We consider an infinite one-dimensional anisotropic $\mathit{XY}$ spin chain with a nearest-neighbor time-dependent Heisenberg coupling $J(t)$ between the spins in presence of a time-dependent magnetic field $h(t)$. We discuss a general solution for the system and present an exact solution for particular choice of $J$ and $h$ of practical interest. We investigate the dynamics of entanglement for different degrees of anisotropy of the system and at both zero and finite temperatures. We find that the time evolution of entanglement in the system shows nonergodic and critical behavior at zero and finite temperatures and different degrees of anisotropy. The asymptotic behavior of entanglement at the infinite time limit at zero temperature and constant $J$ and $h$ depends only the parameter $\lambda =J/h$ rather than the individual values of $J$ and $h$ for all degrees of anisotropy but changes for nonzero temperature. Furthermore, the asymptotic behavior is very sensitive to the initial values of $J$ and $h$ and for particular choices we may create finite asymptotic entanglement regardless of the final values of $J$ and $h$. The persistence of quantum effects in the system as it evolves and as the temperature is raised is studied by monitoring the entanglement. We find that the quantum effects dominate within certain regions of the $\mathit{kT}$-$\lambda$ space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persist in the vicinity of both its critical phase transition point and zero temperature as it evolves in time. Moreover, the interplay between the different system parameters to tune and control the entanglement evolution is explored.

Future quantum technologies rely heavily on good protection of quantum entanglement against environment-induced decoherence. A recent study showed that an extension of Uhrig’s dynamical decoupling (UDD) sequence can (in theory) lock an arbitrary but known two-qubit entangled state to the $N$th order using a sequence of $N$ control pulses [Mukhtar et al., Phys. Rev. A 81, 012331 (2010)]. By nesting three layers of explicitly constructed UDD sequences, here we first consider the protection of unknown two-qubit states as superposition of two known basis states, without making assumptions of the system-environment coupling. It is found that the obtained decoherence suppression can be highly sensitive to the ordering of the three UDD layers and can be remarkably effective with the correct ordering. The detailed theoretical results are useful for general understanding of the nature of controlled quantum dynamics under nested UDD. As an extension of our three-layer UDD, it is finally pointed out that a completely unknown two-qubit state can be protected by nesting four layers of UDD sequences. This work indicates that when UDD is applicable (e.g., when the environment has a sharp frequency cutoff and when control pulses can be taken as instantaneous pulses), dynamical decoupling using nested UDD sequences is a powerful approach for entanglement protection.

We find analytic models that can perfectly transfer, without state initialization or remote collaboration, arbitrary functions in two- and three-dimensional interacting bosonic and fermionic networks. This provides for the possible experimental implementation of state transfer through bosonic or fermionic atoms trapped in optical lattices. A significant finding is that the state of a spin qubit can be perfectly transferred through a fermionic system. Families of Hamiltonians are described that are related to the linear models and that enable the perfect transfer of arbitrary functions. Furthermore, we propose methods for eliminating certain types of errors.

The concept of negativity font, a basic unit of multipartite entanglement, is introduced. Transformation properties of determinants of negativity fonts under local unitary (LU) transformations are exploited to obtain relevant $N$-qubit polynomial invariants and construct entanglement monotones from first principles. It is shown that entanglement monotones that detect the entanglement of specific parts of the composite system may be constructed to distinguish between states with distinct types of entanglement. The structural difference between entanglement monotones for an odd and even number of qubits is brought out.

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

We propose a general measure of nonclassical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.

We study the Bethe binary-encounter (BE) region in the ejected-electron double-differential emission spectrum of ${\mathrm{H}}_2$ and He targets in collisions with 8-keV electrons. We compare the absolute cross sections for these isoelectronic systems at high emission energies. The experimental data are analyzed in terms of a state-of-the-art theoretical model based on a two-effective-center approximation. In the case of the ${\mathrm{H}}_2$ molecule the binary peak in the double-differential cross sections (DDCS) is enhanced due to the two-center Young-type interference. The observed undulation in the DDCS ratio is explained in terms of the combined contributions of the Compton profile mismatch and the interference effect. The influence of the interference effect is thus observed for higher-energy electrons compared to most of the earlier studies which focused on low-energy electrons produced in soft collisions.

Cross sections differential with respect to the energy loss and scattering angle of the projectile have been calculated for ionization of atomic hydrogen by 75-keV proton impact using the classical trajectory Monte Carlo method. The results are compared with the experimental data measured by Laforge et al. [Phys. Rev. Lett. 103, 053201 (2009)] and Schulz et al. [Phys. Rev. A 81, 052705 (2010)], as well as with the predictions of several quantum-mechanical theoretical models. The analysis of the deviations between the classical and the quantum-mechanical results shows that the three-body fragmentation dynamics cannot be understood purely classically; for the description of the process the quantum-mechanical treatment of the interplay between the electron-projectile and the projectile–target-nucleus interaction is unavoidable.

The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H${}_2$, HD, CO, ${\mathrm{O}}_2$, and CO${}_2$) and nonlinear (H${}_2$O and NH${}_3$) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component $\beta$ to the real component $\alpha$ of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, $\beta$ becomes significantly smaller than $\alpha$ as the energy gap for rotational transitions increases. In all cases, $\beta$ decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of ${\mathrm{H}}_2$ and HD appear to be collisionally stable due to the very low values of $\beta /\alpha$. Rotationally excited ${\mathrm{H}}_2$O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of $\beta$.

