We have observed resonant microwave transitions between pairs of atoms. Specifically, we have observed the processes $n{d}_{5/2}n{d}_{5/2}\to (n+1)d_j(n-2)f_{7/2}$ and $n{d}_{5/2}n{d}_{5/2}\to (n+2)p_{3/2}(n-1)d_{5/2}$ for $35\le n\le 44$. These transitions are allowed due to the dipole-dipole-induced configuration interaction between the $n{d}_{5/2}n{d}_{5/2}$ state and the energetically nearby $(n+2)p_{3/2}(n-2)f_{7/2}$ state, which admixes some of the latter into the former. The resulting microwave transitions are analogous to two-photon transitions in which one of the photons has been replaced by the dipole-dipole interaction. We have developed a configuration interaction description of the transitions, which gives a good description of the interaction over the range $35\le n\le 42$. Over this range of $n$ the detuning varies from 0.095 to 1.482 GHz, the microwave frequencies vary from 26.970 to 45.916 GHz, and the requisite microwave powers vary by a factor of over 1000.

Experimental and theoretical triple differential cross sections for intermediate-energy (250 eV) electron-impact single ionization of the ${\mathrm{CO}}_2$ are presented for three fixed projectile scattering angles. Results are presented for ionization of the outermost $1{\pi }_g$ molecular orbital of $\mathrm{C}{\mathrm{O}}_2$ in a coplanar asymmetric geometry. The experimental data are compared to predictions from the three-center Coulomb continuum approximation for triatomic targets, and the molecular three-body distorted wave (M3DW) model. It is observed that while both theories are in reasonable qualitative agreement with experiment, the M3DW is in the best overall agreement with experiment.

A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\omega$. Special emphasis is on the $\omega \text{−}2\omega$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.

We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density-matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.

We study the quantum walks of two interacting spin-1 bosons. We derive an exact solution for the time-dependent wave function, which describes the two-particle dynamics governed by the one-dimensional spin-1 Bose-Hubbard model. We show that propagation dynamics in real space and mixing dynamics in spin space are correlated via the spin-dependent interaction in this system. The spin-mixing dynamics has two characteristic frequencies in the limit of large spin-dependent interactions. One of the characteristic frequencies is determined by the energy difference between two bound states, and the other frequency relates to the cotunneling process of a pair of spin-1 bosons. Furthermore, we numerically analyze the growth of the spin correlations in quantum walks. We find that long-range spin correlations emerge showing a clear dependence on the sign of the spin-dependent interaction and the initial state.

We propose a scheme to realize a $Z_2$ topological insulator in a square optical lattice. Different from the conventional topological insulator protected by the time-reversal symmetry, here the optical lattice possesses a hidden symmetry, which is responsible for the present $Z_2$ topological order. With a properly defined pseudospin, such a topological insulator is characterized by the helical edge states that exhibits pseudo–spin-momentum locking, so it can be considered as a quantum pseudo–spin Hall insulator. The $Z_2$ topological invariant is derived and its experimental detection is discussed as well.

We consider a periodic waveguide array whose unit cell consists of a $\mathcal{PT}$-symmetric quadrimer with two competing loss-gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between the phases are described by a symmetry-adapted nonlocal current which maps the spectral properties to the spatially resolved field, for the lattice as well as for the isolated quadrimer. Its site average acts like a natural order parameter for the general class of one-dimensional $\mathcal{PT}$-symmetric Hamiltonians, vanishing in the unbroken phase and being nonzero in the broken phase. We investigate how the beam dynamics in the array is affected by the presence of competing loss-gain rates in the unit cell, showing that the enriched band structure yields the possibility to control the propagation length before divergence when the system resides in the broken $\mathcal{PT}$ phase.

We present, discuss, and validate an adapted $S$-matrix formalism for an efficient, simplified treatment of stacked homogeneous periodically structured metasurfaces operated under normally incident plane wave excitation. The proposed formalism can be applied to any material system, arbitrarily shaped metaatoms, at any frequency, and with arbitrary subwavelength periods. Circumventing the introduction of any kind of effective parameters we directly use the $S$ parameters of the individual metasurfaces to calculate the response of an arbitrary stack. In fact, the $S$ parameters are the complex parameters of choice fully characterizing the homogeneous metasurfaces, in particular with respect to its polarization manipulating properties. Just as effective material parameters like the permittivity and the permeability or wave parameters like the propagation constant and the impedance, the stacking based upon $S$ matrices can be applied as long as the individual layers are decoupled with respect to their near fields. This requirement eventually sets the limits for using the optical properties of the individual layers to calculate the response of the stacked system—this being the conceptual aim for any homogeneous metasurface or metamaterial layer and therefore the essence of what is eventually possible with homogeneous metasurfaces. As simple and appealing as this approach is, it is as powerful as well: Combining structured metasurfaces with each other as well as with isotropic, anisotropic, or chiral homogeneous layers is possible by simple semianalytical $S$-matrix multiplication. Hence, complex stacks and resonators can be set up, accurately treated and optimized with respect to their dispersive polarization sensitive optical functionality without the need for further rigorous full-wave simulations.

Multiple filamentation of an infrared high-power laser pulse in air is considered. Based on the numerical solution to the unidirectional pulse propagation equation, the effect of radiation external focusing on the spatial structure of the plasma area produced in the filamentation region is studied. We show that the number of generated plasma channels in the beam wake and the density of their spatial distribution over the filamentation region depend on the initial divergence of laser radiation. We found that in a specific range of beam focusing the number of produced plasma channels could be minimized due to the formation of a consolidated thick plasma bunch at the beam axis.

