We present a method for accurate and efficient treatment of the time-dependent Schrödinger equation and electron energy and angular distributions after above-threshold multiphoton ionization. The procedure does not require propagation of the wave packet at large distances, making use of the wave function in the core region. It is based on the extension of the Kramers-Henneberger picture of the ionization process while the final expressions involve the wave function in the laboratory frame only. The approach is illustrated by a case study of above-threshold ionization of the hydrogen atom subject to intense laser pulses. The ejected electron energy and angle distributions have been calculated and analyzed. We explore the electron spectrum dependence on the duration of the laser pulse and carrier-envelope phase.

We study interacting bosons in optical lattices in the weak-tunneling regime in systems that exhibit the coexistence of Mott-insulating and condensed phases. We discuss the nature of the condensed ground state in this regime and the validity of the mean-field treatment thereof. We suggest two experimental signatures of condensate order in the system. (1) We analyze the hyperfine configuration of the system and propose a set of experimental parameters for observing radio-frequency spectra that would demonstrate the existence of the condensed phase between Mott-insulating phases. We derive the structure of the signal from the condensate in a typical trapped system, taking into account Goldstone excitations, and discuss its evolution as a function of temperature. (2) We study matter-wave interference patterns displayed by the system upon release from all confining potentials. We show that as the density profiles evolve very differently for the Mott-insulating phase and the condensed phase, they can be distinguished from one another when the two phases coexist.

Decoherence in simple experiments with Bose-Einstein condensates is of great importance for quantum engineering. We study a system of two colliding condensates in Fock and correlated states. During the collision some atoms are scattered out of the condensates, which leads to the decoherence. The quantum dynamics of the condensates is described by a master equation. In a simplified model we present analytical results. For more realistic conditions numerics is invoked. The depletion of the colliding condensates is accompanied by a decoherence.

An analytical expression is given for the normalization of wave functions of a charge particle inside a circular billiard in presence of an external magnetic field. The physical meaning of this normalizing factor is related to the derivative of the energy eigenvalue with respect to the radius of the billiard. A classical estimate of this factor gives another analytical expression which is in good numerical agreement with the quantum analytical result.

We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schrödinger equation for Bose-Einstein condensate trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.

We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum, and definite conclusions are obtained without evaluation of moments or any other more sophisticated procedures. These nonclassical tests are independent of other typical quantum signatures such as sub-Poissonian statistics, quadrature squeezing, or oscillatory statistics. This approach can be equally well applied to very diverse situations such as single- and two-mode fields, observables with continuous and discrete spectra, finite- and infinite-dimensional systems, and ideal and noisy measurements.

A scheme is presented for realizing long-distance quantum communication with individual atoms and atomic ensembles. In the scheme, deterministic and storable atom-photon entanglement sources can be obtained by adiabatic evolution of dark states, which makes this scheme largely enhance the efficiency for long-distance entanglement distribution. Furthermore, due to many-atom interference effect, requirement of the strong-coupling condition can be greatly relaxed. Thus this scheme opens an alternate avenue for a scalable quantum network.

It is shown that accelerated projective measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The produced state is always entangled and its entanglement increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration where Bell states are produced.

Rearrangement reaction in electron scattering from antiprotonic helium ions $\left(\overline{p}{\text{He}}^{2+}\right)$ in highly excited states, i.e., $e+\overline{p}{\text{He}}^{2+}\to \overline{p}+{\text{He}}^{+}$, is theoretically investigated by using the $R$-matrix method. This type of reaction can be identified as dissociative recombination (DR) which is well known in molecular physics. If the concept of the adiabatic Born-Oppenheimer separation is applied, the present exotic reaction has a similarity to the DR of ${\text{HeH}}^{+}$ molecules in the sense that the system has no crossings of the adiabatic potential curves. The present exotic DR reaction shows a variety of resonances, which can be described as a Rydberg electron attached to a $\overline{p}{\text{He}}^{2+}$ ion excited to an energetically forbidden state. The cross sections and rate coefficients for the present DR are calculated. As the bound motion of $\overline{p}{\text{-He}}^{2+}$ is closer to a circular orbit, the DR reaction, which leads to the destruction of $\overline{p}{\text{He}}^{2+}$, occurs less frequently. For the antiprotonic ion $\overline{p}{\text{He}}^{2+}$, it turns out that the circular states are the most stable against electron impacts.

Lifshitz-type formulas for the free energy and Casimir-Polder force between an atom possessing a permanent magnetic moment and a wall made of different materials are derived. A simple model allowing analytical results is considered where the atomic magnetic susceptibility is frequency independent and the wall is made of an ideal metal. Numerical computations of the Casimir-Polder force are performed for the cases of a H atom interacting with walls made of an ideal metal, a nonmagnetic metal (Au), a ferromagnetic metal (Fe), and a ferromagnetic dielectric. It is shown that for the first three wall materials inclusion of the atomic magnetic moment decreases the magnitude of the Casimir-Polder force, while for the fourth material the force increases.

