By investigating the quantum properties of magnetically trapped $n{S}_{1/2}$ Rydberg atoms, it is demonstrated that the composite nature of Rydberg atoms significantly alters their trapping properties opposed to pointlike particles with the same magnetic moment. We show how the specific signatures of the Rydberg trapping potential can be probed by means of ground-state atoms that are off-resonantly coupled to the Rydberg state via a two photon laser transition. In addition, it is demonstrated how this approach provides an alternative possibility of generating traps for ground-state atoms. Simulated time-of-flight pictures mirroring the experimental situation are provided.

In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with the encryption of the actual secret message. We show that this is also true in the information-theoretic setting—where the public keys are quantum systems—by defining and giving an example of a forward search attack for any deterministic quantum-public-key bit-encryption scheme. However, unlike in the classical setting, we show that any such deterministic scheme can be used as a black box to build a randomized bit-encryption scheme that is no longer susceptible to this attack.

The dynamics of quantum vortices in a two-dimensional annular condensate held under a toroidal trapping potential composed of a harmonic term plus Gaussian term are considered by numerically simulating the Gross-Pitaevskii equation. Families of solitary wave sequences are reported, both without and with a persistent flow, for various values of interaction strength. It is shown that in the toroidal geometry the dispersion curve of solutions is much richer than in the cases of a semi-infinite channel or uniform condensate studied previously. In particular, the toroidal condensate is found to have states of single vortices at the same position and circulation that move with different velocities. The stability of the solitary wave sequences for the annular condensate without a persistent flow is also investigated by numerically evolving the solitary wave solutions in time. In addition, the interaction of vortex-vortex pairs and vortex-antivortex pairs is considered and it is demonstrated that the collisions are either elastic or inelastic depending on the magnitude of the angular velocity. The similarities and differences between numerically simulating the Gross-Pitaevskii equation and using a point vortex model for these collisions are elucidated.

We propose a scheme to simulate and observe massless Dirac fermions with cold atoms in a square optical lattice. A U(1) adiabatic phase is created by two laser beams for the tunneling of atoms between neighbor lattice sites. Properly adjusting the tunneling phase, we find that the energy spectrum has conical points in per Brillouin zone where band crossing occurs. Near these crossing points the quasiparticles and quasiholes can be considered as massless Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions are obtained in the present square lattice model. The Dirac fermions as well as the anisotropic behaviors realized in our system can be experimentally detected with the Bragg spectroscopy technique.

We theoretically describe the quantum properties of a large-Fresnel-number degenerate optical parametric oscillator (DOPO) with spherical mirrors that is pumped by a Gaussian beam and is tuned at the subharmonic frequency to a given transverse-mode family. We first analyze the classical problem and find that only the Laguerre-Gauss modes with lowest orbital angular momentum (OAM) are amplified above threshold. The transverse symmetry of the classically emitted signal field depends on the family index $f$. If $f$ is even the lowest available OAM is zero and emission occurs in a radially symmetric mode; on the contrary, if $f$ is odd the lowest available OAM is 1 and the emitted signal field has the shape of a hybrid Laguerre-Gauss mode (a linear combination of the two Laguerre-Gauss modes with OAM equal to $\pm 1$) that breaks the rotational invariance of the system. Next we focus on the squeezing properties of this DOPO model. As for the modes with lowest OAM we demonstrate that their quantum properties (in the linear approximation) are equal to the standard single-mode DOPO (for even $f$) or to the recently analyzed DOPO tuned to its first transverse-mode family [C. Navarrete-Benlloch, E. Roldán, and G. J. de Valcárcel, Phys. Rev. Lett. 100, 203601 (2008)]. Concerning the rest of (classically empty) modes (having larger OAM) we find that combinations of Laguerre-Gauss modes with opposite OAM (hybrid Laguerre-Gauss modes) exhibit quadrature squeezing. This property is independent of the even or odd character of the family index and hence has nothing to do with the symmetry of the classically emitted signal field. Noticeably the amount of squeezing does not depend on the pump level (it is thus noncritical squeezing) and can be arbitrarily large for the lower OAM nonamplified modes.

We report on the experimental observation of stable double-charge discrete vortex solitons generated in hexagonal photonic lattices created optically in self-focusing nonlinear media and show that single-charge vortex solitons are unstable in analogous conditions. Subsequently, we study, both theoretically and experimentally, the existence and stability of spatial vortex solitons in two-dimensional hexagonal photonic lattices. We demonstrate that the stability of the double-charge vortices is a consequence of the intersite power exchange in the vortex soliton, and we provide a simple stability criterion on the basis of the analysis of the corresponding discrete nonlinear model. We extend our analysis to the case of defocusing nonlinearity and show the inversion of the vortex stability properties resulting in the fact that single-charge vortices become stable while their double-charge counterparts are unstable.

