Planck’s Quantum-Driven Integer Quantum Hall Effect in Chaos

Abstract

The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-1/2 rotor, a Planck's quantum(he)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of critical he-values, but otherwise bounded ('insulating' phase). The latter phase is topological in nature and characterized by a quantum number ('quantized Hall conductance'). The number jumps by unity whenever he decreases passing through each critical value. Our findings, within the reach of cold-atom experiments, indicate that rich topological quantum phenomena may emerge from chaos.

Quantum Walk in Momentum Space with a Bose-Einstein Condensate

“…By manipulating either the walk or coin operator we show how the walk can be biased or reversed. Future applications can build on the implicit spin-momentum coupling of our walk that is also a necessary ingredient for studying topological effects [22][23][24].…”

Quantum simulation of disordered systems with cold atoms

“…While this is conceivable [67] it can be very difficult in practice. However, if this could be done, it will open a wealth of new possibilities, as recent theoretical suggestions including complex spin-orbit-coupled Hamiltonians allow the realization of puzzling systems displaying momentum-space topological insulator properties and opening ways to the realization of a Quantum Hall physics quantum simulator [68,69,49,50].…”

Impact of Lattice Vibrations on the Dynamics of a Spinor Atom-Optics Kicked Rotor

“…This exceptional control and dynamical stability has recently led to the realisation of discrete-time quantum walks [29]. Moreover, there are numerous proposals to investigate the effects of topological invariants based on extended versions of an AOKR [30][31][32][33][34][35]. The latter two applications make it necessary to control not only the momentum of the atomic centre of mass degree of freedom, but to include additional degrees of freedom, typically two internal electronic states [36][37][38] which become entangled with momentum during the temporal evolution.…”