Using a semiclassical model based on tunneling, electron kinematics in the laser field, and phase space volume, we evaluate the ion and electron momentum distributions in nonsequential double ionization of a model atom by an elliptically polarized laser field. For ellipticities exceeding approximately 0.3, we find that the shortest quantum orbit (having the shortest travel time) no longer dominates the double-ionization rate, in contrast to the case of linear polarization. Simultaneously we observe significant violations of symmetry patterns in the ion-momentum distributions and the electron-electron momentum correlations, compared with the case of linear polarization. These violations are very sensitive to the laser pulse duration because of the absence of the late returns for very short pulses. Some of these qualitative effects in the photoelectron distributions should be experimentally detectable. Observation would verify the significance of the late returns and the underlying quantum-orbit concept.

We extend the many-mode Floquet theorem (MMFT) for the investigation of multiphoton resonance dynamics driven by intense frequency-comb laser fields. The frequency comb structure generated by a train of short laser pulses can be exactly represented by a combination of the main frequency and the repetition frequency. MMFT allows non-perturbative and exact treatment of the interaction of a quantum system with the frequency-comb laser fields. We observe simultaneous multiphoton resonance processes between a two-level system and frequency-comb laser. The multiphoton processes can be coherently controlled by tuning the laser parameters such as the carrier-envelope phase (CEP) shift. In particular, high-order harmonic generation shows immense enhancement by tuning the CEP shift, due to simultaneous multiphoton resonances.

The $S$-matrix theory is developed to study the nonsequential double ionization (NSDI) of diatomic molecules ${\text{N}}_2$ and ${\text{O}}_2$ in an intense field. It is shown that electronic structures influence the NSDI process of molecules. Compared to ${\text{N}}_2$, a suppression effect of NSDI of molecule ${\text{O}}_2$ is found and it can be explained by the difference between the angular distributions of the first ionized photoelectrons of ${\text{N}}_2$ and ${\text{O}}_2$. The ratios of the NSDI rate to the single-ionization rate are also obtained and compared with experimental observations.

We theoretically evaluate changes in the magnetic potential arising from the magnetic field near superconducting thin films. An example of an atom chip based on a three-wire configuration has been simulated in the superconducting and the normal conducting state. Inhomogeneous current densities within the superconducting wires were calculated using an energy-minimization routine based on the London theory. The Meissner effect causes changes to both trap position and oscillation frequencies at short distances from the superconducting surface. Superconducting wires produce much shallower microtraps than normal conducting wires. The results presented in this paper demonstrate the importance of taking the Meissner effect into account when designing and carrying out experiments on magnetically trapped neutral atoms near superconducting surfaces.

We design a model of correlated hopping for bosonic atoms in optical lattices. Such a model exhibits three kinds of phases: a Mott insulator, a charge density wave, and a pair quasicondensate. One possible implementation of the model is based on two-state atoms embedded in an optical superlattice and having state-dependent interactions. Contrary to other models of pairing, correlated hopping is not a perturbative effect and should be observable in generalizations of current experiments.

This paper discusses the master equation approach to the derivation of the Esaki-Tsu equation for drift current. It is shown that the relaxation term in the master equation can be identified by measuring the velocity distribution of the carriers. We also show that the standard form of the relaxation term, used earlier to derive the Esaki-Tsu equation, predicts unphysical velocity distribution. We suggest a more elaborate relaxation term, which is argued to correctly capture the effect of a bosonic bath in experiments on atomic current in optical lattices.

We analyze complex spatiotemporal semidiscrete solitons in a model of a set of nonlinear optical fibers which form a square lattice in the cross section. The medium was recently realized as a set of parallel waveguides written in fused silica. The model also applies to a self-attracting Bose-Einstein condensate trapped in a very strong quasi-two-dimensional optical lattice. By means of the variational approximation (VA) and using numerical methods, we construct several species of the semidiscrete solitons, including vortices of rhombus (alias cross) and square types, with vorticity $S=1$ and 2, and quadrupoles. The VA is developed for narrow cross vortices with $S=1$ and quadrupoles, which turn out to be the most stable species. Two finite stability intervals are also found for the square-shaped vortices with $S=1$, while all the vortices with $S=2$ are unstable. For the unstable solitons, several scenarios of the instability development are identified, such as fusion of the entire complex into a single fundamental soliton, or splitting into coherent soliton pairs.

We study the effects of arbitrary laser pulse excitations on quantum correlation, entanglement, and the role of quantum noise. The transient quantities are computed exactly using a method that provides exact solutions of the Langevin field operators for photon pairs produced by a double Raman atom driven by laser pulses. Short pulses with appropriate chirping, delay, and/or detuning can generate broadband photon pairs and yield results that provide insights on how to generate very large nonclassical correlation. We find that short pulses are not favorable for entanglement. Photon correlation and entanglement are favored by exclusively two different initial conditions. We find rapid variations of entanglement with pulse width and strength. Explanation is given based on the pulse area concept and the phase-sensitive nature of entanglement. Analysis of results reinforces our understanding of the two nonclassical concepts and the nature of quantum noise.

