Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.</p

Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.</p

Supplementary information files for Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

(c) the Authors, CC-BY 4.0Supplementary files for article Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition ratesWe investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.</p

Emergence and control of complex behaviors in driven systems of interacting qubits with dissipation

Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle quantum correlations in a large system in the presence of decoherence and external driving is especially topical. Still, the scaling behaviour of dynamics and related emergent phenomena are not yet well understood. We investigate how the dynamics of a driven system of several quantum elements (e.g., qubits or Rydberg atoms) changes with increasing number of elements. Surprisingly, a two-element system exhibits chaotic behaviours. For larger system sizes a highly stochastic, far from equilibrium, hyperchaotic regime emerges. Its complexity systematically scales with the size of the system, proportionally to the number of elements. Finally, we demonstrate that these chaotic dynamics can be efficiently controlled by a periodic driving field. The insights provided by our result indicate the possibility of a reduced description for the behaviour of a large quantum system in terms of the transitions between its qualitatively different dynamical regimes. These transitions are controlled by a relatively small number of parameters, which may prove useful in the design, characterization and control of large artificial quantum structures