We studied angular dependency of the time delay in one-photon two-electron photoionization of the hydrogen molecule. Time delay as a function of the angle between velocities of the escaping electrons was shown to have poles at the point corresponding to the kinematic nodes of the reaction. Study of the delay in the vicinity of a pole can provide information about phases of the amplitudes of the reaction.

We revisit the problem of the electromagnetic Green function for homogeneous hyperbolic media, where longitudinal and transverse components of the dielectric permittivity tensor have different signs. We analyze the dipole emission patterns for both dipole orientations with respect to the symmetry axis and for different signs of dielectric constants, and show that the emission pattern is highly anisotropic and has a characteristic crosslike shape: the waves are propagating within a certain cone and are evanescent outside this cone. We demonstrate the coexistence of the conelike pattern due to emission of the extraordinary TM-polarized waves and elliptical pattern due to emission of ordinary TE-polarized waves. We find a singular complex term in the Green function, proportional to the $\delta$ function and governing the photonic density of states and Purcell effect in hyperbolic media.

We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions.

Two-pulse excitation of a molecular quantum wake in air during filamentary propagation is shown to controllably shape an intense femtosecond probe pulse and to significantly extend the filament compared to single-pulse excitation. The effect is sensitive to pump-probe delay on a ∼10-fs time scale.

The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the test states used in quantum benchmarking experiments may be imperfect as well. Many quantum benchmarks are only valid for states which match some ideal form, such as pure states or Gaussian states. We outline how to perform quantum benchmarking using arbitrary states of light. We demonstrate these results using real data taken from a continuous-variable quantum memory.

The length of signal pulses is finite in practical quantum key distribution. The finite-key analysis of an unconditional quantum key distribution is a burning problem, and the efficient quantum key distribution protocol suitable for practical implementation, measurement-device-independent quantum key distribution (MDI QKD), was proposed very recently. We give the finite-key analysis of MDI QKD, which removes all detector side channels and generates many orders of key rate higher than that of full-device-independent quantum key distribution. The secure bound of the ultimate key rate is obtained under the statistical fluctuations of relative frequency, which can be applied directly to practical threshold detectors with low detection efficiency and highly lossy channels. The bound is evaluated for reasonable values of the observed parameters. The simulation shows that the secure distance is around 10 km when the number of sifted data is ${10}^{10}$. Moreover the secure distance would be much longer in practice because of some simplified treatments used in our paper.

We study an initially inverted three-level atom in the $\Lambda$ configuration embedded in a waveguide, interacting with a propagating single-photon pulse. Depending on the temporal shape of the pulse, the system behaves either as an optimal universal cloning machine or as a highly efficient deterministic source of maximally entangled photon pairs. This quantum transistor operates over a wide range of frequencies and can be implemented with today's solid-state technologies.

We investigate the quantum dynamics of particles on graphs (“quantum random walks”), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on quantum random walks of multiple noninteracting particles on strongly regular graphs (SRGs), a class of graphs with high symmetry that is known to have pairs of graphs that are hard to distinguish. Previous work has already demonstrated analytically that two-particle noninteracting quantum walks cannot distinguish nonisomorphic SRGs of the same family. Here, we demonstrate numerically that three-particle noninteracting quantum walks have significant, but not universal, distinguishing power for pairs of SRGs, proving a fundamental difference between the distinguishing power of two-particle and three-particle noninteracting walks. We show analytically why this distinguishing power is possible, whereas it is forbidden for two-particle noninteracting walks. Based on sampling of SRGs with up to 64 vertices, we find no difference in the distinguishing power of bosonic and fermionic walks. In addition, we find that the four-fermion noninteracting walk has greater distinguishing power than the three-particle walk on SRGs, showing that increasing the particle number increases the distinguishing power. However, we also show analytically that no noninteracting walk with a fixed number of particles can distinguish all SRGs, thus demonstrating a potential fundamental difference in the distinguishing power of interacting versus noninteracting walks.

Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum-walk algorithm can destroy any quantum-mechanical speedup due to Anderson localization. We numerically study the effect of static disorder on a quantum walk on the glued trees graph. For small disorder, we find that the dominant effect is a type of quantum decay, and not quantum localization. For intermediate disorder, there is a crossover to diffusive transport, while a localization transition is observed at large disorder, in agreement with Anderson localization on the Cayley tree.

Level crossings in the ground state of ions occur when the nuclear charge $Z$ and ion charge $Z_{\mathrm{ion}}$ are varied along an isoelectronic sequence until the two outermost shells are nearly degenerate. We examine all available level crossings in the periodic table for both near-neutral ions and highly charged ions (HCIs). Normal $E$1 transitions in HCIs are in x-ray range; however, level crossings allow for optical electromagnetic transitions that could form the reference transition for high-accuracy atomic clocks. Optical $E$1 (due to configuration mixing), $M$1, and $E$2 transitions are available in HCIs near level crossings. We present scaling laws for energies and amplitudes that allow us to make simple estimates of systematic effects of relevance to atomic clocks. HCI clocks could have some advantages over existing optical clocks because certain systematic effects are reduced; for example, they can have much smaller thermal shifts. Other effects such as fine-structure and hyperfine splitting are much larger in HCIs, which can allow for richer spectra. HCIs are excellent candidates for probing variations in the fine-structure constant $\alpha$ in atomic systems as there are transitions with the highest sensitivity to $\alpha$ variation.