We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such dynamics: (1) the collapse and revival of oscillations in the population difference, (2) the simple exponential decay of the oscillations resulting in their steady state with the finite amplitude, and (3) the steady-state stabilization of the equally populated levels. The nonmonotonic Bessel-function-like dependence on the driving strength is also predicted for the decay rate of these oscillations. The features of this dependence are determined by the relative rates of energetic relaxation and pure dephasing.

We analyze resonant light scattering by a cloud of cold atoms with randomly distributed positions in a regime where resonant dipole-dipole interactions between scatterers cannot be neglected. Using a microscopic approach we calculate numerically the collective eigenmodes of the cloud for many realizations. It is found that there always exists a small number of polaritonic modes. Using a macroscopic approach, we show that the atomic cloud is equivalent to a homogeneous particle with an effective permittivity and that there is a one-to-one correspondence between the microscopic polaritonic modes and the modes of the homogeneous particle.

$\mathcal{PT}$ symmetry, that is, a combined parity and time-reversal symmetry, is a key milestone for non-Hermitian systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study $\mathcal{PT}$ symmetry of the time-evolution operator of nonunitary quantum walks. We present the explicit definition of $\mathcal{PT}$ symmetry by employing a concept of symmetry time frames. We provide a necessary and sufficient condition so that the time-evolution operator of the nonunitary quantum walk retains $\mathcal{PT}$ symmetry even when parameters of the model depend on position. It is also shown that there exist extra symmetries embedded in the time-evolution operator. Applying these results, we clarify that the nonunitary quantum walk in the experiment does have $\mathcal{PT}$ symmetry.

Bell inequalities for continuous-variable bipartite systems are studied. The inequalities are expressed in terms of pseudo–spin operators, and quantum expectation values are calculated for generic two-mode squeezed states characterized by a squeezing parameter $r$ and a squeezing angle $\phi$. Allowing for generic values of the squeezing angle is especially relevant when $\phi$ is not under experimental control, such as in cosmic inflation, where small quantum fluctuations in the early universe are responsible for structures formation. Compared to previous studies restricted to $\phi =0$ and to a fixed orientation of the pseudo–spin operators, allowing for $\phi \ne 0$ and optimizing the angular configuration leads to a completely new and rich phenomenology. Two dual schemes of approximation are designed that allow for comprehensive exploration of the squeezing parameter space. In particular, it is found that Bell inequalities can be violated when the squeezing parameter $r$ is large enough, $r\gtrsim 1.12$, and the squeezing angle $\phi$ is small enough, $\phi \lesssim 0.34e^{-r}$.

The concept of flat band plays an important role in strongly correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsic limitations in conventional condensed-matter materials. Here we propose a circuit quantum electrodynamics simulator of the two-dimensional (2D) Lieb lattice exhibiting a flat middle band. By exploiting the parametric conversion method, we design a photonic Lieb lattice with in situ tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only a few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiment and may pave a new way towards the realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall effect without magnetic field.

We demonstrate strong-field-driven impulsive XUV–x-ray parametric amplification (IXPA) processes in high-order harmonic generation at the single-atom level by using ab initio calculations. We consider the example of ${\mathrm{Li}}^{+}$ ions exposed simultaneously to an intense IR pulse and a weak 200-as XUV–x-ray pulse with central photon energies varying from 90 to 400 eV. We determine optimal parameter ranges and the precise delays between the IR and the XUV–x-ray pulses for IXPA to occur. The present results might be a guide to achieve exponential growth of the XUV–x-ray signal in tabletop XUV–x-ray lasers.

We demonstrate that the coherent control of unimolecular reactions by using a waveform-controlled laser fields can lead to a strong modulation on the yield of the reaction. By using a synthesized ω (1800-nm) and 3ω (600-nm) two-color laser field, the probability of photodissociation of ${\mathrm{H}}_2{}^{+}$ can be strongly modulated by varying the relative phase between the two colors. The dissociation probability maximizes at different relative phases for protons with different kinetic energy, and such energy dependence can also be qualitatively reproduced by our simulation. We attribute the observed dissociation probability modulation to the interference between two different dissociation pathways which start from the same electronic states and end with the same kinetic energy.

We develop a technique for modeling of atomic and molecular ionization in superposition of XUV and IR fields with characteristics typical for attosecond streaking and RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) experiments. The method is based on solving the time-dependent Schrödinger equation in the coordinate frame expanding along with the photoelectron wave packet. The efficiency of the method is demonstrated by calculating angular anisotropy of photoemission time delay of the ${\mathrm{H}}_2{}^{+}$ ion in a field configuration of recent RABBITT experiments.

We investigate the effect of coherent population trapping (CPT) in an atom interferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, on the order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the $k$-reversal technique, which consists of averaging inertial measurements performed with two opposite orientations of the Raman wave vector $k$, provided that internal states at the input of the interferometer are kept identical for both configurations.

Spatial profiles of the pressure have been measured in atomic Fermi gases with primarily two-dimensional (2D) kinematics. The in-plane motion of the particles is confined by a Gaussian-shape potential. The two-component deeply degenerate Fermi gases are prepared at different values of the $s$-wave attraction. The pressure profile is found using the force-balance equation, from the measured density profile and the trapping potential. The pressure is compared to zero-temperature models within the local density approximation. In the weakly interacting regime, the pressure lies above a Landau Fermi-liquid theory and below the ideal-Fermi-gas model, whose prediction coincides with that of the Cooper-pair mean-field theory. The values closest to the data are provided by the approach where the mean field of Cooper pairs is supplemented with fluctuations. In the regime of strong interactions, in response to the increasing attraction, the pressure shifts below this model reaching lower values calculated within Monte Carlo methods. Comparison to models shows that interaction-induced departure from 2D kinematics is either small or absent. In particular, comparison with a lattice Monte Carlo suggests that kinematics is two dimensional in the strongly interacting regime.