Joint estimation of a two-phase spin rotation beyond classical limit
arxiv(2023)
Abstract
Quantum metrology employs entanglement to enhance measurement precision. The
focus and progress so far have primarily centered on estimating a single
parameter. In diverse application scenarios, the estimation of more than one
single parameter is often required. Joint estimation of multiple parameters can
benefit from additional advantages for further enhanced precision. Here we
report quantum-enhanced measurement of simultaneous spin rotations around two
orthogonal axes, making use of spin-nematic squeezing in an atomic
Bose-Einstein condensate. Aided by the $F=2$ atomic ground hyperfine manifold
coupled to the nematic-squeezed $F=1$ states as an auxiliary field through a
sequence of microwave (MW) pulses, simultaneous measurement of multiple spin-1
observables is demonstrated, reaching an enhancement of 3.3 to 6.3 decibels
(dB) beyond the classical limit over a wide range of rotation angles. Our work
realizes the first enhanced multi-parameter estimation using entangled massive
particles as a probe. The techniques developed and the protocols implemented
also highlight the application of two-mode squeezed vacuum states in
quantum-enhanced sensing of noncommuting spin rotations simultaneously.
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