Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generates interferences beyond an Ehrenfest timescale, where quantum and classical expectation values diverge. Of great recent interest is the role these interferences play in the spreading of quantum information across the many degrees of freedom, i.e., scrambling. Ultracold atomic gases provide a promising setting to explore these phenomena. Theoretically speaking, the heavily-relied-upon truncated Wigner approximation leaves out these interferences. We develop a semiclassical theory which bridges classical and quantum concepts in many-body bosonic systems and properly incorporates such missing quantum effects. For mesoscopically populated Bose-Hubbard systems, it is shown that this theory captures post-Ehrenfest quantum interference phenomena very accurately, and contains relevant phase information to perform many-body spectroscopy with high precision.

Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backward time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

The relativistic multiconfiguration Dirac-Hartree-Fock and the nonrelativistic multiconfiguration Hartree-Fock methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $4s4p{}^{3}P_1^o$ and $4s4p{}^{3}P_2^o$ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $Q\left({}^{67}\mathrm{Zn}\right)=0.122\left(10\right)$ b. The error bar was evaluated in a quasistatistical approach—the calculations were carried out with 11 different methods, and then the error bar was estimated from the differences between the results obtained with those methods.

The processes of energy gain and redistribution in a dense gas subject to an intense ultrashort laser pulse are investigated theoretically for the case of high-pressure argon. The electrons released via strong-field ionization and driven by an oscillating laser field collide with neutral neighbor atoms, thus effecting the energy gain in the emerging electron gas via a short-range inverse bremsstrahlung interaction. These collisions also cause excitation and impact ionization of the atoms, thus reducing the electron-gas energy. A kinetic model of these competing processes is developed which predicts the prevalence of excited atoms over ionized atoms by the end of the laser pulse. The creation of a significant number of excited atoms during the pulse in high-pressure gases is consistent with the delayed ionization dynamics in the pulse wake, recently reported by Gao et al. [X. H. Gao et al., Phys. Rev. A 95, 013412 (2017)]. This energy redistribution mechanism offers an approach to manage effectively the excitation vs ionization patterns in dense gases interacting with intense laser pulses and thus opens avenues for diagnostics and control in these settings.

We report on electromagnetic modes in space-time-modulated dispersion-engineered media. These modes exhibit unusual dispersion relation, field profile, and scattering properties. They are generated by coupled codirectional space-time harmonic pairs and occur in space-time periodic media whose constituent materials exhibit specific dispersion. Excitation of a slab of such a medium with subluminal modulation results in periodic transfer of energy between the incident frequency and a frequency shifted by a multiple of the modulation frequency, whereas superluminal modulation generates exponentially growing anharmonics. These modes may find applications in optical mixers, terahertz sources, and other optical devices.

We theoretically revisit the problem of the propagation of coherent light pulses through a linear medium when the carrier frequency of the pulses coincides with the minimum of a narrow dip in the medium transmission. Considering realistic contrasts between the maximum and minimum transmission of the medium and incident pulses of strictly finite duration, we combine temporal and spectral approaches to obtain analytical expressions of the transmitted pulse that reproduce the main features of the exact numerical solutions derived by fast Fourier transform. A special attention is paid to the advance of the pulse maximum over that of a pulse covering the same distance in vacuum and the ratio of this advance to the pulse duration (fractional advance) is optimized.

We show that it is possible to independently control both the trajectory and the maximum amplitude along the trajectory of a paraxial accelerating beam. This is accomplished by carefully engineering both the amplitude and the phase of the beam on the input plane. Furthermore, we show that the width of an accelerating beam is related only on the curvature of the trajectory. Therefore, we are able to produce beams with predefined beam widths and amplitudes. These results are useful in applications where precise beam control is important. In addition we consider radially symmetric abruptly autofocusing beams. We identify the important parameters that affect the focal characteristics. Consequently, we can design autofocusing beams with optimized parameters (such as sharper focus and higher intensity contrast). In all our calculations the resulting formulas are presented in an elegant and practical form in direct connection with the geometric properties of the trajectory. Finally we discuss methods that can be utilized to experimentally realize such optical waves.

A discrete-time quantum walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in $(2+1)$ dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the nonrectangular grids, as in graphene-like materials. The latter, in particular, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.

We introduce an analytically treatable discrete time quantum walk in a one-dimensional lattice which combines non-Markovianity and hyperballistic diffusion associated with a Gaussian whose variance ${\sigma }_t^2$ grows cubicly with time $\sigma \propto t^3$. These properties have have been numerically found in several systems, namely, tight-binding lattice models. For its rules, our model can be understood as the quantum version of the classical non-Markovian “elephant random walk” process for which the quantum coin operator only changes the value of the diffusion constant although, contrarily, to the classical coin.