The projectile excitation of high-$Z$ ions has been investigated in relativistic ion-atoms collisions by observing the subsequent x-ray emission. The x-ray spectra from the projectile excitation have been separated from the x-ray emission following electron capture into the excited states using a novel anticoincidence technique. For the particular case of hydrogenlike Au${}^{78+}$ ions colliding with Ar atoms, Coulomb excitation from the ground state into the fine-structure-resolved $n=2$ levels as well as into levels with principal quantum number $n⩾3$ has been measured with excellent statistics. The observed spectra agree well with simulated spectra that are based on Dirac’s relativistic equation and the proper inclusion of the magnetic interaction into the amplitudes for projectile excitation. It is shown that a coherent inclusion of the magnetic part of the Lienard-Wiechert potential leads to the lowering of the excitation cross section by up to 35%. This effect is more pronounced for excitation into states with high angular momentum and is confirmed by our experimental data.

We introduce an adequate integral representation of the wave function in the asymptotic region, valid for the stage postinteraction between a one-electron atom and a laser pulse of short duration, as a superposition of divergent radial spherical waves. Starting with this representation, we derive analytic expressions for the energy and angular distributions of the photoelectrons and we show their connection with expressions used before in the literature. Using our results, we propose a method to extract the photoelectron distributions from the time dependence of the wave function at large distances. Numerical results illustrating the method are presented for the photoionization of hydrogenlike atoms from the ground state and several excited states by extreme ultraviolet pulses with a central wavelength of $13.3$ nm and several intensities around the value $I_0\approx 3.51\times {10}^{16}\hspace{0.5em}{\mathrm{W}/\mathrm{cm}}^2$.

We theoretically investigate the possibility of slowing and cooling a collisionless atomic gas using a phase-modulated pump field. We consider a single-pump ring cavity with asymmetric cavity losses containing a beam of $\mathit{N}$ polarizable pointlike particles. We show using analytical and numerical analysis that different regimes of the atom-light interaction can be identified and for properly chosen parameters this can lead to effective slowing of the atomic ensemble.

We use the assumption that the potential for the $A$-boson system can be written as a sum of pairwise acting forces to decompose the wave function into Faddeev components that fulfill a Faddeev type equation. Expanding these components in terms of potential harmonic (PH) polynomials and projecting on the potential basis for a specific pair of particles results in a two-variable integro-differential equations suitable for $A$-boson bound-state studies. The solution of the equation requires the evaluation of Jacobi polynomials $P_K^{\alpha ,\beta }(x)$ and of the weight function $W(z)$ which give severe numerical problems for very large $A$. However, using appropriate limits for $A\to \infty$ we obtain a variant equation which depends only on the input two-body interaction, and the kernel in the integral part has a simple analytic form. This equation can be readily applied to a variety of bosonic systems such as microclusters of noble gasses. We employ it to obtain results for $A\in (10-100)$ ${}^{87}\mathrm{Rb}$ atoms interacting via interatomic interactions and confined by an externally applied trapping potential $V_{\mathrm{trap}}(r)$. Our results are in excellent agreement with those previously obtained using the potential harmonic expansion method (PHEM) and the diffusion Monte Carlo (DMC) method.

We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than $1/N$ in a nonlinear Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of $N$ atoms. We present numerical simulations that confirm the analytical predictions for the effect of the spreading of the BEC ground-state wave function on the ideal $1/N^{3/2}$ scaling. Numerical integration of the coupled, time-dependent, two-mode Gross-Pitaevskii equations allows us to study the several simplifying assumptions made in the initial analytic study of the proposal and to explore when they can be justified. In particular, we find that the two modes share the same spatial wave function for a length of time that is sufficient to run the metrology scheme.

We study numerically the density of optical states (DOS) in two-dimensional photonic structures with short-range positional order and observe a transition from polycrystalline to amorphous photonic systems. In polycrystals, photonic band gaps (PBGs) are formed within individual domains, which leads to a depletion of the DOS similar to that in periodic structures. In amorphous photonic media, the domain sizes are too small to form PBGs, thus the depletion of the DOS is weakened significantly. The critical domain size that separates the polycrystalline and amorphous regimes is determined by the attenuation length of Bragg scattering, which depends not only on the degree of positional order but also the refractive-index contrast of the photonic material. Even with relatively low-refractive-index contrast, we find that modest short-range positional order in photonic structures enhances light confinement via collective scattering and interference.

In this paper we investigate the properties of self-induced transparency (SIT) solitons, propagating in a $\Lambda$-type medium. We find that the interaction between SIT solitons can lead to trapping with their phases preserved in the ground-state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furthermore, multiple independent SIT solitons can be made to propagate as bisolitons through their mutual interaction with a separate light field. Finally, we demonstrate that control of the SIT soliton phase can be used to implement an optical exclusive-or (xor) gate.

We present a method for finding surface modes at interfaces between two-dimensional photonic crystals (PCs), in which the surface modes are represented as superpositions of the PCs’ propagating and evanescent Bloch modes. We derive an existence condition for surface modes at an air-PC interface in terms of numerically calculated PC impedance matrices, and use the condition to find surface modes in the partial band gap of a PC. We also derive a condition for modes of a three-layer structure with two interfaces, and find both coupled surface modes and waveguide modes. We show that some waveguide modes cross the band edge and become coupled surface modes.

The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables—such as average fidelity susceptibility, order parameter, and concurrence—is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.

We present measurements of the cross-correlation function of photon pairs at $780$ and $1367$ nm, generated in a hot rubidium vapor cell. The temporal character of the biphoton is determined by the dispersive properties of the medium where the pair generation takes place. We show that short correlation times occur for optically thick samples, which can be understood in terms of off-resonant pair generation. By modifying the linear response of the sample, we produce near-resonant photon pairs, which could in principle be used for entanglement distribution.

The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions.