So far all analytic models of heating of clusters in the collisionless domain are based on linear or linearized concepts, like Mie resonance or other linear oscillations. They are characterized by constant eigenfrequencies lying well above the frequencies of most intense lasers. In this paper we show that nonlinear resonant excitation constitutes the basis of absorption in the collisionless domain, for individual electrons as well as for entire electron bunches. With increasing amplitude of the particles oscillating in their own space charge field their eigenperiod increases and at sufficient driver strength it equals and exceeds the constant laser period. At the crossing point, and essentially only there, resonant absorption takes place. Neither nonlinearities in themselves nor asymmetric excitation of the electron cloud of the cluster leads to irreversible energy gain.

In this paper we report the measurement of the frequency Stark shift of the ground-state hyperfine transition of ${}^{133}\mathrm{Cs}$ observed in a vapor cell through a $\Lambda$ excitation scheme. The measured value of the quadratic Stark coefficient is $k=(-2.05\pm 0.04)\times {10}^{-10}\mathrm{Hz}∕{(\mathrm{V}∕\mathrm{m})}^2$ when the electric field is perpendicular to the quantization axis. A comparison with the values previously reported in literature is given in view of its interest for the evaluation of the blackbody radiation shift in the primary frequency standards.

Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at times when the average of the observable reaches its local or global extremum, constitutes a strategy transferable to different control issues. Among them, postpulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.

We consider the feasibility of creating a phase of neutral bosonic atoms in which multiple Mott-insulating states coexist in a shell structure and propose an experiment to spatially resolve such a structure. This spatially inhomogeneous phase of bosons, arising from the interplay between the confining potential and the short-ranged repulsion, has been previously predicted. While the Mott-insulator phase has been observed in an atomic gas, the spatial structure of this phase in the presence of an inhomogeneous potential has not yet been directly probed. In this paper, we give a simple recipe for creating a structure with any desired number of shells, and explore the stability of the structure under typical experimental conditions. The stability analysis gives some constraints on how successfully these states can be employed for quantum information experiments. The experimental probe we propose for observing this phase exploits transitions between two species of bosons, induced by applying a frequency-swept, oscillatory magnetic field. We present the expected experimental signatures of this probe, and show that they reflect the underlying Mott configuration for large lattice potential depth.

The charge-transfer processes ${\mathrm{O}}^{+}({}^{4}S^0,{}^{2}D^0,{}^{2}P^0)+\mathrm{He}\to \mathrm{O}\left({}^{3}P\right)+{\mathrm{He}}^{+}$ have been investigated by using a fully quantal molecular-orbital close-coupling (QMOCC) approach. Cross sections are presented for ion energies from 0.5 to 10 keV and compared with those from recent experiments and semiclassical theory. Good agreement is found between the QMOCC results and the measurements. Particular attention is given to addressing the metastable component of the experimental ion beams. We further argue that the so-called “suppressed electron-capture effect” for metastable ions proposed by Wolfrum et al. is not a viable mechanism to explain their measurements. However, the current QMOCC calculations were found to reproduce neither the ground-state nor metastable-state cross sections predicted by the semiclassical method.

Rigorous calculations of magnetic Feshbach resonances and Zeeman relaxation cross sections in an ultracold and cold chromium gas are reported. This work presents the calculation of such inelastic processes in collisions of atoms with large magnetic moments. Using our recently constructed accurate interaction potentials for the chromium dimer, we compute the positions and widths of magnetically tuned resonances in an optically trapped ultracold Cr gas. We find good agreement with recent experimental data and report that spin-change collision cross sections quickly increase with decreasing collision energy and magnetic-field strength at energies below 1 K and magnetic fields larger than 40 G.

We classify entanglement singularities for various two-mode bosonic systems in terms of catastrophe theory. Employing an abstract phase-space representation, we obtain exact results in limiting cases for the entropy in cusp, butterfly, and two-dimensional catastrophes. We furthermore use numerical results to extract the scaling of the entropy with the nonlinearity parameter, and discuss the role of mixing entropies in more complex systems.

It is shown that the alignment dependence of the yields of high-order harmonic generation (HHG) from molecules by intense lasers is governed by the orbital symmetry of the outermost electron(s). For ${\mathrm{N}}_2$, with its outermost ${\sigma }_g$ electron, the HHG yield is maximal when the molecules are aligned with the laser polarization direction, in agreement with the recent experiment of Itatani et al. [Nature 432, 867 (2004)]. For ${\mathrm{O}}_2$, with its outermost ${\pi }_g$ electron, the HHG yield peaks when the molecules are aligned at about 45° from the polarization axis. We emphasize that the alignment dependence is determined mostly by the orbital symmetry and weakly on the laser parameters or the species.