The transition from a superfluid to a Mott-insulator (MI) phase has been observed in a Bose-Einstein condensate (BEC) of ytterbium (Yb) atoms in an optical lattice. An all-optically produced BEC of ${}^{174}\text{Y}\text{b}$ atoms was loaded into three-dimensional optical lattices produced by a 532 nm laser beam. The interference pattern was measured after releasing the quantum gas from the trapping potential. As increasing the optical lattice depth, we observed the disappearance of the interference patterns, which is a signature of entering the MI regime. This result is an important step into studies by using a combination of the MI state and the ultranarrow optical transition of ultracold alkaline-earth-metal-like atoms.

We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an $S$ parameter of $S=2.653\pm 0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.

Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the two-qubit controlled-sign [or controlled NOT (CNOT)] gate, we provide numerical evidence that the maximum success rate is $S=2/27$ using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the three-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons—less than in any existing scheme—with a maximum $S=0.00340$. This compares well to $S={\left(2/27\right)}^2/2\approx 0.00274$, obtainable by combining two CNOT gates and a passive quantum filter [T. C. Ralph, K. J. Resch, and A. Gilchrist, Phys. Rev. A 75, 022313 (2007)]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [M. M. Wilde and D. B. Uskov, Phys. Rev. A 79, 022305 (2009); G. A. Durkin and J. P. Dowling, Phys. Rev. Lett. 99, 070801 (2007)].

The photoabsorption processes of ${\text{Au}}^{2+}$, ${\text{Au}}^{3+}$, and ${\text{Au}}^{4+}$ have been investigated experimentally and theoretically in the 70–127 eV region. Using the dual laser-produced plasma technique, the $4f$ and $5p$ photoabsorption spectrum has been recorded at 50 ns time delay and was found to be dominated by a great number of lines from $4f\text{−}5d$, $6d$ and $5p\text{−}5d$, $6s$ transitions, which have been identified by comparison with the aid of Hartree-Fock with configuration interaction calculations. The characteristic feature of the spectrum is that satellite lines from excited configurations containing one or two $6s$ electrons are more important than resonance lines, and with increasing ionization, satellite contributions from states with one $6s$ spectator electron gradually become more important than those with two $6s$ spectator electrons. Based on the assumption of a normalized Boltzmann distribution among the excited states and a steady-state collisional-radiative model, we succeeded in reproducing a spectrum which is in good agreement with experiment.

We theoretically investigate the effects of the carrier-envelope phase on atomic ionization by the pulse train in the multiphoton-ionization regime, and show that regardless of the number of pulses, the phase dependence is striking. Similarity and the difference between the phase-dependent phenomena by the pulse train and isolated pulse are clearly understood in the frequency domain.

Dissociation of ${\text{HD}}^{+}$ molecular ion by intense femtosecond laser pulses is studied theoretically using quantum propagation of nuclear vibrational wave packets. Radiative pulses of peak intensity in the range of ${10}^{14}–{10}^{15}\text{W}/{\text{cm}}^2$ with carrier wavelength of 800 nm are applied on the system. In our calculation we have used a four component wave packet in two spatial regions for studying the dynamics of dissociated fragments and the nondissociated molecules simultaneously. This technique enables us to investigate the dynamics by varying the pulse duration (15–75 fs) and the peak amplitude of the field for the initial vibrational state ${\nu }_i=0$. The effect of permanent dipole moments and nonadiabatic mixing coefficients of the system on dissociation probability and the branching ratio of photofragments between two outgoing channels are also discussed. Studies of kinetic energy spectra help us to estimate the number of photon absorption and shift of the field induced resonances from the field free levels. The dissociation spectrum at high intensity has been compared with available experimental results.

Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a four-dimensional harmonic oscillator, subject to a constraint. This regularization makes use of a fictitious time variable, but arbitrary Gaussian wave packets in that time variable in general violate that constraint. The set of “restricted Gaussian wave packets” consistent with the constraint is constructed and shown to provide a complete basis for the expansion of states in the original three-dimensional coordinate space. Using that expansion arbitrary localized Gaussian wave packets of the hydrogen atom can be propagated analytically and exhibit a nondispersive periodic behavior as functions of the fictitious time. Restricted wave packets with and without well-defined angular momentum quantum numbers are constructed. They will be used as trial functions in time-dependent variational computations for the hydrogen atom in static external fields in the subsequent paper [T. Fabčič, J. Main, and G. Wunner, Phys. Rev. A 79, 043417 (2009)].

