We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behavior near a Dirac point, we develop algorithms that solve the problem in a time of $O\left(\sqrt{N}\right)$ for $d>2$ and $O(\sqrt{N}logN)$ in $d=2$. In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-time quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory.

The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx {10}^8–{10}^9$ T are calculated in this study. A pseudospectral method is employed for the computational procedure. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these two- and three-electron systems in a self-consistent manner. The method exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. It is found that the results obtained here for a few of the most tightly bound states of each of the atoms, helium and lithium, are in good agreement with findings elsewhere. In this regard, we report data for two states of lithium that were lacking thus far. It is also seen that the pseudospectral method employed here is considerably more economical, from a computational point of view, than previously employed methods such as a finite-element-based approach. The key enabling advantage of the method described here is the short computational times, which are on the order of seconds for obtaining accurate results for heliumlike systems.

We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional uniform electron gases (UEGs). The fundamental parameters of the GLDA—a generalization of the widely known local-density approximation used in density-functional theory—are the electronic density $\rho$ and a two-electron local parameter called the hole curvature $\eta$. The UEGs considered in this study are finite versions of the conventional infinite homogeneous electron gas and consist of $n$ electrons on an infinitely thin wire with periodic boundary conditions. We perform a comprehensive study of these finite UEGs at high, intermediate, and low densities using perturbation theory and quantum Monte Carlo calculations. We show that the present GLDA functional yields accurate estimates of the correlation energy for both weakly and strongly correlated one-dimensional systems and can be easily generalized to higher-dimensional systems.

We show that the resonant dipole-dipole interaction can give rise to bound states between two and three Rydberg atoms with nonoverlapping electron clouds. The dimer and trimer states arise from avoided level crossings between states converging to different fine-structure manifolds in the limit of separated atoms. We analyze the angular dependence of the potential wells, characterize the quantum dynamics in these potentials, and discuss methods for their production and detection. Typical distances between the atoms are of the order of several micrometers which can be resolved in state-of-the-art experiments. The potential depths and typical oscillation frequencies are about one order of magnitude larger as compared to the dimer and trimer states investigated by M. Kiffner et al. [Phys. Rev. A 86, 031401(R) (2012)] and M. Kiffner, W. Li, and D. Jaksch [Phys. Rev. Lett. 111, 233003 (2013)], respectively. We find that the dimer and trimer molecules can be aligned with respect to the axis of a weak electric field.

Triply differential cross sections for electron-impact ionization of the $1t_2$ and $2a_1$ orbitals of methane are calculated using the complex Kohn variational method. The calculations are carried out for scattered electron energies of 500 eV and coplanar asymmetric kinematics far from the Bethe ridge, where previous experiment and theory are available for comparison. The present results are in reasonably good agreement with experiment for $1t_2$ ionization and in excellent agreement for $2a_1$ ionization, in contrast with previous theory.

We calculate the effect of two kinds of randomness on the coherent motion of an exciton whose transport is governed by the dipole-dipole interaction. As our example, we use the idealized case of stationary Rydberg atoms on a lattice. We present calculations for how fast the excitation can move away from its starting position for different dimensional lattices and for different levels of randomness. We also examine the asymptotic in time final position of the excitation to determine whether or not the excitation can be localized. The one-dimensional system is an example of Anderson localization where the randomness is in the off-diagonal elements although the long-range nature of the interaction leads to nonexponential decay with distance. The two-dimensional square lattice shows a mixture of extended and localized states for large randomness, while there is no visible sign of localized states for weak randomness. The three-dimensional cubic lattice has few localized states even for strong randomness.

A joint experimental and theoretical study of three-photon ionization of the $1s2p{}^3{P}^o$($M_L=0,\pm 1$) states of helium is presented. The ion yield is recorded in the 690–730 nm wavelength range for different laser pulse energies, using an excited helium beam produced by photodetachment of helium negative ions. Two series of asymmetric peaks due to two-photon resonances with $1snp$ and $1snf$ Rydberg states are observed. In one series, the peaks have tails towards higher frequencies, while in the other series the tails change direction for higher Rydberg states. An effective Hamiltonian is built in the dressed state picture, and a numerical model simulating the traversal of the helium atom across the laser pulse is developed. The simulated and observed ion yields are in good qualitative agreement. The observed behavior is shown to result from the contributions of two different resonantly enhanced multiphoton ionization processes, depending on the magnetic quantum number $M_L$ of the initial state. The asymmetry reversal is explained by the strong $1s2p$–$1s3s$ dynamic Stark mixing for $M_L=0$.

