Deterministic Squeezed States with Joint Measurements and Feedback

Joint measurement of many qubits or atoms is a powerful way to create entanglement for precision measurement and quantum information science. However, the random quantum collapse resulting from the joint measurement also leads to randomness in \textit{which } entangled state is created. We present an experiment in which we apply real-time feedback to eliminate the randomness generated during the joint measurement of $5 \times 10^4$ laser-cooled Rb atoms. The feedback effectively steers the quantum state to a desired squeezed state. After feedback, the final state achieves a directly observed phase resolution variance up to 7.4(6) dB below the standard quantum limit for unentangled atoms. The entanglement and improved measurement capability of these states can be realized without retaining knowledge of the joint measurement’s outcome, possibly opening new applications for spin squeezed states generated via joint measurement.