Wannier-Stark states for semiconductor superlattices in strong static fields, where the interband Landau-Zener tunneling cannot be neglected, are rigorously calculated. The lifetime of these metastable states was found to show multiscale oscillations as a function of the static field, which is explained by an interaction with above-barrier resonances. An equation, expressing the absorption spectrum of semiconductor superlattices in terms of the resonance Wannier-Stark states, is obtained and used to calculate the absorption spectrum in the region of high static fields.

We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-V scheme wherein two counter-propagating control fields generate a quasi stationary pattern of two counter-propagating probe fields -so-called stationary light. We show that contrary to previous predictions, there exists a single unique dark-state polariton; it obeys a simple propagation equation.

We present a detailed analysis of the recently demonstrated technique to generate quasi-stationary pulses of light [M. Bajcsy et al., Nature (London) 426, 638 (2003)] based on electromagnetically induced transparency. We show that the use of counterpropagating control fields to retrieve a light pulse, previously stored in a collective atomic Raman excitation, leads to quasi-stationary light field that undergoes a slow diffusive spread. The underlying physics of this process is identified as pulse matching of probe and control fields. We then show that spatially modulated controlfield amplitudes allow us to coherently manipulate and compress the spatial shape of the stationary light pulse. These techniques can provide valuable tools for quantum nonlinear optics and quantum information processing.Key words: electromagnetically induced transparency, slow light, quantum information processing 1 We dedicate this paper to Bruce W. Shore, one of the fathers of the theory of coherent processes in atomic systems, at the occasion of his 70th birthday.

In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coupling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multidimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.PACS numbers: 42.50. Gy, 37.10.De, 42.25.Bs Although cold gases are typically neutral, artificial electromagnetism may be induced by several means, including rotation [1], manipulation of atoms in optical lattices [2,3,4], and the use of laser arrangements [5]. Interestingly, seminal experiments on optically created gauge fields have been recently reported [6]. Artificial electromagnetism has attracted a growing attention in recent years, partially due to the possibility of achieving nonAbelian gauge fields [4,5], which establish fascinating links between cold gases and high-energy physics [4,7,8]. A striking example is given by the possibility of inducing quasi-relativistic physics in cold atoms despite the extremely low velocities involved [9]. In particular, under proper conditions cold atoms may experience an effective spin-orbit coupling, which leads to a Dirac cone in the dispersion [10], resembling the case of yet another paradigm of modern physics, namely graphene [11,12]. Similar phenomena are expected in cold atoms and graphene including Veselago lensing [9,13,14].Interparticle interactions lead to inherent nonlinearities in Bose-Einstein condensates (BECs). At sufficiently low temperatures the BEC physics is described by a nonlinear Schödinger equation similar to that found in nonlinear optics [1]. Resemblances between both fields have been successfully explored in recent years, most remarkably in what concerns the physics of solitons [15,16,17,18,19], for which nonlinearity and dispersion compensate leading to a non-dispersing solution. Nonlinearity plays also an important role in high-energy physics. Indeed, non-linear Dirac equations (NLDEs), and more generally non-linear spinor fields, have been studied extensively, starting with the pioneering works of Ivanenko [20], Weyl [21], and Heisenberg [22]. These equations may present also localized solutions [23,24].In this Letter we explore the nonlinear physics of a multicomponent BEC (also called spinor BEC [25]) in the presence of an optically-induced spin-orbit coupling. In the low-momentum limit, the spinor BEC may be described by a particular type of two-component NLDE. We show that for the case of attractive interactions, the condensate may become self-trapped, rese...

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