Observation of nonlinear spin dynamics and squeezing in a BEC using dynamic decoupling

We study the evolution of a Bose-Einstein Condensate (BEC) in two-state superposition due to inter-state interactions. Using population imbalanced dynamic decoupling scheme, we measure interactions while canceling intra-state density shifts and external noise sources. Our measurements show low statistical uncertainties for both magnetic sensitive insensitive superpositions, indicating that successfully decoupled our system from strong noises. experimentally Bloch sphere representing general states is "twisted" by interactions, twist rate depends on difference between scattering lengths $a_{22}+a_{11}-2a_{12}$. use non-linear spin dynamics scheme demonstrate squeezing gaussian noise, showing $2.79 \pm 0.43$ dB when starting with noisy state applying 160 echo pulses. Which can be used increase sensitivity there are errors preparation. results allow better understanding inter-atomic potentials \textsuperscript{87}Rb. beyond standard quantum limit observing polaron physics close Feshbach resonance, where diverge, noises ever present.