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.