Starting from a microscopic model in the free-carrier approximation, we derive an analytical approximation for the optical susceptibility of uniaxially stressed quantum-well lasers at low temperatures by neglecting second-order contributions of the band-mixing phenomenon. The resulting polarization-dependent peak gains, differential peak gains, transparency carrier densities, and linewidth enhancement factors as induced by the uniaxial planar stress are discussed.

We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spin 1/2 embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one- dimensional $XY$ chain.

We discuss a simplified scheme to teleport a state from one mode to another of the same bimodal cavity, with these two modes having distinct frequencies and orthogonal polarizations. The scheme employs two two-level (Rydberg) atoms plus classical fields (Ramsey zones) and selective atomic state detectors. The result has potential use for the manipulation of quantum information processing.

We report on measurements of the collisional properties of a mixture of ${}^{133}\mathrm{Cs}$ and ${}^{87}\mathrm{Rb}$ atoms in a magnetic trap at $\mu \mathrm{K}$ temperatures. By selectively evaporating the Rb atoms using a radio-frequency field, we achieved sympathetic cooling of Cs down to a few $\mu \mathrm{K}$. The interspecies collisional cross section was determined through rethermalization measurements, leading to good agreement with a theoretical prediction of $595a_0$ for the triplet $s$-wave scattering length for Rb in the $\mid F=2,m_F=2⟩$ and Cs in the $\mid F=4,m_F=4⟩$ magnetic states. We briefly speculate on the prospects for reaching the Bose-Einstein condensation of Cs inside a magnetic trap through sympathetic cooling.

Unconditional security proofs of the Bennett-Brassard 1984 protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols will obtain larger rates over increased distance. In this paper we investigate limits to the error rate and signal losses that can be tolerated by future protocols and proofs.

Energy levels of germanium, tin, and lead, together with their single, double, and triple ionized positive ions have been calculated using the $V^{N-M}$ approximation suggested in previous work [Dzuba, Phys. Rev. A 71, 032512 (2005)] [$M$ is the number of valence electrons $(M=4)$]. Initial Hartree-Fock calculations are done for the quadruply ionized ions with all valence electrons removed. The core-valence correlations are included beyond the second-order of the many-body perturbation theory. Interaction between valence electrons is treated by means of the configuration interaction technique. It is demonstrated that accurate treatment of the core-valence correlations leads to systematic improvement of the accuracy of calculations for all ions and neutral atoms.

During ionization in a strong linearly polarized laser field, a significant part of the ionization probability arises at times when the electric field is different from its maximum value. Therefore applying in the Keldysh theory the Coulomb-Volkov wave function derived recently by [Mishima et al. Phys. Rev. A 66, 053408 (2002)] may lead to some degree of error in the calculated ionization rate.

We report the experimental realization of entanglement swapping over long distances in optical fibers. Two photons separated by more than $2\mathrm{km}$ of optical fibers are entangled, although they never directly interacted. We use two pairs of time-bin entangled qubits created in spatially separated sources and carried by photons at telecommunication wavelengths. A partial Bell-state measurement is performed with one photon from each pair, which projects the two remaining photons, formerly independent onto an entangled state. A visibility high enough to infer a violation of a Bell inequality is reported, after both photons have each traveled through $1.1\mathrm{km}$ of optical fiber.

We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

The Bell-Kochen-Specker theorem establishes the impossibility of a noncontextual hidden variable model of quantum theory, or equivalently, that quantum theory is contextual. In this paper, an operational definition of contextuality is introduced which generalizes the standard notion in three ways: (i) it applies to arbitrary operational theories rather than just quantum theory, (ii) it applies to arbitrary experimental procedures rather than just sharp measurements, and (iii) it applies to a broad class of ontological models of quantum theory rather than just deterministic hidden variable models. We derive three no-go theorems for ontological models, each based on an assumption of noncontextuality for a different sort of experimental procedure; one for preparation procedures, another for unsharp measurement procedures (that is, measurement procedures associated with positive-operator valued measures), and a third for transformation procedures. All three proofs apply to two-dimensional Hilbert spaces, and are therefore stronger than traditional proofs of contextuality.

The mean king’s problem with maximal mutually unbiased bases (MUB’s) in general dimension $d$ is investigated. It is shown that a solution of the problem exists if and only if the maximal number $(d+1)$ of orthogonal Latin squares exists. This implies that there is no solution in $d=6$ or $d=10$ dimensions even if the maximal number of MUB’s exists in these dimensions.

We describe a laboratory demonstration of a quantum error correction procedure that can correct intrinsic measurement errors in linear-optics quantum gates. The procedure involves a two-qubit encoding and fast feed-forward-controlled single-qubit operations. In our demonstration the qubits were represented by the polarization states of two single-photons from a parametric down-conversion source, and the real-time feed-forward control was implemented using an electro-optic device triggered by the output of single-photon detectors.