We consider a system trapped in a resonance state, whose decay at zero scattering angle can be related, through the optical theorem, to the total cross section (TCS). We show that for the resonance to contribute to the TCS a peak structure the resonance conditions must be satisfied: (i) Several rotations of the complex (the Regge trajectory—viz., imaginary part versus the real part of the complex angular momentum—stays close to the real axis) and (ii) coherent addition of forward-scattering subamplitudes (the real part of the Regge pole is close to an integer). We exploit the recent complex angular momentum approach of Macek et al. [Phys. Rev. Lett. 93, 183203 (2004)], used to analyze low-energy oscillations observed in the elastic TCS for proton-H scattering, for a detailed analysis of Regge trajectories and their contributions to the TCS in electron-atom scattering for the case of $Z=75$ using the model Thomas-Fermi potential. We conclude by demonstrating through comparison with existing theory and measurements that the Thomas-Fermi potential when used with the appropriate parameters captures the essential physics (Ramsauer-Townsend minima and the Wigner threshold law) in the near-threshold $e\text{−}\mathrm{Ar}$ and $e\text{−}\mathrm{Kr}$ elastic scattering.

The long-range quadrupole-quadrupole $\left(\sim R^{-5}\right)$ and leading dispersion $\left(\sim R^{-6}\right)$ interactions between all pairs of excited $\text{Hg}\left(6s6p\right)$ ${{}^{3}P}_0$, ${{}^{3}P}_1$, ${{}^{3}P}_2$, and ${{}^{3}P}_1$ atoms are determined. The quadrupole moments are calculated using the ab initio relativistic configuration-interaction method coupled with many-body perturbation theory. The van der Waals coefficients are approximated using previously calculated static polarizabilities and expressions for the dispersion energy that are validated with similar systems. The long-range interactions are critical for associative ionization in thermal and cold collisions, and are found to be quite different for different pairs of interacting states. Based on this knowledge and the short-range parts of previously calculated potential curves, improved estimates of the chemi-ionization cross sections are obtained.

Properties of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation (ICQNLSE) with an external potential are studied. When it is associated with the homogeneous CQNLSE, a general condition exists linking the external potential and inhomogeneous cubic and quintic (ICQ) nonlinearities. Besides for the nonpresence of an external potential, two classes of Jacobian elliptic periodic potentials are discussed in detail, and the corresponding ICQ nonlinearities are found to be either periodic or localized. Exact analytical soliton solutions in these cases are presented, such as the bright, dark, kink, and periodic solitons, etc. An appealing aspect is that the ICQNLSE can support bound states with any number of solitons when the ICQ nonlinearities are localized and an external potential is either applied or not.

A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multimode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have nontrivial spatial structure even in the single-mode limit. In the multimode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic, and random laser media.

We study the resolution of an optical diffraction tomography system in which the objects are either in an homogeneous background or deposited onto a glass prism, a prism surmounted by a thin metallic film or a prism surmounted by a metallic film covered by a periodically nanostructured dielectric layer. For all these configurations, we present an inversion procedure that yields the map of the relative permittivity of the objects from their diffracted far field. When multiple scattering can be neglected, we show that the homogeneous, prism, and metallic film configurations yield a resolution about $\lambda ∕4$ while the grating substrate yields a resolution better than $\lambda ∕10$. When Born approximation fails, we point out that it is possible to neglect the coupling between the object and the substrate and account solely for the multiple scattering within the objects to obtain a satisfactory reconstruction. Last, we present the robustness of our inversion procedure to noise.

We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum, using a multifrequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.

The origin of the spatiotemporal filament dynamics of ultrashort pulses in nonlinear media, including axial-conical emission coupling, temporal splitting, and X waves, is explained by the spatiotemporal instability of spatially localized nonlinear modes. Our experiments support this interpretation.

We investigate the quantum Zeno and anti-Zeno effects in spin bath models: the spin-boson model and a spin-fermion model. We show that the Zeno–anti-Zeno transition is critically controlled by the system-bath coupling parameter, the same parameter that determines spin decoherence rate. We also discuss the crossover in a biased system, at high temperatures, and for a nonequilibrium spin-fermion system, manifesting the counteracting roles of electrical bias, temperature, and magnetic field on the spin decoherence rate.

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the cause of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of nonideal holonomic gates at finite operational time, i.e., long before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite-time gates. The results obtained suggest that the finite-time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of a geometrical feature.

The amount of classical information that is reliably transmitted over two uses of general Pauli channels with memory, modeled as a correlated noise between a single pair of uses, is investigated. The maximum of the mutual information between the input and the output is proven to be achieved by a class of product states that is explicitly given in terms of the relevant channel parameters below some memory threshold, and by maximally entangled states above this threshold. In particular, this proves a conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A 65, 050301(R) (2002)]. Furthermore, it also shows that no other scenario can occur for Pauli channels as for example the existence of an intermediate optimal degree of entanglement reported for some Gaussian channels with memory.

The femtosecond impulsive stimulated x-ray Raman signal from quinolinol is simulated and analyzed using the doorway-window representation of pump-probe spectroscopy. A valence electronic wave packet prepared by the pump, tuned on resonance with a given core hole, is localized in the vicinity of a selected atom and probed by a window localized on a different atom, selected by the probe pulse. All valence electronic states within the pulse bandwidths can be observed with high spatial and temporal resolution by monitoring the variation of the signal with the delay between the pulses. Natural orbital representation of the reduced single-electron density matrix is used to visualize the dynamics of the valence wave packet, described as a linear combination of determinants made of occupied and unoccupied Kohn-Sham orbitals.

