We study the dynamics of a dilute Bose-Einstein condensate confined in a toroidal trap and exposed to a pair of periodically flashed optical lattices. We first prove that in the noninteracting case this system can present a quantum symmetry which forbids the ratchet effect classically expected. We then show how many-body atom-atom interactions, treated within the mean-field approximation, can break this quantum symmetry, thus generating directed transport.

A weak resonant femtosecond pulse propagates through an optically thick atomic medium whose properties have been modified by a strong nonresonant ultrashort pulse. We study the energy redistribution between the spectral components of the weak resonant pulse using both experimental and theoretical methods. The transmitted spectrum exhibits an asymmetric feature that reveals an important gain-dispersion coupling. For light shifts that perturb slightly the propagation of the weak resonant pulse, this asymmetry maps out the asymptotic part of the linear susceptibility.

In a recent experiment, a Bose-Einstein condensate was trapped in an anharmonic potential that is well approximated by a harmonic and a quartic part. The condensate was set into such a fast rotation that the centrifugal force in the corotating frame overcompensates the harmonic part in the plane perpendicular to the rotation axis. Thus, the resulting trap potential becomes sombrero shaped. We present an analysis for an ideal Bose gas that is confined in such an anharmonic rotating trap within a semiclassical approximation, where we calculate the critical temperature, the condensate fraction, and the heat capacity. In particular, we examine in detail how these thermodynamical quantities depend on the rotation frequency.

We study the energetic and dynamic stability of coreless vortices in nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional optical potential and a Ioffe-Pritchard field. The stability of stationary vortex states is investigated by solving the corresponding Bogoliubov equations. We show that the quasiparticle excitations corresponding to axisymmetric stationary states can be taken to be eigenstates of angular momentum in the axial direction. Our results show that coreless vortex states can occur as local or global minima of the condensate energy or become energetically or dynamically unstable depending on the parameters of the Ioffe-Pritchard field. The experimentally most relevant coreless vortex state containing a doubly quantized vortex in one of the hyperfine spin components turned out to have very nontrivial stability regions, and especially a quasiperiodic dynamic instability region which corresponds to splitting of the doubly quantized vortex.

The statistical distributions of the number of secondary electrons (SEs) emitted per projectile from a thin carbon foil under irradiation with the frozen-charged ${\mathrm{H}}^0$ and ${\mathrm{H}}^{+}$ projectiles of $2.5–3.5\mathrm{MeV}$ have been measured as a function of the emergent angle of projectiles in the range from $0.0\text{to}2.0\mathrm{mrad}$ in every $0.5\mathrm{mrad}$ step. The measurement of SEs was carried out in the forward and the backward directions of the incident beam independently. From $0.0\mathrm{mrad}$ to $\sim 1.0\mathrm{mrad}$, the SE yields, that is, the mean number of emitted electrons per incident ion, increase with increasing emergent angle and tend to be saturated at larger angles. This is a common trend, regardless of incident energies and charge states of a projectile and also of emitted directions of SEs. Quantitatively, the saturated SE yields at larger angles for the ${\mathrm{H}}^{+}$ penetration are about 40–50 % larger than those at $0.0\mathrm{mrad}$. On the other hand, the corresponding relative increase for the ${\mathrm{H}}^0$ penetration reaches as high as $\sim 100\%$ or more. The observed proton-hydrogen difference is well reproduced in the calculated energy losses by a Monte Carlo simulation including the impact parameter dependent stopping cross sections in a single collision of a hydrogen or a proton with a carbon atom.

We have observed 28 heteronuclear Feshbach resonances in ten spin combinations of the hyperfine ground states of a ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ mixture. The measurements were performed by observing the loss rates from an atomic mixture at magnetic fields between $0$ and $700\mathrm{G}$. These data were used to significantly refine an interatomic potential derived from molecular spectroscopy, yielding a highly consistent model of the ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ interaction. Thus, the measured resonances can be assigned to the corresponding molecular states. In addition, this potential allows for an accurate calculation of the energy differences between highly excited levels and the rovibrational ground level. This information is of particular relevance for the formation of deeply bound heteronuclear molecules. Finally, the model is used to predict Feshbach resonances in mixtures of ${}^{87}\mathrm{Rb}$ combined with ${}^{39}\mathrm{K}$ or ${}^{41}\mathrm{K}$.

