We construct a simple algorithm to generate any Clauser-Horne-Shimony-Holt- (CHSH-) type Bell inequality involving a party with two local binary measurements from two CHSH-type inequalities without this party. The algorithm readily generalizes to situations where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze a class of symmetric inequalities for four observers and three experimental settings per observer.

The $R$-matrix-with-pseudostates (RMPS) method is used to obtain total cross sections for double photoionization of Be and Mg atoms from their ground singlet and metastable triplet terms. Time-dependent close-coupling (TDCC) calculations are also carried out for the total and energy differential double photoionization cross sections of Mg from its ground term. The RMPS total ground-term cross sections for Be and Mg are in good agreement with results from TDCC and convergent close-coupling calculations at lower energies but are above them at higher energies. They are also in good agreement with the results of synchrotron measurements. The total cross sections for double photoionization from the triplet metastable terms of Be and Mg are found to be two to three times smaller than those from their singlet ground terms.

A theory of high-order harmonic generation by diatomic molecules is introduced. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are investigated. Using examples of homonuclear diatomic molecules such as ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$, it is shown that clear two-center interference minima in the harmonic spectra as a function of the molecular orientation appear only if the final molecular state is undressed. For ${\mathrm{H}}_2$ the positions of these minima are in agreement with the ab initio numerical results. Physically, the returned electron wave packet recombines into a molecular orbital, which is a linear combination of the atomic orbitals having different parities. The interference minima in the harmonic spectrum are caused by the destructive interference of the corresponding partial recombination amplitudes. In accordance with this, we have derived an interference minima condition which is valid for arbitrary homonuclear diatomic molecules.

We study nonlinear light propagation in colloidal suspensions of spherical dielectric nanoparticles. We analyze the existence and properties of one-dimensional self-trapped beams (spatial optical solitons) in such media and demonstrate the existence of a bistability regime. The solitons corresponding to the two bistable branches have very different properties, and they can be easily distinguished by the measurement of the soliton width. We find that both types of solitons can form spontaneously through spatial modulational instability of continuous wave beams, but the solitons corresponding to the upper branch are more robust. This is also confirmed by the study of soliton collisions, where we describe a number of possible scenarios, including soliton amalgamation, destruction, reflection, deflection, and switching to another branch. We also find that the interaction of two mutually coherent solitons corresponding to different branches is phase independent and always repulsive. We provide a simple physical explanation of this phenomenon.

This paper presents a theoretical study of the time-dependent cross-phase-modulation in ${}^{87}\mathrm{Rb}$. A four-level system in the N configuration is constructed by making use of the hyperfine sublevels present in the rubidium $D$ lines. It is shown that a large transient absorption is present on the electromagnetically induced transparency transition when that field is suddenly turned on. Furthermore, the magnitude and rise time of the cross-phase-modulation are shown to be inversely proportional to each other. We also construct the first-order nonadiabatic corrections to the atomic evolution and demonstrate how these affect slow-light pulse propagation in the atomic ensemble.

Three-tangle for a rank-3 mixture composed of Greenberger-Horne-Zeilinger, $W$, and flipped-$W$ states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere $S^8$ of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.

We derive a uniformly frustrated $XY$ model that describes two-dimensional Josephson-junction arrays consisting of rotating Bose-Einstein condensates trapped by both a harmonic trap and a corotating deep optical lattice. The harmonic trap makes the coupling constant of the model have a nonuniform parabolic dependence. We study the ground state through Monte Carlo simulations in a wide range of the frustration parameter $f$, revealing a rich variety of vortex patterns.

Quantum state propagation over binary-tree configurations is studied in the context of quantum spin networks. For a binary tree of order 2, a simple protocol is presented which allows one to achieve arbitrary high transfer fidelity. It does not require fine-tuning of local fields and two-node coupling of the intermediate spins. Instead it assumes simple local operations on the intended receiving node: their role is to brake the transverse symmetry of the network that induces an effective refocusing of the propagating signals. Some ideas on how to scale up these effects to a binary tree of arbitrary order are discussed.

We report both experimental and theoretical studies on x-ray absorption measured using partial Auger yields of gas phase nitrogen, carbon monoxide, and oxygen molecules near the $\mathrm{N}1s\to {\pi }^{*}$, $\mathrm{O}1s\to {\pi }^{*}$, and $\mathrm{O}1s\to {\pi }^{*}$ regions, respectively. The main tool of our study is a two-dimensional map in which resonant Auger yields are plotted as a function of photon and kinetic energy. The partial yields of the three molecules are analyzed in detail by extracting profiles along various directions in the map. Narrowing of the absorption resonances is observed along the direction of constant kinetic energy. It is shown that such profiles are similar to the conventional x-ray-absorption spectrum for a broad class of molecules whose potential energy surfaces of the final and core-excited states are almost parallel. However, substantial differences with the conventional x-ray-absorption profiles are observed in the general case of nonparallel surfaces due to the lifetime vibrational interference. Here, we suggest a systematic way to eliminate the lifetime vibrational interference.

