Topological flat Wannier-Stark bands

Topological flat bands from dipolar spin systems.

We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S=1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hard-core bosons, namely, the dressed spin flip...

Exceptional points in bichromatic Wannier–Stark systems

The resonance spectrum of a tilted periodic quantum system for a bichromatic periodic potential is investigated. For such a bichromatic Wannier–Stark system, exceptional points, degeneracies of the spectrum, can be localized in parameter space by means of an efficient method for computing resonances. Berry phases and Petermann factors are analysed. Finally, the influence of a nonlinearity of th...

Stark-wannier Ladders and Cubic Exponential Sums

Fractal stabilization of Wannier-Stark resonances

– The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to have a fractal structure as function of the so-called electric matching ratio, which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a manifestation of the fractal nature of the spectrum in the system “atom in a standing laser wave”, which is a quantum optical realization of a ...

Lifetime of the Wannier-Stark resonances and perturbation theory

We consider the small field asymptotics of the ladder lifetime for a single ladder model. Using the convergent perturbation series, we prove that the behavior of the lifetime computed by means of the Fermi Golden Rule is proportional to the correct one with the factor ( π 3 )2 . The relation with usual adiabatic problems is briefly discussed.