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All-order momentum correlation functions associated with the time-of-flightspectroscopy of three spinless ultracold bosonic interacting neutral atomsconfined in a linear three-well optical trap are presented. The underlyingHamiltonian employed for the interacting atoms is an augmented three-siteHubbard model. Our investigations target matter-wave interference of massiveparticles, aiming at the establishment of experimental protocols forcharacterizing the quantum states of trapped attractively or repulsivelyinteracting ultracold particles, with variable interaction strength. Themanifested advantages and deep physical insights that can be gained through theemployment of the results of our study for a comprehensive understanding of thenature of the quantum states of interacting many-particle systems, via analysisof the all-order (that is 1st, 2nd and 3rd) momentum correlation functions forthree bosonic atoms in a three well confinement, are illustrated and discussedin the context of time-of-flight inteferometric interrogations of theinteraction-strength-induced emergent quantum phase transition from the Mottinsulating phase to the superfluid one. Furthermore, we discuss that ourinteferometric interrogations establish strong analogies with thequantum-optics interference of three photons, including the aspects of genuinethree-photon interference, which are focal to explorations targeting thedevelopment and implementation of quantum information applications and quantumcomputing.

physical review. a/physical review, a

All-order momentum correlations of three ultracold bosonic atoms  confined in triple-well traps: Signatures of emergent many-body quantum phase  transitions and analogies with three-photon quantum-optics interference