Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC’s) loaded into optical lattices, are often described by the nonlinear Schrödinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single $\delta$ function or a combination of two $\delta$ functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS’s), which reside, respectively, in the semi-infinite or finite gaps of the system’s linear spectrum, being pinned to the $\delta$ functions. Physical realizations of these systems are possible in optics and BEC’s, using diverse variants of the nonlinearity management. First, we demonstrate that the single $\delta$ function multiplying the nonlinear term supports families of stable regular solitons in the self-attractive case, while a family of solitons supported by the attractive $\delta$ function in the absence of the periodic potential is completely unstable. In addition, we show that the $\delta$ function can support stable GS’s in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS’s in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single $\delta$ function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two $\delta$ functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the $\delta$ functions set symmetrically with respect to the minimum or maximum of the underlying potential.

The method of quantum annealing (QA) is a promising way for solving many optimization problems in both classical and quantum information theory. The main advantage of this approach, compared with the gate model, is the robustness of the operations against errors originated from both external controls and the environment. In this work, we succeed in demonstrating experimentally an application of the method of QA to a simplified version of the traveling salesman problem by simulating the corresponding Schrödinger evolution with a NMR quantum simulator. The experimental results unambiguously yielded the optimal traveling route, in good agreement with the theoretical prediction.

Spin-echo techniques are essential for achieving long coherence times in solid-state quantum memories for light because of inhomogeneous broadening of the spin transitions. It has been suggested that unrealistic levels of precision for the radio-frequency control pulses would be necessary for successful decoherence control at the quantum level. Here we study the effects of pulse imperfections in detail, using both a semiclassical and a fully quantum-mechanical approach. Our results show that high efficiencies and low noise-to-signal ratios can be achieved for the quantum memories in the single-photon regime for realistic levels of control pulse precision. We also analyze errors due to imperfect initial-state preparation (optical pumping), showing that they are likely to be more important than control pulse errors in many practical circumstances. These results are crucial for future developments of solid-state quantum memories.

Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupling functions are determined. Finally, the Casimir energy and force in the presence of a nonlinear medium at finite temperature are calculated.

We present a theoretical investigation of the chemical reaction SrF $+$ SrF $\to$ products, focusing on reactions at ultralow temperatures. We find that bond swapping SrF $+$ SrF $\to$ Sr${}_2$ $+$ ${\mathrm{F}}_2$ is energetically forbidden at these temperatures. Rather, the only energetically allowed reaction is SrF $+$ SrF $\to$ SrF${}_2$ $+$ Sr, and even then only singlet states of the SrF${}_2$ trimer can form. A calculation along a reduced reaction path demonstrates that this abstraction reaction is barrierless and proceeds by one SrF molecule “handing off” a fluorine atom to the other molecule.

A dynamically screened three-Coulomb-wave model (DS3C) is applied to study the single ionization of sodium by electron impact. Triply differential cross sections (TDCS) are calculated in doubly symmetric geometry at excess energies of 6, 10, 15, 20, 30, 40, 50, and 60 eV. Comparisons are made among DS3C and the latest experimental data and such theoretical predictions as the three–Coulomb–wave function approach, the distorted-wave Born approximation, and the nonperturbative convergent close-coupling method. The angular distribution and relative magnitude of the present TDCS are found to qualitatively reproduce the reported experimental data. It is shown that dynamically screened effects are important in the geometries studied here.

We have defined and have calculated the two-body and three-body spin-correlative probabilities to study spin correlations. Condensates of spin-2 atoms are chosen as examples; however, the underlying concept is general. These probabilities can directly relate to the experimental data. Therefore, they can be used to discriminate the spin structures and to clarify the interactions of various systems.

