Nonclassicality in an atom-molecule Bose-Einstein condensate: Higher-order squeezing, antibunching and entanglement

The transient quantum statistical properties of the atoms and molecules in an atom-molecule BEC system are investigated by obtaining a third-order perturbative solution of the Heisenberg's equations of motion corresponding to the Hamiltonian of the system, where two atoms can collide to form a molecule. Time dependent quantities, like two boson correlation, entanglement, squeezing, antibunching, etc., are computed, and their properties are compared. It is established that the atom-molecule BEC system is highly nonclassical as lower-order and higher-order squeezing and antibunching in pure (atomic and molecular) modes, squeezing and antibunching in compound mode, and lower-order and higher-order entanglement in compound mode can be observed in the atom-molecule BEC system. Exact numerical results are also reported and the analytic results obtained using the perturbative technique are shown to agree with the exact numerical results.