In the relativistic theory of magnetic molecular properties which involve the magnetic field of a magnetic nucleus, difficulties associated with the divergence of four-component Dirac spinors in the vicinity of the nucleus need be considered with care. Within the point dipole model of the nucleus, singular operators may be involved. This is the case, for instance, of the relativistic calculation of the nuclear magnetic shielding tensor and indirect spin-spin coupling tensor in the context of Kutzelnigg’s minimal coupling approach. We show that matrix elements of the magnetic interaction yield divergent values for every single Fermi contact, spin dipolar, paramagnetic spin orbit, and Kutzelnigg’s anisotropic Dirac’s $\delta$ operator. However, when all terms are added together the divergent results cancel each other and a finite convergent result is obtained. It is concluded that Kutzelnigg’s minimal coupling approach can be safely applied in the case of a point dipole model of the nucleus, and numerical results should be equivalent to those of the direct linear response approach for the operator $V=e\mathit{\alpha }\cdot \mathbf{A}$. The importance of the inclusion of the anisotropic Dirac’s $\delta$ operator is emphasized.

We consider an unambiguous identification of an unknown coherent state with one of two unknown coherent reference states. Specifically, we consider two modes of an electromagnetic field prepared in unknown coherent states $\mid {\alpha }_1⟩$ and $\mid {\alpha }_2⟩$, respectively. The third mode is prepared either in the state $\mid {\alpha }_1⟩$ or in the state $\mid {\alpha }_2⟩$. The task is to identify (unambiguously) which of the two modes are in the same state. We present a scheme consisting of three beam splitters capable to perform this task. Although we do not prove the optimality, we show that the performance of the proposed setup is better than the generalization of the optimal measurement known for a finite-dimensional case. We show that a single beam splitter is capable to perform an unambiguous quantum state comparison for coherent states optimally. Finally, we propose an experimental setup consisting of $2N-1$ beam splitters for unambiguous identification among $N$ unknown coherent states. This setup can be considered as a search in a quantum database. The elements of the database are unknown coherent states encoded in different modes of an electromagnetic field. The task is to specify the two modes that are excited in the same, though unknown, coherent state.

Spin Hamiltonians with degenerate ground states are one potential system for the storage of quantum information at low temperatures. Trapped ions can be used to simulate the dynamics of these Hamiltonians, but the coherence-preserving properties will be lost. This illustrates that a quantum simulation performed in an interaction frame will not thermalize with its environment.

The formation of multipartite quantum entanglement by repeated operation of one- and two-qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one-dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a nonlocal geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single-qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the nonlocal geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and nonlocal interactions between the qubits.

We present a detailed analysis of a robust quantum repeater architecture building on the original Duan-Lukin-Cirac-Zoller (DLCZ) protocol [L.M. Duan et al. Nature (London) 414, 413 (2001)]. The architecture is based on two-photon Hong-Ou-Mandel-type interference which relaxes the long-distance interferometric stability requirements by about seven orders of magnitude, from subwavelength for the single photon interference required by DLCZ to the coherence length of the photons, thereby removing the weakest point in the DLCZ scheme. Our proposal provides an exciting possibility for robust and realistic long-distance quantum communication.

We outline an approach within time-dependent density functional theory that predicts x-ray spectra on an absolute scale. The approach rests on a recent formulation of the resonant-convergent first-order polarization propagator [P. Norman et al., J. Chem. Phys. 123, 194103 (2005)] and corrects for the self-interaction energy of the core orbital. This polarization propagator approach makes it possible to directly calculate the x-ray absorption cross section at a particular frequency without explicitly addressing the excited-state spectrum. The self-interaction correction for the employed density functional accounts for an energy shift of the spectrum, and fully correlated absolute-scale x-ray spectra are thereby obtained based solely on optimization of the electronic ground state. The procedure is benchmarked against experimental spectra of a set of small organic molecules at the carbon, nitrogen, and oxygen $K$ edges.

