We study the ground-state properties of the Bose-Hubbard model with attractive interactions on an $M$-site one-dimensional periodic—necklacelike—lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving $\mathrm{su}\left(M\right)$ coherent state, which results in a set of modified discrete nonlinear Schrödinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only—as expected—in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schrödinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking ground state of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system.

We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.

We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of the monogamy of entanglement: we establish the polygamy of entanglement, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system.

We show that soliton collisions can reduce propagation-induced quantum phase noise. This effect originates from a negative correlation between self- and cross-phase-modulation-induced phase fluctuations. Furthermore, we show how this effect can be applied directly to improve the quality of soliton-based quantum nondemolition measurements, simply by adjusting the parameter regime in which the measurement is performed. Optimal implementation, which we show to be technologically feasible, favors short propagation distances, small wavelength separation between solitons, and approximately equal soliton amplitudes.

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast, directed transport through the network to the opposite corner. This transport is not ballistic in nature, but rather produced by quantum mechanical interference. In the long time limit, certain walks show an asymmetric limiting probability distribution; this feature depends on the starting site and, remarkably, on the precise size of the network. The limiting probability distributions show patterns which are correlated with the initial condition. This might have consequences for the application of continuous-time quantum walk algorithms.

We investigate the detection and characterization of entanglement based on the quantum network introduced in Phys. Rev. Lett. 93, 110501 (2004) for different experimental scenarios. We first give a detailed discussion of the ideal scheme where no errors are present and full spatial resolution is available. Then we analyze the implementation of the network in an optical lattice. We find that even without any spatial resolution entanglement can be detected and characterized in various kinds of states including cluster states and macroscopic superposition states. We also study the effects of detection errors and imperfect dynamics on the detection network. For our scheme to be practical these errors have to be on the order of one over the number of investigated lattice sites. Finally, we consider the case of limited spatial resolution and conclude that significant improvement in entanglement detection and characterization compared to having no spatial resolution is only possible if single lattice sites can be resolved.

We investigate the problem of cloning a set of states that is invariant under the action of an irreducible group representation. We then characterize the cloners that are extremal in the convex set of group covariant cloning machines, among which one can restrict the search for optimal cloners. For a set of states that is invariant under the discrete Weyl-Heisenberg group, we show that all extremal cloners can be unitarily realized using the so-called double-Bell states, whence providing a general proof of the popular ansatz used in the literature for finding optimal cloners in a variety of settings. Our result can also be generalized to continuous-variable optimal cloning in infinite dimensions, where the covariance group is the customary Weyl-Heisenberg group of displacements.

We compare the failure probabilities of ensemble implementations of quantum algorithms which use pseudopure initial states, quantified by their polarization, to those of competing classical probabilistic algorithms. Specifically we consider a class algorithms which require only one bit to output the solution to problems. For large ensemble sizes, we present a general scheme to determine a critical polarization beneath which the quantum algorithm fails with greater probability than its classical competitor. We apply this to the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.

We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential and both the energy and angular momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and triplet scattering lengths. As an example, results for ${}^{23}\mathrm{Na}-{}^{23}\mathrm{Na}$ scattering are presented and compared to close-coupling calculations.

A projectile traveling inside a metal can excite bulk plasmons (collective oscillations of the electron gas) that eventually decay. The two main decay mechanisms are the excitation of a nearly free electron (NFe), also referred to as a Bloch electron, and the excitation of a pair of interacting free electrons $\left(2e\right)$. In recent publications we developed a model to study these mechanisms for proton impact on aluminum. In this paper, we apply that model to other simple metals. Interesting results are obtained for magnesium, sodium, and potassium. The comparison of the NFe energy and angular spectra sheds light on the role the crystal structure plays. Results for the total probability and excitation power can also be understood in terms of the elements’ different characteristics. Some comments are made regarding the relative importance of the two mechanisms for each element and the role that parameters like the electron density, the crystal structure, and the plasmon linewidth might play in this. Also, an approximate scaling rule is found for the plasmon creation probability as well as for the $2e$ contribution to the plasmon decay probability.

We demonstrate laser cooling in an optical lattice that employs Raman transitions. Four laser beams with different frequencies form a one-dimensional lattice with a basic lattice period that is a factor of 2 less than in standard optical lattices. Rb atoms are cooled to $8\mu \mathrm{K}$. We measure the intensity- and detuning-dependence of the cooling mechanism. Our experimental results agree well with theoretical models.

We study the dynamics of many atoms in the recently proposed single-atom-transistor setup [A. Micheli, A. J. Daley, D. Jaksch, and P. Zoller, Phys. Rev. Lett. 93, 140408 (2004)] using recently developed numerical methods. In this setup, a localized spin-$1∕2$ impurity is used to switch the transport of atoms in a one-dimensional optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a single-atom mirror. We calculate time-dependent currents for bosons passing the impurity atom, and find interesting many-body effects. These include substantially different transport properties for bosons in the strongly interacting (Tonks) regime when compared with fermions, and an unexpected decrease in the current when weakly interacting probe atoms are initially accelerated to a nonzero mean momentum. We also provide more insight into the application of our numerical methods to this system, and discuss open questions about the currents approached by the system on long time scales.

