Sub-SQL electronic field sensing by simultaneously using quantum entanglements and squeezings

Abstract: Quantum entanglement and quantum squeezing are two most typical approaches to beat the standard quantum limit (SQL) of the sensitive phase estimations in quantum metrology. Each of them has already been utilized individually to improve the sensitivity of electric field sensing with the trapped ion platform, but the upper bound of the demonstrated sensitivity gain is very limited, i.e., the experimental 3dB and theoretical 6dB, over the SQL. Here, by simultaneously using the internal (spin)-external (oscillator) state entanglements and the oscillator squeezings to effectively amplify the accumulation phase, we show that these sensitivity gains can be effectively surpassed. Hopefully, the proposal provides a novel approach to the stronger beaten of the SQL for the sensitive sensings of the desired electric field and also the other metrologies.