We propose and demonstrate a robust control scheme by an ultrafast nonadiabatic chirped laser pulse, designed for targeting coherent superpositions of two-level systems. Robustness against power fluctuation is proved by our numerical study and a proof-of-principle experiment performed with femtosecond laser interaction on cold atoms. They exhibit for the final driven dynamics a cusp on the Bloch sphere, corresponding to a zero curvature of fidelity. This solution is particularly simple and thus applicable to a wide range of potential applications.

We demonstrate the control of electron-electron correlation in frustrated double ionization (FDI) of the two-electron triatomic molecule ${{\mathrm{D}}_3}^{+}$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semiclassical model that fully accounts for the electron and nuclear motion in strong fields. We analyze the FDI probability and the distribution of the momentum of the escaping electron along the polarization direction of the longer wavelength and more intense laser field. These observables, when considered in conjunction, bear clear signatures of the prevalence or absence of electron-electron correlation in FDI, depending on the time delay between the two laser pulses. We find that ${{\mathrm{D}}_3}^{+}$ is a better candidate than ${\mathrm{H}}_2$ for demonstrating also experimentally that electron-electron correlation indeed underlies FDI.

We study high-order-harmonic generation (HHG) by the incident laser beam in the Laguerre-Gaussian mode with a nonzero topological charge. We find that the harmonic signal in the central spot on the beam axis does not always vanish and depends on the distribution of the medium in the focal region of the incident laser beam. The HHG spectra on the beam axis can be controlled by changing the spatial medium distribution. General theoretical results are confirmed by calculations of HHG in the medium of argon atoms, with the single-atom response obtained by means of the time-dependent density functional theory.

We theoretically demonstrate the phonon-assisted control of the single-photon spectral characteristics such as central frequency and linewidth in a semiconductor quantum dot coupled to a pillar microcavity using a single laser pulse as both excitation and control. We derive the relevant optical Bloch equations from the suitable polaron master equation for taking into account the effects of phonons accurately. We show that with the appropriately chosen parameters of the exciting laser pulse (pump pulse) and cavity, the central frequency and linewidth of the single photon can be controlled simply by controlling the frequency and pulse width of the exciting laser pulse, respectively. Subsequently, we show that these are essentially the phonon-induced processes which ensure that the probability of single-photon emission does not change significantly with the variation of the frequency and pulse width of the exciting laser pulse. Furthermore, we demonstrate that the polarization of the single photon can also be controlled by adjusting the polarization of the pump pulse.

We theoretically derive the lower and upper bounds of quantum Fisher information (QFI) of an SU(1,1) interferometer whatever the input state chosen. According to the QFI, the crucial resource for quantum enhancement is shown to be large intramode correlations indicated by the Mandel $Q$ parameter. The subtraction of photons from the squeezed vacuum state has the effect of increasing the average photon number of the new field state, as well as the intramode correlations. For example, for a coherent state $\otimes$ a squeezed vacuum state with a given fixed input mean number of photons as the input, if $p$ photons are subtracted from the squeezed-vacuum state before inputting the SU(1,1) interferometer, the phase sensitivities can be improved due to the intramode-correlation increment.

A popular quantum system, in which the Pancharatnam-Berry non-Abelian geometric phase has been generated and exploited, is the atomic tripod system. It is conveniently created by linking a single atomic state with three other states by three electromagnetic fields. Such a linkage pattern naturally emerges between the magnetic sublevels of two atomic levels with angular momenta $J=0$ and $J=1$, although tripod implementations between other suitable sublevels are also used. Here we go beyond the limitation of a tripod system and show that it is possible to generate the non-Abelian geometric phase in a quantum system composed of $N$ lower and $N-2$ upper sublevels. The theoretical instrument is the Morris-Shore transformation which reveals the existence of two uncoupled (dark) states composed of the lower sublevels only. A possible physical implementation is the atomic transition $J\leftrightarrow J-1$, with $J$ arbitrary, which is driven, as in the case of tripod system, by three electromagnetic fields of different polarizations. This generalization considerably broadens the range of systems that can be used to generate a geometric phase, with the the same experimental complexity as in the tripod system. Specific calculations of the non-Abelian geometric phase are presented for $J=\frac{3}{2}\leftrightarrow J=\frac{1}{2}$ and $J=2\leftrightarrow J=1$ systems. A method for measuring the geometric phase is proposed.

Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled waveguide lattice are evaluated and we find that the $\mathcal{PT}$-symmetric phase of a $\mathcal{PT}$-symmetric lattice can have different topologies; the edge states depend on the lattice size, boundary configuration, and competition between the coupling and degree of non-Hermiticity. The topologically nontrivial region is extended in the presence of periodic gain and loss. The nonzero geometric phases accumulated by the Bloch bands indicate the existence of topologically protected edge states between the band gaps. The unidirectional amplification and attenuation zero modes appear above a threshold degree of non-Hermiticity, which facilitates the development of a robust optical diode.

Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we show that fundamentally binary theories are experimentally testable with current technology. For that, we identify a feasible Bell-type experiment on pairs of entangled qutrits. In addition, we prove that, for any $n$, quantum $n$-ary correlations are not fundamentally $(n-1)$-ary. For that, we introduce a family of inequalities that hold for fundamentally $(n-1)$-ary theories but are violated by quantum $n$-ary correlations.

Environmental noise leads to dephasing and relaxation in a quantum system. Often, a rigorous treatment of multiple noise sources within a system-bath approach is not possible. We discuss the influence of environmental fluctuations on a quantum system whose dynamics is dephasing already due to a phenomenologically treated additional noise source. For this situation, we develop a path-integral approach, which allows us to treat the system-environment coupling in a numerically exact way, and additionally we extend standard perturbative approaches. We observe strong deviations between the numerically exact and the perturbative results even for weak system-bath coupling. This shows that standard perturbative approaches fail for additional, even weak, system-bath couplings if the system dynamics is already dissipative.

