Measurements of $K$ splittings in high-$L$ Rydberg states of barium are used to deduce electric-dipole and electric-quadrupole matrix elements in ${\text{Ba}}^{+}$. The model used to interpret these splittings is extended here to include the contributions of third- and fourth-order perturbation terms, altering the conclusions of a previous report that omitted those contributions. The analysis leads to improved experimental determinations of dipole $\left(6s\text{−}6p\right)$ and quadrupole $\left(6s\text{−}5d\right)$ transition strengths in ${\text{Ba}}^{+}$ that are in good agreement with recent a priori calculations.

Optimization of quantum systems by closed-loop adaptive pulse shaping offers a rich domain for the development and application of specialized evolutionary algorithms. Derandomized evolution strategies (DESs) are presented here as a robust class of optimizers for experimental quantum control. The combination of stochastic and quasi-local search embodied by these algorithms is especially amenable to the inherent topology of quantum control landscapes. Implementation of DES in the laboratory results in efficiency gains of up to $\sim 9$ times that of the standard genetic algorithm, and thus is a promising tool for optimization of unstable or fragile systems. The statistical learning upon which these algorithms are predicated also provide the means for obtaining a control problem’s Hessian matrix with no additional experimental overhead. The forced optimal covariance adaptive learning (FOCAL) method is introduced to enable retrieval of the Hessian matrix, which can reveal information about the landscape’s local structure and dynamic mechanism. Exploitation of such algorithms in quantum control experiments should enhance their efficiency and provide additional fundamental insights.

We generalize Stark-chirped rapid adiabatic passage (SCRAP) to the case of two and three degenerate-level manifolds. The analysis of a degenerate-level system is facilitated by its subdivision into a set of smaller independently evolving subsystems corresponding to the minimal-sized invariant subspaces of the Hamiltonian. Population transfer from the starting to the final level is examined for different types of the invariant subspaces depending on the presence of dark states. It is shown that the complete transfer is feasible if the initial state is prepared into specific coherent superpositions. Our formalism is applicable to the general case of arbitrary numbers of degenerate states within each level and arbitrary couplings of the appropriate transitions. It represents a generalization of well-known Morris-Shore transformation to the case when the removed degeneracy of the sublevels leads to detuning from two-photon resonance. We give the application of the SCRAP formalism to the ${}^{87}\text{R}\text{b}$ atom.

Isolated attosecond uv pulse provides a robust tool to control the high-order harmonic generation and efficient broadband supercontinua have been generated in this attosecond ionization control scheme at microscopic level. Here, we investigate the influences of propagation effects on the supercontinua. We find that efficient broadband supercontinua, which are enhanced by two or three orders of magnitude, can also be obtained at macroscopic level when the harmonics emitted from the short quantum path are phase matching. Moreover, the modulations in the supercontinua are eliminated and the bandwidths of the supercontinua are broadened after propagation.

We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multiband effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Einstein condensate superfluid state. Differing from the conventional Bardeen-Cooper-Schrieffer (BCS) superfluid transition, this transition shows unconventional properties. In contrast to the one-particle excitation gap scaled by the superfluid order parameter in the conventional BCS transition, because of the multiband effects, a large gap of one-particle density of states is retained all through the transition, although the superfluid order grows continuously from zero. A re-entrant transition with lowering temperature is another unconventionality. The other model is the case with coexisting attractive and repulsive interactions. Within a mean-field treatment, we find a new insulating state, an orbital ordered insulator. This insulator is one candidate for the Mott insulator of molecular bosons and is the first example that the orbital internal degrees of freedom of molecular bosons appears explicitly. Besides the emergence of a new phase, a coexisting phase also appears where superfluidity and an orbital order coexist just by doping holes or particles. The insulating and superfluid particles show differentiation in momentum space as in the high-$T_{\text{c}}$ cuprate superconductors.

We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting nonlinear Schrödinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic-energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.

