Quantum-enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate

Quantum entanglement can provide enhanced measurement precision beyond the standard quantum limit, the highest precision achievable with classical means. However, observations with a large enhancement remain challenging due to experimental limitations in the preparation, control and detection of entanglement. Here we report a nonlinear interferometry protocol with echoed spin-nematic squeezing in a spinor atomic Bose–Einstein condensate. We generate spin-nematic squeezed states through spin-mixing dynamics, an atomic analogue of optical four-wave mixing. The squeezed states are refocused back to the vicinity of the classical initial state by a state-flip operation that resembles spin-echo techniques, which leads to encoded phases preferentially amplified over noise. Using a large ensemble of 26,400 atoms, we observe a sensitivity of 15.6 ± 0.5 dB beyond the standard quantum limit for detecting small-angle Rabi rotation, as well as 16.6 ± 1.1 dB for phase sensing in a Ramsey-like interferometry application. Our results highlight the many-body coherence of spin-nematic squeezed states and point to their possible quantum metrological application in atomic magnetometers, atomic clocks and fundamental tests of Lorentz symmetry violations.