We report an observation of large frequency shifts on the order of several hundred Hz of the electron paramagnetic resonance (EPR) of the gas phase alkali-metal atoms (${}^{87}\mathrm{Rb}$) in a millimeter-sized cell coated with RbH salt. We provide convincing evidence that the observed EPR frequency shift is due to collisions with RbH-coated cell walls. The RbH coating is nuclear spin polarized by spin exchange with optically pumped ${}^{87}\mathrm{Rb}$ vapor, and the observed frequency shift is caused by the Fermi contact interaction between the $s$ electron of the adsorbed ${}^{87}\mathrm{Rb}$ atom and the polarized nucleus on the salt surface. From the measured EPR frequency shift we calculated the ensemble-averaged phase shift $\delta {\varphi }_s$ experienced by the spin polarized ${}^{87}\mathrm{Rb}$ atoms while adsorbed on the surface. Under our experimental conditions, we found the average phase shift $\delta {\varphi }_s\sim 70\mathrm{mrad}$.

We study theoretically the dynamics of two weakly coupled Bose-Josephson junctions, prepared with the same particle number $N$ and Josephson excitation number $\nu$ but with different reduced one-particle purity $\gamma$. An entropy oscillation mode is predicted, in which one-particle coherence is transferred between the Bose-Hubbard dimers with no particle or energy transfer. We explain this purity oscillation using a semiclassical picture.

We investigate the superfluid transition of the unitary Fermi gas by means of the functional renormalization group, aiming at quantitative precision. We extract $T_{\mathrm{c}}/\mu =0.38\left(2\right)$ and $\Delta /\mu =1.04\left(15\right)$ for the critical temperature and the superfluid gap at zero temperature, respectively, within a systematic improvement of the truncation for the effective average action. The key ingredient in comparison to previous approaches consists in the use of regulators which cut off both frequencies and momenta. We incorporate renormalization effects on both the bosonic and the fermionic propagators, include higher-order bosonic scattering processes, and investigate the regulator and specification parameter dependence for an error estimate. The ratio $\Delta /T_{\mathrm{c}}=2.7\left(3\right)$ becomes less sensitive to the relative cutoff scale of bosons and fermions when improving the truncation. The techniques developed in this work are easily carried over to the cases of finite scattering length, lower dimensionality, and spin imbalance.

The emergence of coherent rotating structures is a phenomenon characteristic of both classical and quantum two-dimensional (2D) turbulence. In this work we show theoretically that the coherent vortex structures that emerge in decaying 2D quantum turbulence can approach quasiclassical rigid-body rotation, obeying the Feynman rule of constant average areal vortex density while remaining spatially disordered. By developing a rigorous link between the velocity probability distribution and the quantum kinetic energy spectrum over wave number $k$, we show that the coherent vortex structures are associated with a $k^3$ power law in the infrared region of the spectrum, and a well-defined spectral peak that is a physical manifestation of the largest structures. We discuss the possibility of realizing coherent structures in Bose-Einstein condensate experiments and present Gross-Pitaevskii simulations showing that this phenomenon, and its associated spectral signatures, can emerge dynamically from feasible initial vortex configurations.

Using a combination of temporal coupled-mode theory and nonlinear finite-difference time-domain (FDTD) simulations, we study the nonlinear dynamics of all-resonant four-wave mixing processes and demonstrate the possibility of achieving high-efficiency limit cycles and steady states that lead to $\approx 100\%$ depletion of the incident light at low input (critical) powers. Our analysis extends previous predictions to capture important effects associated with losses, self- and cross-phase modulation, and imperfect frequency matching (detuning) of the cavity frequencies. We find that maximum steady-state conversion is hypersensitive to frequency mismatch, resulting in high-efficiency limit cycles that arise from the presence of a homoclinic bifurcation in the solution phase space, but that a judicious choice of incident frequencies and input powers, in conjuction with self-phase and cross-phase modulation, can restore high-efficiency steady-state conversion even for large frequency mismatch. Assuming operation in the telecom range, we predict close to perfect quantum efficiencies at reasonably low $\sim 50\mathrm{m}\mathrm{W}$ input powers in silicon micrometer-scale PhC nanobeam cavities.

In this paper, we report results regarding how ${\mathrm{LiH}}_2^{+}$ fragments as a result of a low-energy collision with an electron (dissociative recombination), a reaction that contains only elements and particles created during the very first phase of the universe. The collision-energy-dependent reaction rate and cross sections show detailed structures, more so than predicted by theory, suggesting significant rovibrational coupling in the ion and a complex reaction surface. From the structure of the molecule, the reaction predominantly results in the formation of Li + H${}_2$. However, 23% of the reaction flux leads to more interesting products, with 17% producing Li + 2H and 6% producing LiH + H. These last two channels break the strongest molecular bond in the system and, in the case of the latter channel, form a significantly weaker ionic bond. Possible reasons behind this interesting behavior are discussed, together with the interaction between the available reaction channels.