It was recently shown that dielectronic recombination measurements can be used for accurately inferring changes in the nuclear mean-square charge radii of highly charged lithiumlike neodymium [Brandau et al., Phys. Rev. Lett. 100, 073201 (2008)]. To make use of this method to derive information about the nuclear charge distribution for other elements and isotopes, accurate electronic isotope shift parameters are required. In this work, we calculate and discuss the relativistic mass- and field-shift factors for the two $2s{}^2{S}_{1/2}-2p{}^2{P}_{1/2,3/2}^o$ transitions along the lithium isoelectronic sequence. Based on the multiconfiguration Dirac-Hartree-Fock method, the electron correlation and the Breit interaction are taken into account systematically. The analysis of the isotope shifts for these two transitions along the isoelectronic sequence demonstrates the importance and competition between the mass shifts and the field shifts.

We describe cooling and trapping of both ${}^{85}$Rb and ${}^{87}$Rb in a range of magnetic fields up to 2.6 T. Atoms are injected from a low-field pyramidal magneto-optical trap and recaptured in a high-magnetic-field atom trap. The atoms are cooled and trapped by a six-beam optical molasses via the $5S_{1/2}|m_I,m_J=$ 1/2$\rangle$$\to$ $5P_{3/2}|m_I,m_J=$ 3/2$\rangle$ transition ($m_I=$ 5/2 for ${}^{85}$Rb and $m_I=$ 3/2 for ${}^{87}$Rb). We study the trap fluorescence spectra, atom temperatures, density distributions, and lifetimes as a function of magnetic field and detuning parameters. The trap fluorescence spectra are both narrow and asymmetric, as is characteristic for laser cooling of atoms in an external trapping potential. The trap is modeled using a Monte Carlo trajectory simulation technique.

We explore the possibility of decelerating and Doppler cooling an ensemble of three-level $\Lambda$-type atoms by a coherent train of short, nonoverlapping laser pulses. We show that $\Lambda$ atoms can be Doppler cooled without additional repumping of the population from the intermediate ground state. We derive an analytical expression for the scattering force in the quasi-steady-state regime and analyze its dependence on pulse-train parameters. Based on this analysis we propose a method of choosing pulse-train parameters to optimize the cooling process.

We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the “activated complex” that mediates the collapse of the condensate. For a certain value of the $s$-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading-order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows the bifurcation to be smoothly passed.

We study the onset of particle statistics effects as the temperature is lowered in strongly correlated two-dimensional Hubbard models. We utilize numerical linked-cluster expansions and focus on the properties of interacting lattice fermions and two-component hard-core bosons. In the weak-coupling regime, where the ground state of the bosonic system is a superfluid, the thermodynamic properties of the two systems at half filling exhibit very large differences even at high temperatures. In the strong-coupling regime, where the low-temperature behavior is governed by a Mott insulator for either particle statistics, the agreement between the thermodynamic properties of both systems extends to regions where the antiferromagnetic (iso)spin correlations are exponentially large. We analyze how particle statistics affects adiabatic cooling in those systems.

A scheme is proposed to prepare squeezed states and Schrödinger-cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective $J_x$ interaction implemented by a resonant Raman coupling between the atomic ground states. Dynamical evolution both with a constant Hamiltonian and with adiabatic variation of the two interaction terms is studied. We show that by the application of further resonant laser fields, we can suppress nonadiabatic transfer under the time-varying Hamiltonian and significantly speed up the evolution towards a maximally squeezed, $J_z=0$, collective spin state.

We have analyzed numerically the localization length of light $\xi$ for nearly periodic arrangements of homogeneous stacks (formed exclusively by right-handed materials) and mixed stacks (with alternating right- and left-handed metamaterials). Layers with index of refraction $n_1$ and thickness $L_1$ alternate with layers of index of refraction $n_2$ and thickness $L_2$. Positional disorder has been considered by shifting randomly the positions of the layer boundaries with respect to periodic values. For homogeneous stacks, we have shown that the localization length is modulated by the corresponding bands and that $\xi$ is enhanced at the center of each allowed band. In the limit of long wavelengths $\lambda$, the parabolic behavior previously found in purely disordered systems is recovered, whereas for $\lambda \ll L_1+L_2$ a saturation is reached. In the case of nearly periodic mixed stacks with the condition $|n_1{L}_1|=|n_2{L}_2|$, instead of bands there is a periodic arrangement of Lorenztian resonances, which again is reflected in the behavior of the localization length. For wavelengths of several orders of magnitude greater than $L_1+L_2$, the localization length $\xi$ depends linearly on $\lambda$ with a slope inversely proportional to the modulus of the reflection amplitude between alternating layers. When the condition $|n_1{L}_1|=|n_2{L}_2|$ is no longer satisfied, the transmission spectrum is very irregular and this considerably affects the localization length.

Based on the Mie theory and on the incident beam model via superposition of two plane waves, we analyze numerically the momentum flux of the field scattered by a spherical, nonmagnetic microparticle placed within the spatially inhomogeneous circularly polarized paraxial light beam. The asymmetry between the forward- and backward-scattered momentum fluxes in the Rayleigh scattering regime appears due to the spin part of the internal energy flow in the incident beam. The transverse ponderomotive forces exerted on dielectric and conducting particles of different sizes are calculated and special features of the mechanical actions produced by the spin and orbital parts of the internal energy flow are recognized. In particular, the transverse orbital flow exerts the transverse force that grows as $a^3$ for conducting and as $a^6$ for dielectric subwavelength particle with radius $a$, in compliance with the dipole mechanism of the field-particle interaction; the force associated with the spin flow behaves as $a^8$ in both cases, which testifies for the nondipole mechanism. The results can be used for experimental identification and separate investigation of the spin and orbital parts of the internal energy flow in light fields.

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which has been conjectured before [D. Girolami and G. Adesso, Phys. Rev. A 84, 052110 (2011)]. We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically for Werner states and for families of bound entangled states.