Various quantum-walk-based algorithms have been proposed to analyze and rank the centrality of graph vertices. However, issues arise when working with directed graphs: the resulting non-Hermitian Hamiltonian leads to nonunitary dynamics, and the total probability of the quantum walker is no longer conserved. In this paper, we discuss a method for simulating directed graphs using $PT$-symmetric quantum walks, allowing probability-conserving nonunitary evolution. This method is equivalent to mapping the directed graph to an undirected, yet weighted, complete graph over the same vertex set, and can be extended to cover interdependent networks of directed graphs. Previous work has shown centrality measures based on the continuous-time quantum walk provide an eigenvectorlike quantum centrality; using the $PT$-symmetric framework, we extend these centrality algorithms to directed graphs with a significantly reduced Hilbert space compared to previous proposals. In certain cases, this centrality measure provides an advantage over classical algorithms used in network analysis, for example, by breaking vertex rank degeneracy. Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.

We calculate the one-loop electron self-energy correction of order $\alpha {\left(Z\alpha \right)}^5$ to the bound-electron $g$ factor. Our result is in agreement with the extrapolated numerical value and paves the way for the calculation of the analogous, but as yet unknown, two-loop correction.

We report measurements of the nonresonant x-ray emission spectroscopy (XES) from Ni metal in an energy range spanning the $K\beta$ diagram line, valence-to-core emission, and double-ionization (DI) satellites that appear beyond the single-particle Fermi level. We make special use of a laboratory-based x-ray spectrometer capable of both x-ray emission and x-ray absorption measurements to accurately align the XES and x-ray absorption spectra to a common energy scale. The careful alignment of energy scales is requisite for correction of the strong sample absorption of DI fluorescence above the Ni $K$-edge energy. The successful correction of absorption effects allows a determination of the branching ratios for the $\left[1s3d\right],\left[1s3p\right],\left[1s2p\right]$ and $\left[1s2s\right]$ satellites with respect to their corresponding diagram lines. We compare our results with other work, finding good agreement with prior experiments and with theoretical calculations in the multiconfiguration Dirac-Fock framework.

The long-range interaction of excited neutral atoms has a number of interesting and surprising properties such as the prevalence of long-range oscillatory tails and the emergence of numerically large van der Waals $C_6$ coefficients. Furthermore, the energetically quasidegenerate $nP$ states require special attention and lead to mathematical subtleties. Here we analyze the interaction of excited hydrogen atoms in $nS$ states ($3\le n\le 12$) with ground-state hydrogen atoms and find that the $C_6$ coefficients roughly grow with the fourth power of the principal quantum number and can reach values in excess of $240000$ (in atomic units) for states with $n=12$. The nonretarded van der Waals result is relevant to the distance range $R\ll a_0/\alpha$, where $a_0$ is the Bohr radius and $\alpha$ is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range $a_0/\alpha \ll R\ll \hslash c/\mathcal{L}$, where $\mathcal{L}$ is the Lamb shift energy. In this range, the contribution of quasidegenerate excited $nP$ states remains nonretarded and competes with the $1/R^2$ and $1/R^4$ tails of the pole terms, which are generated by lower-lying $mP$ states with $2\le m\le n-1$, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range $R\gg \hslash c/\mathcal{L}$. The familiar $1/R^7$ asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation for highly excited states.

Understanding strong-field double ionization of many-electron systems is an important fundamental problem with potential implications for molecular imaging within this regime. Using mid-IR radiation, we unambiguously identify the transition from nonsequential ($e, 2e$) to sequential double ionization in Xe at an intensity below ${10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. Ionization from excited orbitals is found to be decisive at low intensities, but we demonstrate that such mechanisms are unimportant in the sequential regime. We utilize these facts to successfully image a molecular dication using laser-induced electron diffraction. This methodology can be used to study molecular dynamics on unprecedented few-femtosecond time scales.

We investigate the limiting factors in the standard implementation of the Ca magneto-optical trap. We find that intercombination transitions from the $4s5p{}^1{P}_1$ state used to repump the electronic population from the $3d4s{}^1{D}_2$ state severely reduce the trap lifetime. We explore seven alternative repumping schemes theoretically and investigate five of them experimentally. We find that all five of these schemes yield a significant increase in the trap lifetime and consequently improve the number of atoms and peak atom density by as much as $\sim 20$ times and $\sim 6$ times, respectively. One of these transitions, at 453 nm, is shown to approach the fundamental limit for a Ca magneto-optical trap with repumping only from the dark $3d4s{}^1{D}_2$ state, yielding a trap lifetime of $\sim 5$ s.

Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real-space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.

The discrete truncated Wigner approximation (DTWA) is a semiclassical phase-space method useful for the exploration of many-body quantum dynamics. In this work we investigate many-body localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a one-dimensional random field Heisenberg spin chain with short-range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long-range interactions and/or systems in higher dimensions.

A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realize topological superfluids with time-reversal symmetry (TRS). The induced interaction between the fermions mediated by the BEC gives rise to a competition between $p$-wave pairing within each layer and $s$-wave pairing between the layers. When the layers are far apart, intralayer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, interlayer pairing sets in. We show that this leads either to a second-order transition breaking TRS where the edge modes gradually become gapped or to a first-order transition to a topologically trivial $s$-wave superfluid. Our results provide a realistic road map for experimentally realizing a topological superfluid with TRS in a cold atomic system.

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior, which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides an extremely well-controlled model for studying defect-induced superfluidity.