We demonstrate that reversible dephasing via inhomogeneous broadening can greatly reduce collective quantum state rotation errors, and observe the suppression of rotation errors by more than 21 dB in the context of collective population measurements of the spin states of an ensemble of laser cooled and trapped 87Rb atoms. The large reduction in rotation noise enables direct resolution of spin state populations 13(1) dB below the fundamental quantum projection noise limit. Further, the spin state measurement projects the system into an entangled state with 9.5(5) dB of directly observed spectroscopic enhancement (squeezing) relative to the standard quantum limit, whereas no enhancement would have been obtained without the suppression of rotation errors.
References
A different measurement sequence (Ref. 24) that avoids any rotations achieved a comparable amount of directly observed spin squeezing in the same system without relying on dephased rotations, but only by sacrificing a factor of two in fundamental measurement resolution. This additional factor of two was not realized in this work due to the probe laser's frequency noise coupling more strongly into the measurement sequence of Fig. 3.
The noise sources contributing to R in our experiment are characterized in the supplementary material of Ref. [24]. The primary source of noise which correlates Rbck and Rrot is noise from state-changing transitions. This causes a negligible over-estimation of rotation-added noise at high Mp in the sequence of Fig. 3(b) by a value approximately 27 dB below the projection noise level.
