We calculate the quantum motion of ultracold atoms in an accelerating optical potential, and show how they may be used to observe Landau-Zener tunneling and Wannier-Stark ladders, two fundamental quantum effects in solid state physics. The optical potential is spatially periodic, yielding an energy spectrum of Bloch bands for the atoms. The acceleration provides an inertial force in the moving ...

We quantize sl n Toda field theories in a periodic lattice. We find the quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the case of the defining representation. In the sl 3 case we extend the analysis also to the second fundamental representation. We clarify, in particular, the relation of Jimbo and Rosso's quantum R matrix with the quantum R matrix in the Bloch wave ba...

We extend earlier examples provided by Schoen, Nori and Bloch to show that when a surface has the property that the kernel of its Albanese map is non-zero over the field of complex numbers, this kernel is non-zero over a field of transcendence degree one. This says that the conjecture of Bloch and Beilinson that this kernel is zero for varieties over number fields is precise in the sense that i...

We report the operation of a Bloch oscillator. The active medium was a staticvoltage driven, doped GaAs/AlAs superlattice which was electromagnetically coupled to a resonator. The oscillator produced tuneable microwave radiation (frequency ~ 60 GHz; power ~ 0.5 mW; efficiency ~ 4 %). The gain (~ 10 cm) was due to the nonlinearity mediated by miniband electrons. We also present a theory of the o...

Bloch oscillations excited in a biased GaAs/AlxGa12xAs superlattice are investigated in a time-resolved two-color electro-optic detection scheme. The detection of resonantly excited Bloch oscillations is based on the Pockels effect probed at a wavelength in the center of the band gap. The observed birefringence is induced by the macroscopic polarization of the electronic wave packets relative t...

The electromagnetic modeling of practical finite periodic structures is a topic of growing interest. Due to the truncation of the infinite periodic structures, surface waves will be excited and localized near the discontinuous interfaces leading to the edge effect of finite structures. In this work, surface waves are numerically disentangled from the propagating Bloch waves contributions. Based...

We study a cross-ratio of four generic points of S which comes from spherical CR geometry. We construct a homomorphism from a certain group generated by generic configurations of four points in S to the pre-Bloch group P(C). If M is a 3-dimensional spherical CR manifold with a CR triangulation, by our homomorphism, we get a P(C)-valued invariant for M . We show that when applying to it the Bloc...

We present a general, rigorous, modal formalism for modeling light propagation and light emission in three-dimensional (3D) periodic waveguides and in aggregates of them. In essence, the formalism is a generalization of well-known modal concepts for translation-invariant waveguides to situations involving stacks of periodic waveguides. By surrounding the actual stack by perfectly-matched layers...

We investigate the collective gyrotropicmodes in a linear chain of ferromagnetic nanodots in a skyrmionmagnetization state. Individual skyrmions in the dots (with thickness about of 1 nmand radius about of 100 nm) are assumed to be stabilized by interplay of isotropic exchange and Dzyaloshinskii-Moriya exchange interactions,magnetic anisotropy andmagnetostatic interactions. We consider the dipo...