The while-you-wait computing paradigm combines elements of digital and analog quantum computation with the aim of minimizing the need of external control. In this architecture the computer is split into logic units, each continuously implementing a single recurring multigate operation via the unmodulated Hamiltonian evolution of a quantum many-body system. Here we use evolutionary algorithms to engineer such many-body dynamics, and develop logic units capable of continuously implementing a quantum half-adder in a time-independent four-qubit network, where qubits are coupled with either Ising or Heisenberg interactions. Our results provide a step for the development of larger modules for full quantum arithmetics.

The electromagnetic Casimir interaction between two spheres is studied within the scattering approach using the plane-wave basis. It is demonstrated that the proximity force approximation (PFA) corresponds to the specular-reflection limit of Mie scattering. Using the leading-order semiclassical WKB approximation for the direct reflection term in the Debye expansion for the scattering amplitudes, we prove that PFA provides the correct leading-order term in the small-distance limit for arbitrary materials and temperatures in the sphere-sphere and the plane-sphere geometry. Our derivation implies that only a small section around the points of closest approach between the interacting spherical surfaces contributes in the PFA regime. The corresponding characteristic length scale is estimated from the width of the Gaussian integrand obtained within the saddle-point approximation. At low temperatures, the area relevant for the thermal corrections is much larger than the area contributing to the zero-temperature result.

The charge-state dynamics of the nitrogen-vacancy (NV) center in diamond play a key role in a wide range of applications, yet remain imperfectly understood. Using single picosecond pulses and pulse pairs, we quantitatively investigate the charge dynamics associated with excitation and fluorescence depletion of a single NV center. Our pulsed excitation approach permits significant modeling simplifications and allows us to extract relative rates of excitation, stimulated emission, ionization, and recombination under 531 and 766 nm illumination. By varying the duration between paired pulses, we can also investigate ionization and recombination out of metastable states. Our results are directly applicable to experiments employing stimulated emission-depletion imaging and can be used to predict optimal operating regimes where excitation and stimulated emission are maximized relative to charge-state-switching processes.

The role of the Coulomb potential of the atomic core for the creation of caustics in the photoelectron momentum distribution for tunneling ionization in a linearly polarized strong laser field, commonly termed Coulomb focusing, is investigated within classical theory beyond the dipole approximation. Coulomb focusing is addressed by analytical calculation of Coulomb momentum transfer to the tunneled electron due to rescatterings, while applying perturbation theory and classifying the recollisions either as fast or as slow. With the help of the derived analytical treatment, we analyze the origin of the counterintuitive energy-dependent bend of the Coulomb focusing cusp in the photoelectron momentum distribution in a linearly polarized laser field in the nondipole regime, and its scaling with the field parameters. The high-order recollisions are shown to be responsible for a decrease of the bend of the cusp at very low energies in this regime.

An analytical method for treating Coulomb focusing in strong-field ionization in a linearly polarized laser field has been proposed in the first paper of this series, where analytical formulas have been derived for the Coulomb momentum transfer to the tunneled electron at the tunnel exit and due to rescatterings. In this paper, we analytically investigate a buildup of the Coulomb momentum transfer during multiple laser driven recollisions of the tunneled electron on the parent ion. We find that the momentum transfer at rescattering events, while being a perturbation with respect to the instantaneous electron momentum at the rescattering, induces a significant nonperturbative contribution to the total momentum transfer. Moreover, we show that the higher-order recollisions contribute considerably to the total momentum transfer and cannot be omitted for the proper description of the Coulomb focusing. We also show that our analytical approach to Coulomb focusing is well suitable for proper description of the Coulomb focusing cusps of the photoelectron momentum distribution at energies larger than 50 meV.

We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which the Bogoliubov excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential. A rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect, which can be characterized by measuring the density-density correlation function. It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of the created quasiparticle pairs with opposite momenta, resulting from the quench, displays an enhanced potential for the presence of entanglement (represented by nonseparable and steerable quasiparticle states), when compared to a gas with solely repulsive contact interactions. Steerable quasiparticle pairs contain momenta from close to the roton, and hence quantum correlations significantly increase in the presence of a deep roton minimum.

Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By the use of the Kirchhoff approximation, a closed-form mathematical expression for the angular dependence of the mean differential reflection coefficient is derived under the assumption that the surface is illuminated by a plane incident wave. It is shown that this quantity can be expressed in terms of the isotropic, bivariate ($\alpha$-stable) Lévy distribution of a stability parameter that is two times the Hurst exponent of the underlying surface. Features of the expression for the mean differential reflection coefficient are discussed, and its predictions compare favorably over large regions of parameter space to results obtained from rigorous computer simulations based on equations of scattering theory. It is demonstrated how the Hurst exponent and the topothesy of the self-affine surface can be inferred from scattering data it produces. Finally, several possible scattering configurations are discussed that allow for an efficient extraction of these self-affine parameters.