We examine in analytic and numeric ways the imaging effects of temporal neutron lenses created by traveling magnetic fields. For fields of parabolic shape we derive the imaging equations, investigate the time magnification, the evolution of the phase-space element, the gain factor, and the effect of finite beam size. The main aberration effects are calculated numerically. The system is technologically feasible and should convert neutron time-of-flight instruments from pinhole to imaging configuration in time, thus enhancing intensity and/or time resolution. Further fields of application for high-resolution spectrometry may be opened.

The ground-state electronic and structural properties and the electronic excitations of the lowest-energy isomers of the ${\mathrm{Ag}}_8$ cluster are calculated using density functional theory (DFT) and time-dependent DFT (TDDFT) in real-time and real-space schemes, respectively. The optical spectra provided by TDDFT predict that the $D_{2d}$ dodecahedron isomer is the structural minimum of the ${\mathrm{Ag}}_8$ cluster. Indeed, it is borne out by the experimental findings.

We provide the first uniform explanation basis for the laser intensity dependence of the momentum distributions that have been reported in atomic nonsequential double-ionization experiments. Our theoretical work covers laser irradiation at $780\mathrm{nm}$ and intensities in the range $I=(1-6.5)\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, which are relevant to experiments. We use a completely classical method introduced previously [Phay J. Ho, R. Panfili, S. L. Haan, and J. H. Eberly, Phys. Rev. Lett. 94, 093002 (2005)]. Our calculated results suggest that just two distinct categories of electron trajectories are relevant.

We present time-dependent ab initio calculations of fragmenting $\mathrm{H}_2{}^{+}$ and ${\mathrm{H}}_2$ molecules in strong laser fields, taking into account all nuclear and electronic degrees of freedom. In particular, very different and apparently contradicting experimental observations on the alignment of fragmenting hydrogen molecules are naturally explained and consistently interpreted. In addition, striking differences in the alignment of fragmenting $\mathrm{H}_2{}^{+}$ and ${\mathrm{H}}_2$ are predicted. Whereas ${\mathrm{H}}_2$ fragments show decreasing alignment with increasing laser intensity, the alignment of $\mathrm{H}_2{}^{+}$ fragments is nearly independent of the intensity. This is in contrast to existing intuitive expectations, but in accord with available experimental data.

We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schrödinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields along the condensate axis into account, we are able to reproduce and explain many of the characteristic features observed in the experiments of Inouye et al. [Science 285, 571 (1999)] and Schneble et al. [Science 300, 475 (2003)], such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering.

We discuss a sympathetic cooling strategy that can successfully mitigate fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the temperature regime in which the fermions behave as a Fermi liquid. We introduce an energy-based formalism to describe the temperature dynamics with which we study a specific and promising mixture, composed of ${}^6\mathrm{Li}$ and ${}^{87}\mathrm{Rb}$. Analyzing the harmonically trapped mixture, we find that the favorable features of this mixture are further enhanced by using different trapping frequencies for the two species.

The bosonic quantum channels have recently attracted a growing interest, motivated by the hope that they open a tractable approach to the generally hard problem of evaluating quantum channel capacities. These studies, however, have always been restricted to memoryless channels. Here, it is shown that the classical capacity of a bosonic Gaussian channel with memory can be significantly enhanced if entangled symbols are used instead of product symbols. For example, the capacity of a photonic channel with 70%-correlated thermal noise of one-third the shot noise is enhanced by about 11% when using 3.8-dB entangled light with a modulation variance equal to the shot noise.

In this paper, we demonstrate how optimal control methods can be used to speed up the implementation of modules of quantum algorithms or quantum simulations in networks of coupled qubits. The gain is most prominent in realistic cases, where the qubits are not all mutually coupled. Thus the shortest times obtained depend on the coupling topology as well as on the characteristic ratio of the time scales for local controls vs nonlocal (i.e., coupling) evolutions in the specific experimental setting. Relating these minimal times to the number of qubits gives the tightest known upper bounds to the actual time complexity of the quantum modules. As will be shown, time complexity is a more realistic measure of the experimental cost than the usual gate complexity. In the limit of fast local controls (as, e.g., in NMR), time-optimized realizations are shown for the quantum Fourier transform (QFT) and the multiply controlled NOT gate $\left({\mathrm{C}}^{n-1}\mathrm{NOT}\right)$ in various coupling topologies of $n$ qubits. The speed-ups are substantial: in a chain of six qubits the quantum Fourier transform so far obtained by optimal control is more than eight times faster than the standard decomposition into controlled phase, Hadamard and SWAP gates, while the ${\mathrm{C}}^{n-1}\mathrm{NOT}$ gate for a completely coupled network of six qubits is nearly seven times faster.