I worked on cold atomic and optical systems and investigated non-classical properties of these systems during my PhD. In this talk, I will start with very brief introduction of cold atoms and present two projects of my work. The project I will talk about first is about spin-orbit coupling in ultracold gases. Spin-obit coupled (SOC) systems have become an interesting laboratory for exploring new physics in ultracold gases. However, as condensates are only weakly correlated, the influence of interactions on the spin-orbit coupling is only weak. In the project, we have explored the influence of strong contact interactions on a SOC quantum system, using exact solutions to the paradigmatic two particle model. Several distinct effects that are not present in the mean-field limit can be identified. Even though the system we consider is bosonic, we find that a regime exists in which the competition between the contact and spin-orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. 
The second topic is about proposing a new condition for quantum simulation. If one aims to perform quantum simulation, one usually designs a system such that its Hamiltonian or time evolution operator is the same as the target system. This often requires quantum simulators to be quite complex setups. In this work, we have proposed a way to relax the requirement by not only designing the Hamiltonian but also considering the initial state. As an example, we showed that one-axis twisting, which is the dynamics governed by infinite range interactions, can be simulated by using a nearest-neighbour interaction system (Heisenberg XXX model) with an external field.