In this work we introduce a distorted-wave method, based on the initial value representation approach of the quantum evolution operator, in order to improve the description of rainbow effects given by the surface eikonal (SE) model for diffraction from crystal surfaces produced by grazing scattering of fast atoms. The proposed theory, named the surface initial value representation (SIVR) approximation, is applied to He atoms colliding with a LiF(001) surface along low-indexed crystallographic channels. For this collision system the SIVR approach provides a very good representation of the quantum interference structures of experimental projectile distributions, even in the angular region around classical rainbow angles where the semiclassical SE method diverges.

We use the dressed potentials obtained in the adiabatic representation of two coupled channels to calculate $s$-wave Feshbach resonances in a three-dimensional spherically symmetric potential with an open channel interacting with a closed channel. Analytic expressions for the $s$-wave scattering length $a$ and number of resonances are obtained for a piecewise constant model with a piecewise constant interaction of the open and closed channels near the origin. We show analytically and numerically that, for strong enough coupling strength, Feshbach resonances can exist even when the closed channel does not have a bound state.

First-principles quantum-mechanical calculations of an intense-field ultrafast two-color core-hole stimulated Raman process in nitric oxide are presented. They employ the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method with all 15 electrons active. These calculations demonstrate a robust excitation localized on an atom through a core-electron stimulated Raman transition, the first step in proposed stimulated x-ray Raman spectroscopy experiments. A total population transfer of approximately 41% into valence excited states and 30% ionization is obtained via two concurrent 1.31-fs pulses with maximum intensities of 0.5 and $3\times {10}^{17}\text{W}{\mathrm{cm}}^{-2}$. It is found that both resonant and nonresonant (via the continuum) Raman transitions contribute. All aspects of these calculations except for ac Stark shifts are converged with a modest basis of 11 orbitals, demonstrating the efficiency of MCTDHF for the treatment of nonperturbative electronic dynamics in molecules.

The large-distance behavior of the density-density correlation function in the Lieb-Liniger model at finite temperature is investigated by means of the recently derived nonlinear integral equations characterizing the correlation lengths. We present extensive numerical results covering all the physical regimes from weak to strong interaction and all temperatures. We find that the leading term of the asymptotic expansion becomes oscillatory at a critical temperature which decreases with the strength of the interaction. As we approach the Tonks-Girardeau limit the asymptotic behavior becomes more complex with a double crossover of the largest and next-largest correlation lengths. The crossovers exist only for intermediate couplings and vanish for $\gamma =0$ and $\infty$.

We discuss the effect of semitransparency in a quantum-Zeno-like interaction-free measurement setup, a quantum-physics based approach that might significantly reduce sample damage in imaging and microscopy. With an emphasis on applications in electron microscopy, we simulate the behavior of probe particles in an interaction-free measurement setup with semitransparent samples, and we show that the transparency of a sample can be measured in such a setup. However, such a measurement is not possible without losing (i.e., absorbing or scattering) probe particles in general, which causes sample damage. We show how the amount of lost particles can be minimized by adjusting the number of round trips through the setup, and we explicitly calculate the amount of lost particles in measurements which either aim at distinguishing two transparencies or at measuring an unknown transparency precisely. We also discuss the effect of the sample causing phase shifts in interaction-free measurements. Comparing the resulting loss of probe particles with a classical measurement of transparency, we find that interaction-free measurements only provide a benefit in two cases: first, if two semitransparent samples with a high contrast are to be distinguished, interaction-free measurements lose less particles than classical measurements by a factor that increases with the contrast. This implies that interaction-free measurements with zero loss are possible if one of the samples is perfectly transparent. A second case where interaction-free measurements outperform classical measurements is if three conditions are met: the particle source exhibits Poissonian number statistics, the number of lost particles cannot be measured, and the transparency is larger than approximately $\frac{1}{2}$. In all other cases, interaction-free measurements lose as many probe particles as classical measurements or more. Aside from imaging of gray levels, another possible application for interaction-free measurements is the detection of arbitrarily small phase shifts in transparent samples.

We study how non-Markovianity of an open two-level system can be detected when continuously monitoring a part of its bosonic environment. Considering a physical scenario of an atom in a lossy cavity, we demonstrate that the properties of the time-dependent flux of the photons from the cavity allows the detection of memory effects in the atomic dynamics. This framework overlaps with effective descriptions for the memory part of the environment using pseudomode methods. Our central results show how the Markovian measurement record on the environment of an enlarged open system allows us to draw conclusions on the non-Markovianity of the original system of interest.

We present a cavity piezo-optomechanical system where microwave and optical degrees of freedom are coupled through an ultrahigh-frequency mechanical resonator. By utilizing the coherence among the three interacting modes, we demonstrate optical amplification, coherent absorption, and a more general asymmetric Fano resonance. The strong piezoelectric drive further allows access to the large-amplitude-induced optomechanical nonlinearity, with which optical transparency at higher harmonics through multiphonon scattering is demonstrated.

We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wave functions expressed in terms of special functions (namely, Whittaker functions), while the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical band gaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.

We demonstrate a scheme to generate noncoherent and coherent correlations, i.e., a tunable degree of entanglement, between degrees of freedom of a single photon. Its nature is analogous to the tuning of the purity (first-order coherence) of a single photon forming part of a two-photon state by tailoring the correlations between the paired photons. Therefore, well-known tools such as the Clauser-Horne-Shimony-Holt (CHSH) Bell-like inequality can also be used to characterize entanglement between degrees of freedom. More specifically, CHSH inequality tests are performed, making use of the polarization and the spatial shape of a single photon. The four modes required are two polarization modes and two spatial modes with different orbital angular momentum.

