It is shown that every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha I+T$ with $\alpha$ a non-negative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing an entanglement witness and apply them to obtain some entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

The reliable and precise generation of quantum unitary transformations is essential for the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal control problem of generating such unitary transformations as a surface-optimization problem over the quantum control landscape, defined as a metric for realizing a desired unitary transformation as a function of the control variables. It was found that under the assumption of nondissipative and controllable dynamics, the landscape topology is trap free, which implies that any reasonable optimization heuristic should be able to identify globally optimal solutions. The present work is a control landscape analysis, which incorporates specific constraints in the Hamiltonian that correspond to certain dynamical symmetries in the underlying physical system. It is found that the presence of such symmetries does not destroy the trap-free topology. These findings expand the class of quantum dynamical systems on which control problems are intrinsically amenable to a solution by optimal control.

We calculate the entanglement-assisted and -unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.

An improved parametrization of the two-electron reduced density matrix (2-RDM) [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] was recently shown to yield energies and properties that are markedly better than those calculated by traditional ab initio methods of similar computational scaling. In this paper a family of such energy functionals, generalizing the ones obtained previously, is derived through the use of (i) $p$-particle contraction relations based on the contraction of the cumulant expansions of $p$-particle RDMs and (ii) Cauchy-Schwarz relations that arise from an important set of $N$-representability constraints known as the two-positivity conditions. The 2-RDMs are explicitly parameterized in terms of the first-order part of the cumulant 2-RDM and, for the inclusion of single excitations, a second-order part of the 1-RDM. In contrast to earlier formulations based on the coefficients from configuration interaction with single and double excitations (CISD), the cumulant-based parametric 2-RDM methods, from the properties of cumulants, are rigorously size extensive. We also show that writing the energy functionals in terms of correlated 1-RDMs and cumulant 2-RDMs reduces the computational cost of the parametric 2-RDM methods to that of CISD. Applications are made to ground-state energies of several molecules, equilibrium bond distances, and frequencies of HF, ${\mathrm{F}}_2$, and CO, the relative energy of the cis and trans isomers of ${\mathrm{HO}}_3$${}^{-}$, and the HCN-HNC isomerization reaction. For bond breaking in hydrogen fluoride the improved and more efficient parametric 2-RDM methods yield energies with similar accuracies at both equilibrium and nonequilibrium geometries in 6-31G** and polarized valence quadruple-$\zeta$ basis sets. Computed 2-RDMs very nearly satisfy well-known $N$-representability conditions.

Absolute cross sections are reported for single, double, and triple charge exchange of Fe${}^q$${}^{+}$ ($q=5–13$) ions with CO and CO${}_2$. The highly charged Fe ions are generated in an electron cyclotron resonance ion source. Absolute data are derived from knowledge of the target gas pressure, target path length, and incident and charge-exchanged ion currents. Experimental results are compared with new calculations of these cross sections in the $n$-electron classical trajectory Monte Carlo approximation in which the ensuing radiative and nonradiative cascades are approximated with scaled hydrogenic transition probabilities and scaled Auger rates. The present data are needed in astrophysical applications of solar- and stellar-wind charge exchange with comets, planetary atmospheres, and circumstellar clouds.

We report normalized experimental and theoretical differential cross sections for elastic electron scattering by ${\mathrm{C}}_4$H${}_4$O (furan) molecules from a collaborative project between several Brazilian theoretical groups and an experimental group at California State Fullerton, USA. The measurements are obtained by using the relative flow method with helium as the standard gas and a thin aperture target gas collimating source. The relative flow method is applied without the restriction imposed by the relative flow pressure condition on helium and the unknown gas. The experimental data were taken at incident electron energies of 1, 1.5, 1.73, 2, 2.7, 3, 5, 7, 10, 20, 30, and 50 eV and covered the angular range between ${10}^{°}$ and ${130}^{°}$. The measurements verify observed ${\pi }^{*}$ shape resonances at $1.65\pm 0.05$eV and $3.10\pm 0.05$ eV scattering energies, in good agreement with the transmission electron data of Modelli and Burrow [J. Phys. Chem. A 108, 5721 (2004)]. Furthermore, the present results also indicated both resonances dominantly in the $d$-wave channel. The differential cross sections are integrated in the standard way to obtain integral elastic cross sections and momentum transfer cross sections. The calculations employed the Schwinger multichannel method with pseudopotentials and were performed in the static-exchange and in the static-exchange plus polarization approximations. The calculated integral and momentum transfer cross sections clearly revealed the presence of two shape resonances located at 1.95 and 3.56 eV and ascribed to the $B_1$ and $A_2$ symmetries of the $C_{2v}$ point group, respectively, in very good agreement with the experimental findings. Overall agreement between theory and experiment regarding the differential, momentum transfer, and integral cross sections is very good, especially for energies below 10 eV.

