noise-limited measurements. adaptations use apparatus with shorter, higher-intensity required measurement, well characterization photodetection system these modified conditions. Calibration polarization versus probe laser detuning allows us produce nearly pure signal. Finally, are presented showing over three orders magnitude photon number N. consistent models confirm major prediction work, two-photon interaction gives scaling sensitivity as N^{-3/2}. A brief discussion relates observation discussions ?Heiseinberg limit? metrology, possible further applications techniques.