The Lamb shift $(2P_{1∕2}-2S_{1∕2})$ in the muonic helium ion ${\left(\mu \text{−}{}_2{}^4\mathrm{He}\right)}^{+}$ is calculated with the account of contributions of orders ${\alpha }^3$, ${\alpha }^4$, ${\alpha }^5$, and ${\alpha }^6$. Special attention is given to corrections of the electron vacuum polarization, the nuclear structure, and recoil effects. The obtained numerical value of the Lamb shift $1381.72\mathrm{meV}$ can be considered as a reliable estimate for the comparison with experimental data.

We examine the energy spectrum of hydrogen in weak near-perpendicular electric and magnetic fields using quantum computations and semiclassical analysis. The spectral structure is displayed in a lattice constructed by plotting the difference between total energy and first order energy versus first order energy, for all states of a given principal quantum number $n$. We have used classical perturbation theory to derive three approximate constants of the motion. Quantization of the resulting approximate actions produces a corresponding lattice in agreement with our quantum calculations. For some field arrangements, one of the actions is an intrinsically multivalued function of the constants of the motion. This produces defects in the lattices and signifies the presence of a classical phenomenon called monodromy. The presence of monodromy in the case of exactly perpendicular fields was previously predicted by Sadovskií and Cushman. Our quantum calculations and independent semiclassical analysis confirm their prediction, and show that the presence of monodromy not only persists into near-perpendicular fields, but also assumes other manifestations over a wider range of field strength ratios. We find that in near-perpendicular fields the structure of the spectrum is divided into six distinct parameter regions, which we characterize by the presence and type of lattice defect.

Cold atoms in optical lattices are described in real space by the multiorbital mean-field approach. We consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons, (iii) Bose-Bose mixtures, and (iv) Bose-Fermi mixtures, and derive in each case the corresponding multiorbital mean-field energy functional and working equations. The general equations as well as those obtained by explicitly utilizing the translational symmetry of lattices are presented. We discuss the effects of particle-particle interactions and translational symmetry on properties of the solutions.

We derive general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of the material interior, as it only uses knowledge of the reflection amplitudes for its surface. Therefore, our results are valid for all homogeneous surfaces, including layered systems and metamaterials, at all temperatures. In particular, we obtain formulas for the near-field region, which are important for interpreting the numerous current experiments probing proximity effects for macroscopic and/or microscopic bodies separated by small empty gaps. By use of Onsager’s reciprocity relations, we obtain also the general symmetry properties that must be satisfied by the reflection matrix of any material.

A unified theory is advanced to describe both the lateral Goos-Hänchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a three-dimensional light beam in terms of a two-form angular spectrum consisting of its two orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the two orthogonal linear polarizations in this two-form representation, and the eigenstates of the IF displacement are the two orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.

An analytical quantum theory of Thirring solitons is developed using a linearized perturbation analysis. This theory is used to study the vacuum-induced fluctuations of Thirring soliton propagation and collision. We show that squeezing occurs due to phase diffusion and wave packet spreading, as expected. It is also shown that Thirring soliton collisions can lead to a reduction in quantum phase and position noise. Due to similar phenomena that occur for solitons of the one- and two-component nonlinear Schrödinger model, this seems to point to a more general effect of quantum noise reduction in soliton collisions. These results may find relevance in optics, Bose-Einstein condensates, and other areas in which the observation of Thirring solitons is possible.

We show that direct feedback based on quantum-jump detection can be used to generate entangled steady states. We present a strategy that is insensitive to detection inefficiencies and robust against errors in the control Hamiltonian. This feedback procedure is also shown to overcome spontaneous emission effects by stabilizing states with a high degree of entanglement.

In order to acquire an extended Salecker-Wigner formula from which to derive the optimal accuracy in reading a clock with a massive particle as the signal, von Neumann’s classical measurement is employed, by which simultaneously both position and momentum of the signal particle can be measured approximately. By an appropriate selection of wave function for the initial state of the composite system (a clock and a signal particle), the formula is derived accurately. Valid ranges of the running time of a clock with a given optimal accuracy are also given. The extended formula means that contrary to the Salecker-Wigner formula there exists the possibility of a higher accuracy of time measurement, even if the mass of the clock is very small.

A parametric down-conversion (PDC) source can be used as either a triggered single-photon source or an entangled-photon source in quantum key distribution (QKD). The triggering PDC QKD has already been studied in the literature. On the other hand, a model and a post-processing protocol for the entanglement PDC QKD are still missing. We fill in this important gap by proposing such a model and a post-processing protocol for the entanglement PDC QKD. Although the PDC model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. Since an entangled PDC source is a basis-independent source, we apply Koashi and Preskill’s security analysis to the entanglement PDC QKD. We also investigate the entanglement PDC QKD with two-way classical communications. We find that the recurrence scheme increases the key rate and the Gottesman-Lo protocol helps tolerate higher channel losses. By simulating a recent $144\text{−}\mathrm{km}$ open-air PDC experiment, we compare three implementations: entanglement PDC QKD, triggering PDC QKD, and coherent-state QKD. The simulation result suggests that the entanglement PDC QKD can tolerate higher channel losses than the coherent-state QKD. The coherent-state QKD with decoy states is able to achieve highest key rate in the low- and medium-loss regions. By applying the Gottesman-Lo two-way post-processing protocol, the entanglement PDC QKD can tolerate up to $70\mathrm{dB}$ combined channel losses ($35\mathrm{dB}$ for each channel) provided that the PDC source is placed in between Alice and Bob. After considering statistical fluctuations, the PDC setup can tolerate up to $53\mathrm{dB}$ channel losses.