Parametric photon creation via the dynamical Casimir effect (DCE) is evaluated numerically, in a three-dimensional rectangular resonant cavity bisected by a semiconductor diaphragm (SD), which is irradiated by a pulsed laser with frequency of GHz order. The aim of this paper is to determine some of the optimum conditions required to detect DCE photons relevant to an experimental detection system. We expand upon the thin plasma sheet model [M. Crocce et al., Phys. Rev. A 70, 033811 (2004)] to estimate the number of photons for both transverse electric (TE) and transverse magnetic (TM) modes at any given SD position. Numerical calculations are performed considering up to 51 intermode couplings by varying the SD location, driving period and laser power without any perturbations. It is found that the number of photons created for TE modes strongly depends on SD position, where the strongest enhancement occurs at the midpoint (not near the cavity wall); while TM modes have weak dependence on SD position. Another important finding is the fact that significant photon production for ${\text{TM}}_{111}$ modes still takes place at the midpoint even for a low-laser power of $0.01\mu \text{J}/\text{pulse}$, although the number of ${\text{TE}}_{111}$ photons decreases almost proportionately with laser power. We also find a relatively wide tuning range for both TE and TM modes that is correlated with the frequency variation in the instantaneous mode functions caused by the interaction between the cavity photons and conduction electrons in the SD excited by a pulsed laser.

We consider the phase space for $n$ identical qudits (each one of dimension $d$, with $d$ a primer number) as a grid of $d^n\times d^n$ points and use the finite Galois field $\text{GF}\left(d^n\right)$ to label the corresponding axes. The associated displacement operators permit to define $s$-parametrized quasidistributions on this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states of different qudits.

In order to fulfill the continuity requirements for electric- and magnetic-field amplitudes at discontinuities of ${\chi }^{\left(2\right)}$ nonlinearity, additional photon pairs have to be emitted in the area of discontinuity. Generalized two-photon spectral amplitudes can be used to describe properties of photon pairs generated in this process that we call surface spontaneous parametric down-conversion. The spectral structure of such photon pairs is similar to that derived for photon pairs generated in the volume. Surface and volume contributions to spontaneous down-conversion can be comparable as an example of nonlinear layered structures shows.

We present an analysis of the cooling of a micromechanical resonator by means of measurement and feedback. The measurements are performed via the coupling to a Cooper-pair box, and although the coupling does not lead to net cooling, the extraction of information and hence entropy from the system leads to a pure quantum state. Under suitable circumstances, the states become very close to coherent states, conditioned on the measurement record, and can hence be displaced to the oscillator ground state.

We propose a simplification of the time-dependent self-interaction correction (TD-SIC) method using two sets of orbitals, applying the optimized effective potential (OEP) method. The resulting scheme is called time-dependent “generalized SIC-OEP.” A straightforward approximation, using the spatial localization of one set of orbitals, leads to the “generalized SIC-Slater” formalism. We show that it represents a great improvement compared to the traditional SIC-Slater and Krieger-Li-Iafrate formalisms.

We report on the dark pulse emission of an all-normal dispersion erbium-doped fiber laser with a polarizer in cavity. We found experimentally that apart from the bright pulse emission, under appropriate conditions the fiber laser could also emit single or multiple dark pulses. Based on numerical simulations we interpret the dark pulse formation in the laser as a result of dark soliton shaping.

The two-loop self-energy correction to the ground-state Lamb shift is calculated for hydrogenlike ions with the nuclear charge $Z=10–30$ without any expansion in the binding field of the nucleus. A calculational technique is reported for treatment of Feynman diagrams in the mixed coordinate-momentum representation, which yields significant improvement in numerical accuracy as compared to previous results. An extrapolation of the all-order numerical data yields a result for the higher-order remainder function for hydrogen. The previously reported disagreement between the all-order and the perturbative approaches is reduced to the marginal agreement.

