Measurements with prediction and retrodiction on the collective spin of 10^{11} atoms beat the standard quantum limit

Understand

Quantum probes using $N$ uncorrelated particles give a limit on the measurement sensitivity referred to as the standard quantum limit (SQL).

• The SQL, however, can be overcome by exploiting quantum entangled states, such as spin squeezed states.
• We report generation of a quantum state, that surpasses the SQL for probing of the collective spin of $10^{11}$ $\text{Rb}$ atoms contained in a vapor cell.
• The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements, and we apply the theory of past quantum states to obtain the spin state information from the outcomes of both earlier and later QND measurements.