We investigate coherent atomic tunneling of a dilute gas Bose-Einstein condensate (BEC) in a three-well system. In particular, we generalize stimulated Raman adiabatic passage (STIRAP) to adiabatically transport a BEC of 2000 ${}^7\mathrm{Li}$ atoms between two wells with minimal occupation in the intervening well. This protocol paves the way for a robust method of control in atom-optical devices.

For quantum-information processing (QIP) with trapped ions, the isotope ${{}^{43}\text{C}\text{a}}^{+}$ offers the combined advantages of a quantum memory with long coherence time, a high-fidelity readout, and the possibility of performing two-qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, ${{}^{43}\text{C}\text{a}}^{+}$ has a relatively complicated level structure. We discuss how to meet the basic requirements for QIP and demonstrate ground-state cooling, robust state initialization, and efficient readout for the hyperfine qubit with a single ${{}^{43}\text{C}\text{a}}^{+}$ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum-information storage time of many seconds for the hyperfine qubit.

We demonstrate that the Byzantine agreement (detectable broadcast) is also solvable in the continuous-variable scenario with multipartite entangled Gaussian states and Gaussian operations (homodyne detection). Within this scheme we find that Byzantine agreement requires a minimum amount of entanglement in the multipartite states used in order to achieve a solution. We discuss realistic implementations of the protocol, which consider the possibility of having inefficient homodyne detectors, not perfectly correlated outcomes, and noise in the preparation of the resource states. The proposed protocol is proven to be robust and efficiently applicable under such nonideal conditions.

In this paper, the symmetry property of time reversal, which is a consequence of the fundamental quantum-mechanical microreversibility principle, is analyzed in the context of relativistic open-shell and multireference coupled cluster theory. The fact is discussed that in projective theories, in contrast to variational theories such as configuration interaction models, the implementation of time-reversal symmetry is far less straightforward and even depends on the projective model theory in question. An operator basis of time reversal even $n$-body operators is introduced which allows for the formulation of a fully time-reversal-adapted and practical general coupled cluster theory, i.e., covering open-shell models and various types of multireference approaches. The resulting model theory is noncommuting but truncating, albeit at a higher order of commutator nesting.

A detailed experiment on $2p$ photoionization and subsequent Auger decay of atomic silicon is presented. Fine-structure-resolved photoelectron and Auger electron spectra are interpreted with the aid of large-scale multiconfiguration calculations. Energy separation and the relative cross sections of the $2p$ ionized fine-structure states of ${\text{Si}}^{+}$ are given. The complete $2p$ Auger electron spectrum of Si is interpreted, and the intensity distribution to individual doubly ionized final states is studied.

The $B$-spline $R$-matrix method with nonorthogonal orbital sets is extended to a fully relativistic version based on the solution of the many-electron Dirac equation. The $B$-spline basis is used to generate both the target description and the $R$-matrix basis functions in the inner region. Using $B$-splines of different orders for the large and small components prevents the appearance of pseudostates in the spectrum of the Dirac equation. Using term-dependent and thus nonorthogonal sets of one-electron functions enables us to generate accurate and flexible representations of the target states and the scattering function. Our method is based upon the all-electron Dirac-Coulomb Hamiltonian and thus may be employed for any complex atom or ion, without the use of phenomenological core potentials. As a first test of the method, we consider elastic electron scattering from Cs atoms in their ground state. Close agreement with experiment is obtained for the total and the angle differential cross sections at various energies between 1 eV to 7 eV, as well as for several spin asymmetry parameters. The results represent a substantial improvement over those obtained in previous Breit-Pauli and Dirac $R$-matrix calculations.

We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose (PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.

It is usually presumed that spontaneous emission is necessary to remove the entropy lost by laser-cooled atoms. Here we show that the changes in the laser beams themselves constitute a sufficiently large reservoir of $N$ states accessible to the system that their entropy $S=k_B\ln \left(N\right)$ is sufficient to absorb the entropy lost by the atoms in the cooling process. Proper choice of laser parameters could possibly produce cooling of atoms or molecules over a wide range of temperatures without spontaneous emission.

We present results on phase-locking dynamics of coupled lasers near threshold, and their dependence on spontaneous emission. Our experimental and analytical results clearly reveal that phase locking depends strongly on quantum noise when the coupled lasers oscillate near threshold.

We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $\mathit{N}$ elementary subsystems, they are defined as the distances from the sets of $\mathit{K}$-separable states $\left(K=2,\dots ,N\right)$. The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows discrimination among the different contributions. The extended measures are applied to the study of entanglement in different classes of $\mathit{N}$-qubit pure states. These classes include $\mathit{W}$ and Greenberger-Horne-Zeilinger (GHZ) states, and their symmetric superpositions; symmetric multimagnon states; cluster states; and, finally, asymmetric generalized $\mathit{W}$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between GHZ and $\mathit{W}$ states, clarifying the original result of Wei and Goldbart that $\mathit{W}$ states possess a larger global entanglement than GHZ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.

We study the dynamics of entanglement in an $XY$ spin chain subject to a staggered magnetic field and contrast it to the previously discussed uniform field case. We find that in the isotropic $\left(XX\right)$ limit a staggered field can provide almost equally favorable conditions for a high-fidelity transfer of entanglement, while even a modest amount of exchange anisotropy appears to have a strong detrimental effect. We also study interactions between different waves of entanglement and assess the possibility of simultaneous transmission of multiple bits of quantum information.