By investigating the third-order nonlinearity of a four-level ladder-type atomic system, it is found that, with spontaneously generated coherence (SGC) present, the nonlinear absorption or refraction can be significantly enhanced with vanishing linear absorption. We attribute the enhancement of nonlinearity mainly to quantum interference in the two decay pathways from the two upper closely lying levels. With a standing-wave trigger field, absorption or phase grating, which effectively diffracts a weak probe into high-order direction, can be induced by the SGC-enhanced absorptive or refractive nonlinear modulation. In contrast to the schemes for enhancing nonlinearity, no additional coupling field is required. Moreover, the present gratings result from the nonlinear modulation, which differs from the recent investigations based on linear modulation.

We present a study of the total force on a small lossless dielectric particle, which presents both an electric and magnetic response, in a optical vortex wave field. We show that the force is a simple combination of conservative and nonconservative steady forces that can rectify the flow of magnetodielectric particles. In a vortex lattice the electric-magnetic dipolar interaction can spin the particles either in or out of the whirl sites leading to trapping or diffusion. Specifically, we analyze force effects on submicron silicon spheres in the near infrared, proving that the results previously discussed for hypothetical magnetodielectric particles can be observed for these Si particles.

We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the black-body radiation shift of the Al${}^{+}$ clock has been estimated precisely. The computed shift relative to the frequency of the $3s^2\hspace{0.5em}{}^1{S}_0^e\to 3s3p\hspace{0.5em}{}^3{P}_0^o$ clock transition given by $(-3.66\pm 0.60)\times {10}^{-18}$ calls for an improvement over the recent measurement with a reported result of $(-9\pm 3)\times {10}^{-18}$ [Phys. Rev. Lett. 104, 070802 (2010)].

We propose a protocol for the creation of photonic Greenberger-Horne-Zeilinger and linear cluster states emitted from a single atom—or ion—coupled to an optical cavity field. The method is based on laser pulses with different polarizations and exploits the atomic transition amplitudes to state-selectively achieve the desired transitions. The scheme lies within reach of current technology.

We study superradiant scattering from a Bose-Einstein condensate using a pump laser incident at variable angle and show the presence of asymmetrically populated scattering modes. Experimental data reveal that the direction of the pump laser plays a significant role in the formation of this asymmetry, a result which is in good agreement with numerical simulations based on coupled Maxwell-Schrödinger equations. Our study complements the gap of previous work in which the pump laser was applied only along the short axis or the long axis of a condensate, and extends our knowledge about cooperative scattering processes.

We study the effects of an external periodic potential on the critical velocity of a superfluid Fermi gas in the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and Bose-Einstein condensation (BEC). We numerically solve the Bogoliubov–de Gennes equations to model a three-dimensional gas of ultracold atoms in the superfluid phase flowing through a one-dimensional optical lattice. We find that when the recoil energy is comparable to the Fermi energy, the presence of the periodic potential reduces the effect of pair-breaking excitations. This behavior is a consequence of the peculiar band structure of the quasiparticle energy spectrum in the lattice. When the lattice height is much larger than the Fermi energy, the periodic potential makes pairs of atoms to be strongly bound, even in the BCS regime, and pair-breaking excitations are further suppressed. We have also found that when the recoil energy is comparable to or larger than the Fermi energy, the critical velocity due to long-wavelength phonon excitations shows a nonmonotonic behavior along the BCS-BEC crossover.

A correlated pair of an electron and its parent ion is generated when a molecule is irradiated by an intense laser pulse. The accelerated electron will be driven back when the laser's electric field changes its sign and it may collide with the parent ion. In the present work, we experimentally study the electron-ion recollision process of oxygen in few-cycle laser fields. Two reaction channels are identified through coincident measurements. One is initiated by the recollision-induced dissociation and the other by the recollision-induced ionization. Angular distributions of the atomic ions are also measured for these two reaction channels. Although the angular distributions are mainly determined by angle-dependent ionization rates of molecules, we find that they are also affected by the symmetry of the recollision-related molecular orbitals.

