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We propose several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.

We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.

We review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices. We discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians. Then we describe connections and differences to condensed matter physics and present applications in the fields of quantum computing and quantum simulations. Finally we explain how defects and atomic quantum dots can be introduced in a controlled way in optical lattice systems.Comment: Review article, 31 pages, 14 figures, to be published in Annals of Physic

We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This setup is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields -which is not experimentally accessible for electrons in metals -where a fractal band structure, the Hofstadter butterfly, characterizes the system.

We show that by using cold controlled collisions between two atoms one can achieve conditional dynamics in moving trap potentials. We discuss implementing two qubit quantum-gates and efficient creation of highly entangled states of many atoms in optical lattices. 32.80.Pj, 03.67.Lx, 34.90.+q.The controlled manipulation of entangled states of Nparticle systems is fundamental to the study of basic aspects of quantum theory [1,2], and provides the basis of applications such as quantum computing and quantum communications [3,4]. Engineering entanglement in real physical systems requires precise control of the Hamiltonian operations and a high degree of coherence. Achieving these conditions is extremely demanding, and only a few systems, including trapped ions, cavity QED and NMR, have been identified as possible candidates to implement quantum logic in the laboratory [3]. On the other hand, in atomic physics with neutral atoms recent advances in cooling and trapping have led to an exciting new generation of experiments with Bose condensates [5], experiments with optical lattices [6], and atom optics and interferometry. The question therefore arises, to what extent these new experimental possibilities and the underlying physics can be adapted to provide a new perspective in the field of experimental quantum computing.In this Letter we propose coherent cold collisions as the basic mechanism to entangle neutral atoms. The picture of atomic collisions as coherent interactions has emerged during the last few years in the studies of Bose Einstein condensation (BEC) of ultracold gases. In a field theoretic language these interactions correspond to Hamiltonians which are quartic in the atomic field operators, analogous to Kerr nonlinearities between photons in quantum optics. By storing ultracold atoms in arrays of microscopic potentials provided, for example, by optical lattices these collisional interactions can be controlled via laser parameters. Furthermore, these nonlinear atomatom interactions can be large [7], even for interactions between individual pairs of atoms, thus providing the necessary ingredients to implement quantum logic.Let us consider a situation where two atoms |a and |b are trapped in the ground states ψ a,b 0 of two potential wells V a,b . Initially, at time t = −τ , these wells are centered at positionsx a andx b , sufficiently far apart (distance d =x b −x a ) so that the particles do not interact. The positions of the potentials are moved along trajectoriesx a (t) andx b (t) so that the wavepackets of the atoms overlap for certain time, until finally they are restored to the initial position at the final time t = τ . This situation is described by the HamiltonianHere, x a,b and p a,b are position and momentum operators, V a,b x a,b −x a,b (t) describe the displaced trap potentials and u ab is the atom-atom interaction term. Ideally, we would like to implement the transformationwhere each atom remains in the ground state of its trapping potential and and preserves its internal state. The phase φ w...

The non-equilibrium control of emergent phenomena in solids is an important research frontier, encompassing effects like the optical enhancement of superconductivity 1 . Recently, nonlinear excitation 2 , 3 of certain phonons in bilayer cuprates was shown to induce superconducting-like optical properties at temperatures far above T c 4,5,6 . This effect was accompanied by the disruption of competing charge-density-wave correlations 7,8 , which explained some but not all of the experimental results. Here, we report a similar phenomenon in a very different compound. By exciting metallic K 3 C 60 with mid-infrared optical pulses, we induce a large increase in carrier mobility, accompanied by the opening of a gap in the optical conductivity. Strikingly, these sameReprints and permissions information is available online at www.nature.com/reprints.Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use:http://www.nature.com/authors/editorial_policies/license.html#termsCorrespondence and request for materials should be addressed to An.C. (andrea.cavalleri@mpsd.mpg.de). Author Contributions

We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d GrossPitaevskii equation and obtain a four-parameter model. Identifying 'extreme parameter regimes', the model is accessible to analytical perturbation theory, which justifies formal procedures well known in the physical literature: reduction to 2d and 1d GPEs, approximation of ground state solutions of the GPE and geometrical optics approximations. Then we use a time-splitting spectral method to discretize the time-dependent GPE. Again, perturbation theory is used to understand the discretization scheme and to choose the spatial/temporal grid in dependence of the perturbation parameter. Extensive numerical examples in 1d, 2d and 3d for weak/strong interactions, defocusing/focusing nonlinearity, and zero/nonzero initial phase data are presented to demonstrate the power of the numerical method and to discuss the physics of Bose-Einstein condensation. *