Motional quantum sensing beyond the standard quantum limit with 2D arrays of trapped ions*

Quantum sensing protocols using trapped-ions can enable the detection of weak electric fields (<1 nV/m) by sensing displacements surpassing the Standard Quantum Limit (SQL) – the sensitivity achievable with a motional coherent state. Here, we present experiments of a many-body quantum-enhanced sensor to detect weak displacements and electric fields using large 2D crystal arrays of approximately 150 trapped ions. The center-of-mass vibrational mode of the crystal serves as a high-Q mechanical oscillator and the collective electronic spin as the measurement device.

The oscillator and collective spin are entangled using a spin-dependent optical dipole force, and a many-body echo protocol allows us to avoid quantum back-action and effectively cancel detrimental thermal noise.  We report a quantum enhanced sensitivity to displacements of  8.8 ± 0.4 dB below the SQL and a sensitivity for measuring electric fields of 240 ± 40 nV/m in 1 second (240 nVm^-1Hz^-1/2).  These sensitivities are currently limited by 40 Hz frequency fluctuations of the 1.6 MHz vibrational mode.  With future improvements, electric field sensitivities below 1 nV/m may be possible, which could enable searches for dark matter.