Controlling many-body synchronous revival dynamics and entanglement cycle of ultracold atoms with synthetic gauge fields

The exploration of tunneling dynamics in many-body quantum systems plays a pivotal role in realizing groundbreaking atomtronic devices and achieving precise control over entanglement. Here, we delve into the intricate many-body tunneling dynamics of ultracold atoms confined within a quadruple-well potential, with a particular emphasis on the manipulative role played by interatomic interactions and synthetic gauge fields. The quantum dynamics displayed by the system closely mimic the operations of qudit hybrid gates, which are comprised of two relatively independent sets of qudits. In the Rabi regime, which is characterized by strong coupling, we observe an intriguing phenomenon: the cyclic collapse and revival of discrete tunneling dynamics within two distinct qudits. Notably, this intricate dynamical behavior exhibits remarkable synchronous and anti-synchronous revival features, offering a unique opportunity to engineer many-body synchronization pulse signals. In the resonant tunneling regime, distinguished by strong interatomic interactions, we made a remarkable observation: the hybrid qudits undergo a dimensionality reduction, effectively transforming into a qudit. This dimensionality reduction is accompanied by an intriguing phenomenon: the periodicity of its dynamics is intimately intertwined with the occurrence of the entanglement cycle. Remarkably, synthetic gauge fields emerge as potent regulators of this entanglement cycle. Our results uncover the profound implications of synthetic gauge fields on quantum tunneling processes within many-body systems, which hold promising potential applications for engineering atomtronic devices and controlling quantum entanglement.