Measurable entanglement criterion for extended Bose-Hubbard model

Abstract: Cold atoms in optical lattice represent a quantum system of fundamental importance as they enable the study of many-body physics in a controllable way. It is thus essential to develop theoretical and experimental tools to explore quantum correlation in such systems to advance our understanding of many-body interactions. While previous works have identified some profound aspects of quantum entanglement via e.g. entanglement entropy, there exists a critical demand to have an experimentally accessible tool to investigate many-body quantum entanglement in a broad context. We present an entanglement criterion characterizing collective entanglement among lattice sites and enabling experimental observation readily. Our criterion witnesses phase transitions such as Mott insulator--superfluid and Mott insulator--charge density wave transitions in a measurable way and can be experimentally tested via Raman scattering or time-of-flight expansion approach thus within the reach of current technology.