The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein condensate is investigated. The Heisenberg equations of motions for the condensate and the Rydberg atom are derived. Neglecting the back action of the Rydberg atom onto the condensate decouples the equations describing the condensate and Rydberg atom. In this case the spectral structure of the Rydberg atom is completely determined by an effective potential which depends on the density distribution of the condensate. We study the spectral properties for the situation of an isotropic harmonic and anharmonic as well as axially symmetric confinement. In the latter case an intriguing analogy with Rydberg atoms in magnetic fields is encountered.

We present space-time-resolved measurements of electromagnetic pulses tunneling through a coaxial electromagnetic band gap structure. The results show that during the tunneling process the field distribution inside the barrier is an exponentially decaying standing wave whose amplitude increases and decreases as it slowly follows the temporal evolution of the input pulse. At no time is a pulse maximum found inside the barrier, and hence the transmitted peak is not the incident peak that has propagated to the exit. The results support the quasistatic interpretation of tunneling dynamics and confirm that the group delay is not the traversal time of the input pulse peak.

We propose a pairing-based method for cooling an atomic Fermi gas. A three-component (labels 1, 2, 3) mixture of fermions is considered where components 1 and 2 interact and, for instance, form pairs whereas component 3 is in the normal state. For cooling, components 2 and 3 are coupled by an electromagnetic field. Since the quasiparticle distributions in the paired and in the normal states are different, the coupling leads to cooling of the normal state even when initially $T_{\mathit{\text{paired}}}⩾T_{\mathit{\text{normal}}}$. The cooling efficiency is given by the pairing energy and by the linewidth of the coupling field. No superfluidity is required. The method has a conceptual analogy to cooling based on superconductor–normal-metal tunneling junctions. The main differences arise from the exact momentum conservation in the case of the field-matter coupling versus nonconservation of momentum in the solid-state tunneling process. Moreover, the role of processes that relax the energy conservation requirement in the tunneling—e.g., thermal fluctuations of an external reservoir—is now played by the linewidth of the field. The proposed method should be experimentally feasible due to its close connection to the rf spectroscopy of ultracold gases which is already in use.

For pure bipartite superposed states, the entanglement quantified by negativity is studied. If the entanglement is quantified by concurrence, we show that two pure states with high fidelity to one another have nearly the same entanglement. We deduce an inequality in which the concurrence is known to be a continuous function in infinite dimensions. The main result of this paper is to give the bounds on the negativity of a bipartite state in terms of the entanglement of the states being superposed. These bounds may be used in estimating the entanglement of a given state.

We examine the role that interference plays in quantum state transfer through several types of finite spin chains, including chains with isotropic Heisenberg interaction between nearest neighbors, chains with reduced coupling constants to the spins at the end of the chain, and chains with anisotropic coupling constants. We evaluate quantitatively both the interference corresponding to the propagation of the entire chain and the interference in the effective propagation of the first and last spins only, treating the rest of the chain as a black box. We show that perfect quantum state transfer is possible without quantum interference and provide evidence that the spin chains examined realize interference-free quantum state transfer to a good approximation.

We investigate a family of mixed entangled states wherein there exist common stabilizers among the mixtures of the corresponding density matrix. The nonlocality of these mixed entangled states can be verified by the maximal violation of stabilizer-based Bell-type inequalities. Some of these states with specific probability distributions are bound entangled, which can be superactivated. Potential applications of these mixed states in quantum key distribution and quantum repeaters are also introduced.

The $N$ to $M$ $(M⩾N)$ universal quantum broadcasting of mixed states ${\rho }^{\otimes N}$ is proposed for a qubit system. The broadcasting of mixed states is universal and optimal in the sense that the shrinking factor is independent of the input state and achieves the upper bound. The quantum broadcasting of mixed qubits is a generalization of the universal quantum cloning machine for identical pure input states. A pure state decomposition of the identical mixed qubits ${\rho }^{\otimes N}$ is obtained.