We propose an all-optical setup, which couples different degrees of freedom of a single photon, to investigate entanglement generation by a common environment. The two qubits are represented by the photon polarization and Hermite-Gauss transverse modes, while the environment corresponds to the photon path. For an initially two-qubit separable state, the increase of entanglement is analyzed as the probability of an environment-induced transition ranges from 0 to 1. An entanglement witness that is invariant throughout the evolution of the system yields a direct measurement of the concurrence of the two-qubit state.

The bound-free electron-positron pair production is considered for relativistic heavy ion collisions. In particular, cross sections are calculated for the pair production with the simultaneous capture of the electron into the $1s$ ground state of one of the ions and for energies that are relevant for the relativistic heavy ion collider and the large hadron colliders. In the framework of perturbation theory, we applied Monte Carlo integration techniques to compute the lowest-order Feynman diagrams amplitudes by using Darwin wave functions for the bound states of the electrons and Sommerfeld-Maue wave functions for the continuum states of the positrons. Calculations were performed especially for the collision of $\text{Au}+\text{Au}$ at 100 GeV/nucleon and $\text{Pb}+\text{Pb}$ at 3400 GeV/nucleon.

The dynamics of an $F=1$ spinor condensate in a two-well potential is studied within the framework of the Gross-Pitaevskii equation. We derive two-mode equations relating the population imbalances, the phase differences among the condensates at each side of the barrier and the time evolution of the different Zeeman populations for the case of small population imbalances. The case of zero total magnetization is scrutinized in this limit demonstrating the ability of a two-mode analysis to describe to a large extent the dynamics observed in the Gross-Pitaevskii equations. It is also demonstrated that the time evolution of the different total populations fully decouples from the Josephson tunneling phenomena. All the relevant time scales are clearly identified with microscopic properties of the atom-atom interactions.

We propose to probe the quantum ground state of a spin-1 Bose-Einstein condensate with the transmission spectra of an optical cavity. By choosing a circularly polarized cavity mode with an appropriate frequency, we can realize coupling between the cavity mode and the magnetization of the condensate. The cavity transmission spectra then contain information of the magnetization statistics of the condensate and thus can be used to distinguish the ferromagnetic and antiferromagnetic quantum ground states. This technique may also be useful for continuous observation of the spin dynamics of a spinor Bose-Einstein condensate.

Squeezed vacuum pulses up to $-1.7\text{dB}$ at telecom-band $\left(\sim 1550\text{nm}\right)$ is generated with femtosecond laser pulses using cascaded ${\chi }^{\left(2\right)}$ optical nonlinearity in a periodically poled lithium niobate crystal placed in a Sagnac interferometer. In spite of group velocity mismatch at short laser pulse pumping, sufficient cascaded nonlinear wave mixing is obtainable at the wavelength shifted from the phase matching wavelength for second harmonic generation. The theoretical model prediction agrees well with the experimental results.

We consider electromagnetic waves propagating in the system of coupled waveguides. One of the system components is a standard waveguide fabricated from nonlinear material having positive refraction index and another component is a waveguide produced from an artificial material having negative refraction index. In this waveguide a wave propagates in the direction opposite to direction of energy flux. We suppose that constituting metamaterial has linear properties. It is found that the coupled nonlinear solitary waves propagating both in the same direction are exist in this oppositely directed coupler due to linear coupling between nonlinear positive refractive waveguide and linear negative refractive waveguide. The corresponding analytical solution is found and it is used for numerical simulation to illustrate that the results of the solitary wave collisions are sensible to the relative velocity of the colliding solitary waves. The effect of linear losses in negative refractive waveguide is considered numerically.

We predict and experimentally observe the enhancement by three orders of magnitude of phase mismatched second and third harmonic generation in a GaAs cavity at 650 and 433 nm, respectively, well above the absorption edge. Phase locking between the pump and the harmonics changes the effective dispersion of the medium and inhibits absorption. Despite hostile conditions the harmonics resonate inside the cavity and become amplified leading to relatively large conversion efficiencies. Field localization thus plays a pivotal role despite the presence of absorption, and ushers in a new class of semiconductor-based devices in the visible and uv ranges.