We present an efficient method to extract the amount of true randomness that can be obtained by a quantum random number generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min-entropy and max-entropy. We tested our method with two different QRNGs by using a train of qubits or ququart and demonstrated the scalability toward practical applications.

We have studied the pump-probe spectroscopy of rubidium vapor confined to the micrometric interstices of a random porous glass. Due to the propagation in the highly scattering medium, the light fields are randomized inside the sample with significant consequences for the atomic spectra. A two-frequency modulation technique was used to isolate the atomic response proportional to the product of the intensities of the pump and probe fields. Unusual line shapes were observed which include relatively narrow structures that are present in spite of the Doppler broadening due to the atomic velocity distribution. A simple theoretical modeling of the light-atom interaction that assumes statistical isotropy of the diffuse light field and mutual temporal incoherence of the pump and probe fields is presented. Using a single adjustable parameter to account for the atomic confinement, the model successfully describes the diversity of the observed spectral line shapes.

A pseudopotential for positronium-atom interaction, based on electron-atom and positron-atom phase shifts, is constructed, and the phase shifts for Ps-Kr and Ps-Ar scattering are calculated. This approach allows us to extend the Ps-atom cross sections, obtained previously in the impulse approximation [I. I. Fabrikant and G. F. Gribakin, Phys. Rev. Lett. 112, 243201 (2014)], to energies below the Ps ionization threshold. Although experimental data are not available in this low-energy region, our results describe well the tendency of the measured cross sections to drop with decreasing velocity at $v<1$ a.u. Our results show that the effect of the Ps-atom van der Waals interaction is weak compared to the polarization interaction in electron-atom and positron-atom scattering. As a result, the Ps scattering length for both Ar and Kr is positive, and the Ramsauer-Townsend minimum is not observed for Ps scattering from these targets. This makes Ps scattering quite different from electron scattering in the low-energy region, in contrast to the intermediate energy range from the Ps ionization threshold up to $v\sim 2$ a.u., where the two are similar.

We describe a method for determining saturation peak intensities of nonlinear intense field processes. The Z-scan method takes advantage of the balance between nonlinear response and interaction volume change as an intense laser pulse is focused onto a sample. We derive a robust geometric factor, directly relating the peak intensity at optimal target displacement from the focal plane and the corresponding saturation intensity. The Z-scan method allows obtaining saturation intensities with no need of a priori assumptions about the nonlinear process; surprisingly even for unfavorable finite depth samples. The method is demonstrated experimentally for an intense laser pulse interaction with molecular anions.

The alignment- and internuclear-distance-dependent ionization of ${\mathrm{H}}_2$ exposed to intense, ultrashort laser fields is studied by solving the time-dependent two-electron Schrödinger equation. In the regime of perturbative few-photon ionization, a strong dependence of the ionization yield on the internuclear distance is found. While this finding confirms a previously reported breakdown of the fixed-nuclei approximation for parallel alignment, a simpler explanation is provided and it is demonstrated that this breakdown is not due to vibrational dynamics during the laser pulse. The persistence of this effect even for randomly aligned molecules is demonstrated. Furthermore, the transition from the multiphoton to the quasistatic (tunneling) regime is investigated considering intense 800 nm laser pulses. While the obtained ionization yields differ significantly from the prediction of Ammosov-Delone-Krainov rates, we find a surprisingly good quantitative agreement after introducing a simple frequency-dependent correction to the standard tunneling formula.

We study the topological phases in spin-orbit-coupled dipolar bosons in a one-dimensional optical lattice. The magnetic dipolar interactions between atoms give rise to intersite interactions. In the Mott-insulating regime, this system can be described by the quantum XYZ spin model with Dzyaloshinskii-Moriya interactions in a transverse field. We focus on investigating the effect of dipolar interactions on the topological phase. The topological phase can be shown when spin-orbit coupling combines with the repulsive dipolar interaction. We find that the dipolar interaction can broaden the range of parameters of spin-orbit coupling and transverse field for exhibiting the topological phase. The sum of spin correlations between the two nearest-neighboring atoms can be used to indicate the topological phase. This may be useful for detecting topological phases in experiments.

We compute the normal form description of a semiconductor laser near its threshold, with the sole assumption that the polarization be related to the electric field through the susceptibility (dependent on laser frequency and population inversion). We prove both analytically and numerically the possible existence of a phase-unstable regime, characterized by a periodic oscillation of the optical frequency and a constant intensity. This regime bears close resemblance to the mode-switching behavior, with constant total output power, experimentally observed in semiconductor lasers. In addition, our model predicts the appearance of a phase- and amplitude-turbulent regime, compatible with experimental observations. Both regimes are well known in fluid dynamics under the name Benjamin-Feir instability.

We study the impact of double- and triple-scattering contributions on coherent backscattering of laser light from saturated isotropic atoms in the helicity-preserving polarization channel. By using the recently proposed diagrammatic pump-probe approach, we analytically derive single-atom spectral responses to a classical polychromatic driving field, combine them self-consistently to double- and triple-scattering processes, and numerically deduce the corresponding elastic and inelastic spectra, as well as the total backscattered intensities. We find that accounting for the triple-scattering contribution leads to a faster decay of phase-coherence with increasing saturation of the atomic transition as compared with double scattering alone and to a better agreement with the experiment on strontium atoms.