We present integral and momentum transfer cross sections for elastic scattering of low-energy electrons by formamide (HCONH${}_2$) from $1$ to $12$ eV. To calculate the cross sections we employed the Schwinger multichannel method with pseudopotentials in the static-exchange and in the static-exchange-polarization approximations. We found a ${\pi }^{*}$ shape resonance belonging to the $A^{″}$ symmetry which is located at around $4.5$ eV in the static-exchange approximation, and at around $2.5$ eV in the static-exchange-polarization approximation. This result is in close agreement with the observations of Seydou et al. [Eur. Phys. J. D 35, 199 (2005)] which reported the value of $2.05$ eV to the vertical electron attachment energy, and is lower than the value of $3.77$ eV computed by Goumans et al. [J. Chem. Theory Comp. 5, 217 (2009)]. We carried out additional minimal basis set electronic structure calculations to help in the interpretation of our results. Our results support the conclusions of Goumans et al., namely, that this resonance may initiate the indirect dissociation mechanism of formamide by electron impact.

We study a washboard potential in a light-driven ensemble of three-level atoms induced by the externally applied magnetic fields under electromagnetically induced transparency (EIT). We find that a dark-state polariton, which is formed by an atomic ensemble dressed by the photon can display a typical quantum interference effect (i.e., the quasiparticle Bloch oscillation). The dark-state polariton is subjected to a washboard configuration potential with a spatially uniform force and a periodic potential provided by the linearly and periodically external magnetic fields, respectively. Due to the slower group velocity of the photons in the EIT medium, the period of Bloch oscillation can achieve a millisecond order of magnitude. Also, in our protocol, the Bloch oscillation of the dark-state polariton is feasibly modulated through the applied control and magnetic fields.

We demonstrate theoretically and experimentally the extraction of detailed information on the density matrix of very-high-$n$ ($>300)$ near-circular Rydberg wave packets through Fourier analysis of the quantum beat and quantum revival signals. The remarkably long coherence times associated with circular wave packets facilitate the preservation and read-out of phase information encoded in this matrix. We illustrate the power of the method by determining the angular localization of the components of a wave packet.

The Floquet resonance states of a periodically driven system are obtained using a special weighted power method which forces the dynamical symmetry into regular wave propagation methods. We demonstrate the utility of this method for the calculation of high harmonic generation spectra in rare gases. By using this method the resonance Floquet state which dominates the spectrum is obtained directly at a low computational cost. This may allow the calculation of resonance Floquet states in parameter regimes not accessible before. Implementation involves only slight adjustments to the standard wave propagation codes. The method’s unique advantage is explained and demonstrated.

We solve the time-dependent Schrödinger equation for atomic hydrogen in an intense field using spherical coordinates with a radial grid and a spherical harmonic basis for the angular part. We present the high-order harmonic spectra based on three different forms, the dipole, dipole velocity, and acceleration forms, and two gauges, the length and velocity gauges. The relationships among the harmonic phases obtained from the Fourier transform of the three forms are discussed in detail. Although quantum mechanics is gauge invariant and the length and velocity gauges should give identical results, the two gauges present different computation efficiencies, which reflects the different behavior in terms of characteristics of the physical couplings acting in the two gauges. In order to obtain convergence, more angular momentum states are required in the length gauge, while more grid points are required in the velocity gauge. At lower laser intensity, the calculation in the length gauge is faster than that in the velocity gauge, while at high laser intensity, the calculation in the velocity gauge is more efficient. The velocity gauge is also expected to be more efficient in higher-dimensional calculations.