Experimental quantum simulation of a Hamiltonian $H$ requires unitary operator decomposition (UOD) of its evolution unitary $U=\text{exp}(-iHt)$ in terms of native unitary operators of the experimental system. Here, using a genetic algorithm, we numerically evaluate the most generic UOD (valid over a continuous range of Hamiltonian parameters) of the unitary operator $U,$ termed fidelity-profile optimization. The optimization is obtained by systematically evaluating the functional dependence of experimental unitary operators (such as single-qubit rotations and time-evolution unitaries of the system interactions) to the Hamiltonian ($H$) parameters. Using this technique, we have solved the experimental unitary decomposition of a controlled-phase gate (for any phase value), the evolution unitary of the Heisenberg XY interaction, and simulation of the Dzyaloshinskii-Moriya (DM) interaction in the presence of the Heisenberg XY interaction. Using these decompositions, we studied the entanglement dynamics of a Bell state in the DM interaction and experimentally verified the entanglement preservation procedure of Hou et al. [Ann. Phys. (N.Y.) 327, 292 (2012)] in a nuclear magnetic resonance quantum information processor.

We control the entanglement of motion between two colliding particles by dynamically varying the frequency of their common trap. In particular, we restrict the possible frequencies to a narrow interval and limit the average energy of the particles to a maximal value. In order to solve this restricted optimization problem we propose a modified gradient method. It turns out that the motional entanglement generated by collisions can be considerably improved.

Measurement-device-independent quantum key distribution (MDI-QKD) has been demonstrated in both laboratories and field tests using attenuated lasers combined with the decoy-state technique. Although researchers have studied various decoy-state MDI-QKD protocols with two or three decoy states, a clear comparison between these protocols is still missing. This invokes the question of how many types of decoy states are needed for practical MDI-QKD. Moreover, the system parameters to implement decoy-state MDI-QKD are only partially optimized in all previous works, which casts doubt on the actual performance of former demonstrations. Here, we present analytical and numerical decoy-state methods with one, two, and three decoy states. We provide a clear comparison among these methods and find that two decoy states already enable a near-optimal estimation and more decoy states cannot improve the key rate much in either asymptotic or finite-data settings. Furthermore, we perform a full optimization of system parameters and show that full optimization can significantly improve the key rate in the finite-data setting. By simulating a real experiment, we find that full optimization can increase the key rate by more than one order of magnitude compared to nonoptimization. A local search method to optimize efficiently the system parameters is proposed. This method can be four orders of magnitude faster than a trivial exhaustive search to achieve a similar optimal key rate. We expect that this local search method could be valuable for general fields in physics.

The decay of metastable states of the water radical cation ${\text{H}}_2{\text{O}}^{+}$ has been observed in an experiment that combines photofragment momentum imaging and electrostatic ion-beam trapping in a crossed-beam geometry. Photoabsorption of 532-nm laser light from a fast beam of ${\text{H}}_2{\text{O}}^{+}$ is observed to yield fragmentation into both OH${}^0+{\mathrm{H}}^{+}$ and OH${}^{+}+{\mathrm{H}}^0$. Using coincident photofragment momentum imaging, the initial state of the observed photofragmentation is associated with low vibrational levels of the second excited $\tilde{B}{}^2{B}_2$ state of ${\text{H}}_2{\text{O}}^{+}$, dissociating via absorption onto a repulsive part of the $\tilde{A}{}^2{A}_1$ state. Electrostatic ion trapping in the laser interaction region is used to follow the photofragment intensity as a function of time and to determine the lifetime of the metastable states to be ${\tau }_{\tilde{B}{}^2{B}_2}=198\pm 11$ $\mu$s.

We calculate the dc Stark effect for three molecular hydrogen ions in the nonrelativistic approximation. The effect is calculated both in dependence on the rovibrational state and in dependence on the hyperfine state. We discuss special cases and approximations. We also calculate the ac polarizabilities for several rovibrational levels and therefrom evaluate accurately the blackbody radiation shift, including the effects of excited electronic states. The results enable the detailed evaluation of certain systematic shifts of the transitions frequencies for the purpose of ultrahigh-precision optical, microwave, or radio-frequency spectroscopy in ion traps.

The universal aspects of two-body collisions in the presence of a harmonic confinement are investigated for both bosons and fermions. The main focus of this study are the confinement-induced resonances (CIRs) which are attributed to different angular momentum states $\ell$, and we explicitly show that in alkaline collisions only four universal $\ell$-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of $\ell$-wave CIRs is studied. In particular we show that all the $\ell$-wave CIRs may emerge even when the underlying two-body potential cannot support any bound state. We observe that the intricate dependence on the energy yields resonant features where the colliding system within the confining potential experiences an effective free-space scattering. Our analysis is done within the framework of the generalized $K$-matrix theory, and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.

The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a ${\text{C}}_{60}$ cage have been studied theoretically using both relativistic and nonrelativistic random phase approximations. The results indicate clearly the resonant character of the confinement oscillations in time delay of the $4d$ shell of Xe@${\text{C}}_{60}$ and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@${\text{C}}_{60}$ [Phys. Rev. Lett. 111, 203003 (2013)].