Arnold web and dynamical tunneling in a four-site Bose-Hubbard model
arXiv:2106.10215 · doi:10.1016/j.physd.2021.133006
Abstract
We present the quantum and classical study of a four-well trapped Bose-Einstein condensate (BEC) modeled by the Bose-Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer.
arXiv comment14 pages 8 figures; Modified as per referee suggestions; Accepted in Physica D special issue on Chaos indicators
References in corpus (38)
- Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
- Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
- The cold atom Hubbard toolbox
- Classical bifurcation at the transition from Rabi to Josephson dynamics
- Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
- Detecting order and chaos in Hamiltonian systems by the SALI method
- Quantum phase space picture of Bose-Einstein Condensates in a double well: Proposals for creating macroscopic quantum superposition states and a study of quantum chaos
- Resonance-assisted tunneling in near-integrable systems
- Collective modes, chaotic behavior and self-trapping in the dynamics of three coupled Bose-Einstein condensates
- Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap
- Transistor-Like Behavior of a Bose-Einstein Condensate in a Triple Well Potential
- Quantum Dynamics of Three Coupled Atomic Bose-Einstein Condensates
- Quantum dynamics in the bosonic Josephson junction
- Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
- Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective
- Dynamical tunneling in molecules: Quantum routes to energy flow
- Semiclassical quantization of the Bogoliubov spectrum
- Control of tunneling in an atomtronic switching device
- Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river
- The speed of Arnold diffusion
- Chaos-assisted tunneling resonances in a synthetic Floquet superlattice
- Phase separation can be stronger than chaos
- Transport and interaction blockade of cold bosonic atoms in a triple-well potential
- Quantum dynamics of a four-well Bose-Hubbard model with two different tunneling rates
- On dynamical tunneling and classical resonances
- Scaling perspective on Intramolecular vibrational energy flow: analogies, insights, and challenges
- Resonance-assisted tunneling in three degrees of freedom without discrete symmetry
- Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis
- NOON states with ultracold bosonic atoms via resonance- and chaos-assisted tunneling
- Adiabatic passage through chaos
- Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions
- Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
- Quantum thermalization via percolation
- Dynamics in multiple-well Bose-Einstein condensates
- Spatial two-particle NOON-states in periodically shaken three-well potentials
- Semiclassical theory of strong localization for quantum thermalization
- Coherence oscillations between weakly coupled Bose-Hubbard dimers
- Resonance-assisted tunneling in 4D normal-form Hamiltonians