The $4d$ photoelectron and satellite spectra of ${\mathrm{Sb}}_4$ clusters are presented together with the subsequent $CVV$ (core-valence-valence) Auger electron spectra. Theoretical molecular calculations were used together with semiempirical methods combining negative ion atomic calculations and existing experimental data on the noble gas xenon to predict the structure of the electron spectra. A detailed experimental analysis of the fragmentation pathways of ${\mathrm{Sb}}_4$ after $4d$ photoionization and subsequent Auger decay was performed with the use of ion time-of-flight spectroscopy, electron-ion coincidence, and electron-ion-ion coincidence techniques. The bonding properties of the molecular orbitals have been used to qualitatively describe the observed fragmentation pathways.

We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of an external magnetic $\left(B\right)$ field according to atomic parameters for intra- and interspecies spin-exchange coupling and singlet-pairing interaction. Ignoring the interspecies singlet-pairing interaction, the ground-state phases are found analytically. A numerical approach of simulated annealing is adopted when the singlet-pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, which can be induced through the tuning of optical traps and atom numbers. They provide insight and guidance for several ongoing experiments on mixtures of spinor condensates.

We show that strong inelastic interactions between bosons in one dimension create a Tonks-Girardeau gas, much as in the case of elastic interactions. We derive a Markovian master equation that describes the loss caused by the inelastic collisions. This yields a loss rate equation and a dissipative Lieb-Liniger model for short times. We obtain an analytic expression for the pair correlation function in the limit of strong dissipation. Numerical calculations show how a diverging dissipation strength leads to a vanishing of the actual loss rate and renders an additional elastic part of the interaction irrelevant.

We give a simple multiround strategy that permits us to beat the shot-noise limit when performing interferometric measurements even in the presence of loss. In terms of the average photon number employed, our procedure can achieve twice the sensitivity of conventional interferometric ones in the noiseless case. In addition, it is more precise than the (recently proposed) optimal two-mode strategy even in the presence of loss.

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modeling optical tweezers. These simplifications are based on neglecting the Minkowski tensor’s material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions that must be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett et al., we find their prediction in agreement with that obtained using the total energy-momentum tensor.

We optimize number squeezing when splitting a mesoscopic Bose-Einstein condensate. Applying optimal control theory to a realistic description of the condensate allowed us to identify a form of the splitting ramp, which drastically outperforms the adiabatic splitting. The results can be interpreted in terms of a generic two-mode model mapped onto a parametric harmonic oscillator. This optimal route to squeezing paves the way to a much longer phase coherence and atom interferometry close to the Heisenberg limit.

We investigate the decay of entanglement, due to decoherence, of multiqubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness-optimization problem that only involves states equivalent, under local unitary transformations, to the Greenberger-Horne-Zeilinger $|\text{GHZ}⟩$ state.

We examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum-state tomography. We find that, in some important circumstances, an elaborate and time-consuming numerical optimization to obtain the optimum density matrix corresponding to a given data set is not necessary and that cruder, faster numerical techniques may well be sufficient; in other words, “the best” is the enemy of “good enough.”

The entanglement dynamics of Fermi resonance coupling vibrations in a spectroscopic Hamiltonian for molecules $\mathrm{C}\mathrm{H}{\mathrm{D}}_3$, $\mathrm{C}\mathrm{H}{\mathrm{Cl}}_3$, and $\mathrm{C}\mathrm{H}{\mathrm{F}}_3$ is studied in terms of the von Neumann entropy and negativity with three kinds of initial states that are direct products of coherent states, thermal states, and squeezed states of each mode. It is demonstrated that the increasing rate of entanglement in the early-time evolution is the largest for the squeezed states, while that is the smallest for the coherent states. For small parameters in the coherent and thermal states, entanglement displays a quasiperiodicity with the quasiperiod in $\mathrm{C}\mathrm{H}{\mathrm{F}}_3$ being the longest. Furthermore, the dynamical correlation between the von Neumann entropy and negativity shows that positively correlated or anticorrelated behaviors of both measures strongly depend on initial states and molecules. For those states with small parameters, both measures exhibit dominantly positive correlation. These are useful for molecular quantum computing and information processing.

We present a protocol to prepare decoherence-free cluster states using ultracold atoms loaded in a two dimensional superlattice. The superlattice geometry leads to an array of $2\times 2$ plaquettes, each of them holding four spin-$1∕2$ particles that can be used for encoding a single logical qubit in the twofold singlet subspace, insensitive to uniform magnetic field fluctuations in any direction. Dynamical manipulation of the supperlattice yields distinct inter- and intraplaquette interactions and permits us to realize one qubit and two qubit gates with high fidelity, leading to the generation of universal cluster states for measurement based quantum computation. Our proposal based on inter- and intraplaquette interactions also opens the path to study polymerized Hamiltonians which support ground states describing arbitrary quantum circuits.