In the preceding paper [T. Fabčič, J. Main, and G. Wunner, Phys. Rev. A 79, 043416 (2009)] “restricted Gaussian wave packets” were introduced for the regularized Coulomb problem in the four-dimensional Kustaanheimo-Stiefel coordinates, and their exact time propagation was derived analytically in a fictitious-time variable. We now establish the Gaussian wave-packet method for the hydrogen atom in static external fields. A superposition of restricted Gaussian wave packets is used as a trial function in the application of the time-dependent variational principle. The external fields introduce couplings between the basis states. The set of coupled wave packets is propagated numerically, and eigenvalues of the Schrödinger equation are obtained by the frequency analysis of the time autocorrelation function. The advantage of the wave-packet propagation in the fictitious-time variable is that the computations are exact for the field-free hydrogen atom and approximations from the time-dependent variational principle only stem from the external fields. Examples are presented for the hydrogen atom in a magnetic field and in crossed electric and magnetic fields.

The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform one-dimensional Bose gas with repulsive contact interactions at finite temperatures. Long-, medium-, and short-range effects are investigated. The results span the entire range of physical regimes from ideal gas to strongly interacting and from zero temperature to high temperature (Gross-Pitaevskii) and strongly interacting (Tonks-Girardeau) gases. We present perturbative analytic methods, available at strong and weak couplings, and first-principles numerical results using imaginary time simulations with the gauge-$P$ representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure but nonmaximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols, and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations.

We investigate signatures of nonclassicality in quantum states, in particular, those involved in the DQC1 model of mixed-state quantum computation [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)]. To do so, we consider two known nonclassicality criteria. The first quantifies disturbance of a quantum state under locally noneffective unitary operations (LNUs), which are local unitaries acting invariantly on a subsystem. The second quantifies measurement-induced disturbance (MID) in the eigenbasis of the reduced density matrices. We study the role of both figures of nonclassicality in the exponential speedup of the deterministic quantum computation with one qubit (DQC1) model and compare them vis-à-vis the interpretation provided in terms of quantum discord. In particular, we prove that a nonzero quantum discord implies a nonzero shift under LNUs. We also use the MID measure to study the locking of classical correlations [D. P. DiVincenzo et al., Phys. Rev. Lett. 92, 067902 (2004)] using two mutually unbiased bases (MUBs). We find the MID measure to exactly correspond to the number of locked bits of correlation. For three or more MUBs, it predicts the possibility of superior locking effects.

We present a systematic study of atomic four-body fragmentation dynamics. To this end we have measured a variety of multiple differential double ionization cross sections for 6 MeV $p+\text{He}$ collisions. The data are compared to a first-order calculation with correlated electrons and to a simulation representing a second-order process, with some experimental results seemingly in favor of the first, others in agreement with the second approach. This apparent conflict can be resolved by accounting for elastic scattering between the projectile and one electron already promoted to the continuum through electron-electron correlation in the first-order process.

The guiding of multiply charged ${\text{Ne}}^{7+}$ ions through nanocapillaries in highly insulating polymers was investigated. Highly parallel capillaries with a density of $\lesssim {10}^7{\text{cm}}^{-2}$ and diameters of $\lesssim 100\text{nm}$ were utilized. The widths of the angular profiles were measured for ${\text{Ne}}^{7+}$ ions transmitted through the capillaries. Moreover, the fractions of transmitted ions were measured as a function of the capillary tilt angle. The results were used to evaluate the characteristic guiding angle, which is a measure of the guiding power specifying the ability of a material to guide ions. Results for the polyethylene terephthalate (PET) and polycarbonate (PC) samples were compared to verify the role of the material of the capillary wall. Relatively high projectile energies of up to 50 keV were used to extend the validity of previous scaling laws based on the projectile charge-to-energy ratio. The profile widths and the guiding angles for both polymers are found to compare well with the scaling laws showing that PET and PC have nearly equal guiding properties.

The commonly accepted theory of light-induced atomic desorption (LIAD) [S. N. Atutov et al., Phys. Rev. A 60, 4693 (1999)] explains the dynamics of this effect by referring to a light-enhanced diffusion process proceeding in the absorbing medium. On the other hand, recently performed measurements show that in siloxane films which are used in LIAD experiments, the characteristic time of diffusion is extremely short (a fraction of 1 s) compared to the duration of the LIAD effect (hundreds of seconds). This is in contradiction to the conceptual basis of the theory of Atutov et al. that requires the characteristic diffusion time to be sufficiently long. What is more, the theory of Atutov et al. relies on an unjustified assumption about the dependence of the diffusion coefficient on the light intensity. In consequence, the theoretical results of Atutov et al. yield unsatisfactory predictions and do not fit well with experimental data. In this paper, we consider a partially illuminated siloxane-coated cell and propose an alternative theory of LIAD dynamics based on an assumption about lateral diffusion proceeding in the siloxane coating. Our theory provides a unique solution for the desorbed atoms’ density regardless of the power of the laser light, explains the lengthy duration of LIAD, and accurately reproduces experimental results. A reasoning which explains how the boundary condition at the siloxane surface is established by the incident light gives us a proper relation between the desorbed atoms’ density and the intensity of the desorbing light.