We model two bosons in an optical lattice near a Feshbach or photoassociation resonance, focusing on the Bose-Hubbard model in one dimension. Whereas the usual atoms-only theory with a tunable scattering length yields one bound state for a molecular dimer for either an attractive or repulsive atom-atom interaction, for a sufficiently small direct background interaction between the atoms a two-channel atom-molecule theory may give two bound states that represent attractively and repulsively bound dimers occurring simultaneously. Such unusual molecular physics may be observable for an atom-molecule coupling strength comparable to the width of the dissociation continuum of the lattice dimer, which is the case, for instance, with narrow Feshbach resonances in Na, ${}^{87}\mathrm{Rb}$, and ${}^{133}\mathrm{Cs}$ or low-intensity photoassociation in ${}^{174}\mathrm{Yb}$.

The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the “time-variable” exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treat with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller’s thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.

We have studied quantum phase transition induced by a quench in different one-dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one-dimensional spin chains. At the critical region, the entanglement entropy of a block of $L$ spins with the rest of the system is also estimated which is found to increase logarithmically with $L$. The dependence on the quench time puts a constraint on the block size $L$. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the $\mathit{XXX}$ model and Ising model with magnetic field in the negative $z$ axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.

A theoretical study of the polarization entanglement of two photons emitted in the decay of metastable ionic states is performed within the framework of density-matrix theory and second-order perturbative approach. Particular attention is paid to relativistic and nondipole effects that become important for medium- and high-$Z$ ions. To analyze these effects, the degree of entanglement is evaluated both in the dipole approximation and within rigorous relativistic theory. Detailed calculations are performed for the two-photon $2s_{1/2}\to 1s_{1/2}$ transition in hydrogenlike ions as well as for the $1s_{1/2}\hspace{0.5em}2s_{1/2}\hspace{0.5em}{}^1{S}_0\to 1s_{1/2}^2\hspace{0.5em}{}^1{S}_0$, $1s_{1/2}\hspace{0.5em}2s_{1/2}\hspace{0.5em}{}^3{S}_1\to 1s_{1/2}^2\hspace{0.5em}{}^1{S}_0$, and $1s_{1/2}\hspace{0.5em}2p_{1/2}\hspace{0.5em}{}^3{P}_0\to 1s_{1/2}^2\hspace{0.5em}{}^1{S}_0$ transitions in heliumlike ions.

Multiphoton ionization of helium is investigated in the superintense field regime, with particular emphasis on the role of the electron-electron interaction in the ionization and stabilization dynamics. To accomplish this, we solve ab initio the time-dependent Schrödinger equation with the full electron-electron interaction included. By comparing the ionization yields obtained from the full calculations with the corresponding results of an independent-electron model, we come to the somewhat counterintuitive conclusion that the single-particle picture breaks down at superstrong field strengths. We explain this finding from the perspective of the so-called Kramers-Henneberger frame, the reference frame of a free (classical) electron moving in the field. The breakdown is tied to the fact that shake-up and shake-off processes cannot be properly accounted for in commonly used independent-electron models. In addition, we see evidence of a change from the multiphoton to the shake-off ionization regime in the energy distributions of the electrons. From the angular distribution, it is apparent that the correlation is an important factor even in this regime.

We introduce a method for the efficient computation of non-Markovian quantum dynamics for strong (and time-dependent) system-bath interactions. The past history of the system dynamics is incorporated by expanding the memory kernel in exponential functions thereby transforming in an exact fashion the non-Markovian integrodifferential equations into a (larger) set of “effective modes” differential equations (EMDE). We have devised a method which easily diagonalizes the EMDE, thereby allowing for the efficient construction of an adiabatic basis and the fast propagation of the EMDE in time. We have applied this method to three-dimensional photodissociation of the ${\mathrm{H}}_2^{+}$ molecule by strong laser fields. Our calculations properly include resonance-Raman scattering via the continuum, resulting in extensive rotational and vibrational excitations. The calculated final kinetic and angular distribution of the photofragments are in overall excellent agreement with experiments, both when transform-limited pulses and when chirped pulses are used.