Measurements lay at the foundation of physical science, and their ultimate precision is normally set by the standard quantum limit (SQL). Entangled states such as spin squeezed states, can be used to break such limit, but previous experiments have largely been proof-of-principle, i.e., the absolute precision of those measurements, although beyond SQL, is relatively low. We have recently achieved spin squeezing for more than 100 billion atoms in a macroscopic vapor cell by quantum non-demolition measurements, exceeding the best angular resolving power in any spin squeezed state so far by 1000 times, with the aid of adiabatic pulse control and motional averaging. Then, we show that retrodiction measurements can further enhance the precision of traditional forward prediction measurements, which enables a quantum enhanced atomic magnetometer with femto-tesla-level sensitivity. Finally, we experimentally demonstrate that the combination of prediction and retrodiction measurements allow measurements of two non-commuting variables such as x and p, both below the SQL, “violating” the Heisenberg uncertainty relation.
 Bao et.al., Spin squeezing of 1011 atoms by prediction and retrodiction measurements, Nature 581, 159 (2020).
 Bao et.al., Retrodiction beyond Heisenberg uncertainty relation, Nat. Commun. 11, 5658 (2020)
Yanhong Xiao obtain
Seminar by the NYU-ECNU Institute of Physics at NYU Shanghai