  Quantum simulators built from ultracold atoms promise to study quantum
phenomena in interacting many-body systems. However, it remains a challenge to
experimentally prepare strongly correlated continuous systems such that the
properties are dominated by quantum fluctuations. Here, we show how to enhance
the quantum correlations in a one-dimensional multimode bosonic Josephson
junction, which is a quantum simulator of the sine-Gordon field theory. Our
approach is based on the ability to track the non-equilibrium dynamics of
quantum properties. After creating a bosonic Josephson junction at the stable
fixed point of the classical phase space, we observe squeezing oscillations in
the two conjugate variables. We show that the squeezing oscillation frequency
can be tuned by more than one order of magnitude, and we are able to achieve a
spin squeezing close to 10 dB by utilising these oscillatory dynamics. The
impact of improved spin squeezing is directly revealed by detecting enhanced
spatial phase correlations between decoupled condensates. Our work provides new
ways for engineering correlations and entanglement in the external degree of
freedom of interacting many-body systems.