We study the excitation dynamics of Rydberg atoms in a one-dimensional lattice with periodic boundary conditions where the atomic Rydberg states are resonantly excited from the electronic ground state. Our description of the corresponding dynamics is numerically exact within the perfect blockade regime, i.e., no two atoms in a given range can be excited. The time evolution of the mean Rydberg density, density-density correlations, as well as entanglement properties is analyzed in detail. We demonstrate that the short-time dynamics is universal and dominated by quantum phenomena, while for larger time the characteristics of the lattice become important and the classical features determine the dynamics. The results of the perfect blockade approach are compared to the predictions of an effective Hamiltonian which includes the interaction of two neighboring Rydberg atoms up to the second-order perturbation theory.

We demonstrate that Berry phases may greatly affect the dynamics of spin-orbit-coupled Bose-Einstein condensates. The effective model Hamiltonian under consideration is shown to be equivalent to the $E\times \epsilon$ Jahn-Teller model first introduced in molecular physics. The corresponding conical intersection is identified and the Berry phase acquired for a wave packet encircling the intersection is studied. It is found that this phase manifests itself in the density profile of the condensate, making it a directly measurable quantity via time-of-flight detection. Moreover, the non-Abelian gauge structure of the system is addressed and we verify how it affects the dynamics.

We demonstrate self-similar evolution of fundamental and higher-order dark soliton stripes on a paraboloidal background in a bulk graded-index waveguide with self-defocusing nonlinearity. The results show that the dark soliton stripes can self-similarly evolve on the paraboloidal background when they pass through the nonlinear well or barrier, and their evolutions may lead to the generation of the optical vortex when the initial dark soliton stripes deviate from the central position of the paraboloidal background. In addition, the interactions between neighboring dark soliton stripes on the paraboloidal background are investigated, which exhibits some complicated vortex patterns.

The characteristics of attosecond-pulse trains (APT) obtained from high-order harmonics are investigated by using a nonadiabatic three-dimensional model. A time-dependent phase matching approach is used in order to analyze the macroscopic formation of the APT. Under high ionization conditions, the process of APT formation is found to be the result of an interlace among the driving laser field, single atom response, phase matching effects in the near field and burst interference in the far field.

We investigate how relativity influences the spin correlation of entangled fermions described by wave packets and measured by moving detectors. In particular, we show that the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality is not violated by quantum mechanics when the left and right spin detectors move fast enough. We also show that the violation of the Bell-CHSH inequality measured by the moving detectors decreases with increasing width of the initial wave packet.

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.

We consider spatially two-dimensional Madelung fluid whose irrotational motion reduces into the Schrödinger equation for a single free particle. In this respect, we regard the former as a direct generalization of the latter, allowing a rotational quantum flow. We then ask for the most likely wave function possessing a given average energy by maximizing the Shannon information entropy over the quantum probability density. We show that there exists a class of solutions in which the wave function is self-trapped, rotationally symmetric, spatially localized with finite support, and spinning around its center, yet stationary. The stationarity comes from the balance between the attractive quantum force field of a trapping quantum potential generated by quantum probability density and the repulsive centrifugal force of a rotating velocity vector field. We further show that there is a limiting case where the wave function is nonspinning and yet still stationary. This special state turns out to be the lowest stationary state of the ordinary Schrödinger equation for a particle in a cylindrical tube external classical potential.

We demonstrate that an optically driven spin of a carrier in a quantum dot undergoes indirect dephasing via conditional optically induced charge evolution even in the absence of any direct interaction between the spin and its environment. A generic model for the indirect dephasing with a three-component system with spin, charge, and reservoir is proposed. This indirect decoherence channel is studied for the optical spin manipulation in a quantum dot with a microscopic description of the charge-phonon interaction taking into account its non-Markovian nature.

The multiple electron loss of heavy projectiles in fast ion-atom collisions has been studied in the framework of the sudden perturbation approximation. Especially, a model is developed to calculate the cross sections for the loss of any number of electrons from the projectile ion, including the ionization of a single electron and up to the complete stripping of the projectile. For a given collision system, that is specified by the (type and charge state of the) projectile and target as well as the collision energy, in fact, the experimental cross sections for just three final states of the projectile are required by this model in order to predict the loss of any number, $N$, of electrons for the same collision system or for any similar system that differs only in the energy or the initial charge state of the projectile ion. The model is simple and can be utilized for both the projectile and target ionization, and without that large computer resources are requested. Detailed computations have been carried out for the multiple electron loss of ${\text{Xe}}^{18+}$ and ${\text{U}}^{6+,10+,28+}$ projectiles in collision with neutral Ar and Ne gas targets.

The effects of combined external electric and magnetic fields on elastic collisions in ultracold Li-Rb mixtures are studied using recently obtained experimentally verified potentials. Our analysis provides both quantitative predictions for and a detailed physical interpretation of the phenomena arising from electric-field-induced interactions. It is shown that the electric field shifts the positions of intrinsic magnetic Feshbach resonances, generates copies of resonances previously restricted to a particular partial-wave collision to other partial-wave channels, and splits Feshbach resonances into multiple resonances for states of nonzero angular momenta. It was recently observed that the magnetic dipole-dipole interaction can also lift the degeneracy of a $p$-wave state splitting of the associated $p$-wave Feshbach resonance into two distinct resonances at different magnetic fields. Our work shows that the splitting of the resonances produced by an applied electric field is more than 1 order of magnitude larger. This phenomenon offers a complementary way to produce and tune an anisotropic interaction and to study its effect on the many-body physics of heteronuclear atomic gases.