Simulating spin-orbit coupled Bose-Einstein condensates: a concise overview for non-experts

Cold ensembles of bosons are a useful platform for studying many-body quantum states present in quantum technologies, and simulations of these systems are convenient for streamlining design of such technologies. This paper provides an overview of spin-orbit coupled Bose-Einstein condensates (SOC BECs), along with an overview of simulation methods and a case study on a novel "microemulsion" phase. These SOC-BECs are further described in the context of coherent states quantum field theory, utilizing the complex Langevin sampling scheme as a numerical algorithm. This approach for studying SOC BECs is a versatile and powerful alternative to particle-based methods and has promise for simulating other bosonic quantum states.