Deterministic Squeezed States with Joint Measurements and Feedback

Abstract

We demonstrate the creation of entangled, spin-squeezed states using a collective, or joint, measurement and real-time feedback. The pseudospin state of an ensemble of $N= 5\times 10^4$ laser-cooled $^{87}$Rb atoms is deterministically driven to a specified population state with angular resolution that is a factor of 5.5(8) [7.4(6)~dB] in variance below the standard quantum limit for unentangled atoms --- comparable to the best enhancements using only unitary evolution. Without feedback, conditioning on the outcome of the joint premeasurement, we directly observe up to 59(8) times [17.7(6)~dB] improvement in quantum phase variance relative to the standard quantum limit for $N=4\times 10^5$ atoms. This is one of the largest reported entanglement enhancements to date in any system.