Quantum hydrodynamics of spin-current squeezing in spinor Bose-Einstein condensates

Hydrodynamic description of spinor Bose-Einstein condensates provides a mean-field description equivalent to the multi-component Gross-Pitaevskii equation. We generalize it in the second quantized formalism so that it can treat highly nonclassical systems that cannot be analyzed by the perturbation theory. This formalism can be used to explore strongly quantum-mechanically correlated systems such as spin squeezed states and entangled spin currents propagating to the different directions. We numerically solve the second quantized hydrodynamic equations under the single-mode approximation and show that the spin-current squeezing can be realized in spin-squeezed systems.