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

Enhanced precision beyond standard quantum limit (SQL) can be provided by quantum entanglement. However, due to the difficulty of preparing, maintaining, manipulating and detecting entanglement, observing large enhancement is still a challenge. Here, we present interaction-based readout interferometry protocols based on echoing spin-nematic squeezing to achieve record high enhancement factors in atomic Bose-Einstein condensate. The echo is realized by a state-flip of the spin-nematic squeezed vacuum, which serves as the probe state and is refocused back to the vicinity of the initial coherent state while carrying out near noiseless amplification of a signal encoded. We observe a sensitivity of 15.6±0.5 decibels (dB) for a small-angle Rabi rotation beyond the three-mode SQL of 26400 atoms as well as 16.6±1.3 dB for phase sensing in a Ramsey interferometer. The absolute phase sensitivity for the latter extrapolates to 103 pT/√Hz at a probe volume of 18 μm³ for near-resonant microwave field sensing. Our work highlights the power of spin-nematic squeezing echo for quantum metrology. It could potentially find practical applications in atomic magnetometer, atomic clock, and atomic momentum interferometer.