Photoionization processes in highly charged atomic ions are studied by direct solution of the time-dependent Dirac equation. Expansion of a one-electron wave function in spin-orbit eigenfunctions yields close-coupled equations for bi-spinor radial wave functions. Expansion of a two-electron wave function in coupled spin-orbit eigenfunctions yields close-coupled equations for quad-spinor radial wave functions. Single photoionization cross sections using the close-coupled bi-spinor equations are calculated for Ne${}^{9+}$ and ${\mathrm{U}}^{91+}$. Single- and double-photoionization cross sections using the close-coupled quad-spinor equations are calculated for Ne${}^{8+}$ and ${\mathrm{U}}^{90+}$. All single photoionization cross sections are found to be in good agreement with fully relativistic perturbation theory results.

We report the photoionization studies of cesium from the 6$p$ ${}^2{P}_{3/2}$ excited state to measure the photoionization cross section at and above the first ionization threshold, oscillator strength of the highly excited transitions, and extension in the Rydberg series. The photoionization cross section at the first ionization threshold is measured as 25 (4) Mb and at excess energies 0.02, 0.04, 0.07, and 0.09 eV as 21, 19, 17, and 16 Mb, respectively. Oscillator strength of the 6$p$ ${}^2{P}_{3/2}$ $\to$ $nd$ ${}^2{D}_{5/2}$ (23 $⩽$ $n$ $⩽$ 60) Rydberg transitions has been extracted utilizing the threshold value of photoionization cross section and the recorded $nd$ ${}^2{D}_{5/2}$ photoionization spectra.

We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.

We apply the Hartree-Fock-Bogoliubov theory to a system of uniform dipolar fermionic polar molecules, which recently has attracted much attention due to rapid experimental progress in achieving such systems. By calculating the anisotropic superfluid-order parameter and the critical temperature $T_c$, we show that high-$T_c$ superfluid can be achieved with a quite modest value of interaction strength for polar molecules. In addition, we also show that the presence of the Fock-exchange interaction enhances superfluid pairing.

We discuss the stochastic mean-field theory (SMFT) method, which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and re-entrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [M. Pasienski, D. McKay, M. White, and B. DeMarco, e-print arXiv:0908.1182]. Including off-diagonal hopping disorder as well, we investigate its effect on the phase diagram in addition to pure on-site disorder. To make connection to present experiments on a quantitative level, we also combine SMFT with an LDA approach and obtain the condensate fraction in the presence of an external trapping potential.

We investigate an experimentally feasible intracavity coupled down-conversion scheme to generate quadripartite entanglement using concurrent nonlinearities. We verify that quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of optimized inequalities of the van Loock–Furusawa type. The entanglement characteristics both above and below the oscillation threshold are considered. We also present analytic solutions for the quadrature operators and the van Loock–Furusawa correlations in the undepleted pump approximation.

Pulses in fibers establish analogs of the event horizon [Philbin et al., Science 319, 1367 (2008)]. At a group-velocity horizon, the frequency of a probe wave is shifted. We present a theoretical model of this frequency shifting, taking into account the deceleration of the pulse caused by the Raman effect. The theory shows that the probe-wave spectrum is sensitive to details of the probe-pulse interaction. Our results indicate an additional loss mechanism in the experiment [Philbin et al., Science 319, 1367 (2008)] that has not been accounted for. Our analysis is also valid for more general cases of the interaction of dispersive waves with decelerated solitons.

We present two experiments that achieve phase super-resolution at telecommunication wavelengths. One of the experiments is realized in the space domain and the other is realized in the time domain. Both experiments show high visibility and are performed with standard lasers and single-photon detectors. The first experiment uses six-photon coincidences, whereas the latter experiment needs no coincidence measurements, is easy to perform, and achieves, in principle, arbitrarily high phase super-resolution. Here, we demonstrate a 30-fold increase of the resolution. We stress that neither entanglement nor joint detection is needed in these experiments, which demonstrates that neither is necessary to achieve phase super-resolution.

The quantum dynamics of the coupling between a cavity optical field and a resonator microwave field via the electro-optic effect is studied. This coupling has the same form as the optomechanical coupling via radiation pressure, so all previously considered optomechanical effects can in principle be observed in electro-optic systems as well. In particular, I point out the possibilities of laser cooling of the microwave mode, entanglement between the optical mode and the microwave mode via electro-optic parametric amplification, and back-action-evading optical measurements of a microwave quadrature.