We demonstrate a complete, probabilistic quantum dynamical simulation of the standard nonlinear Hamiltonian of optomechanics, including decoherence at finite temperatures. Robust entanglement of an optical pulse with the oscillator is predicted, as well as strong quantum steering between the optical and mechanical systems. Importantly, our probabilistic quantum simulation method uses the positive-P technique, which is scalable to large Hilbert spaces.
Criteria suitable for measuring entanglement between two different potential wells in a Bose- Einstein condensation (BEC) are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen (EPR) paradox.
