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8 pages, 6 figuresThis papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found

This paper presents a formalism describing the dynamics of a quantum particle in a onedimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework allowing fully-analytical developments. Analytic solutions describing the particle motion are explicit derived, and the resulting dynamics is studied.

We present an approach of the kicked rotor quantum resonances in position-space, based on its analogy with the optical Talbot effect. This approach leads to a very simple picture of the physical mechanism underlying the dynamics and to analytical expressions for relevant physical quantities, such as mean momentum or kinetic energy. The ballistic behavior, which is closely associated to quantum resonances, is analyzed and shown to emerge from a coherent adding of successive kicks applied to the rotor thanks to a periodic reconstruction of the spatial wavepacket.

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We present a general model allowing "quantum simulation" of one-dimensional Dirac models with 2- and 4-component spinors using ultracold atoms in driven 1D tilted optical latices. The resulting Dirac physics is illustrated by one of its well-known manifestations, Zitterbewegung. This general model can be extended and applied with great flexibility to more complex situations.Comment: 12 pages, 6 figures, accepted for Physical Review

It is shown that the energies and the lifetimes of unstable modes of quantum propagation of neutral atoms in a quadrupole magnetic guide can be calculated simply by diagonalizing the complex scaled Hamiltonian. The results reproduce those obtained for the same geometry, but by a different method, by E. A. Hinds and C. Eberlein ͓Phys. Rev. A 61, 033614 ͑2000͔͒. The destabilizing effect of a weak bias magnetic field on the l ϭ0 propagation mode of sϭ1/2 atoms is illustrated.