Energies and lifetimes (widths) of vibrational states above the lowest dissociation limit of ${}^{16}\mathrm{O}_3$ were determined using a previously developed efficient approach, which combines hyperspherical coordinates and a complex absorbing potential. The calculations are based on a recently computed potential energy surface of ozone determined with a spectroscopic accuracy [Tyuterev et al., J. Chem. Phys. 139, 134307 (2013)]. The effect of permutational symmetry on rovibrational dynamics and the density of resonance states in ${\mathrm{O}}_3$ is discussed in detail. Correspondence between quantum numbers appropriate for short- and long-range parts of wave functions of the rovibrational continuum is established. It is shown, by symmetry arguments, that the allowed purely vibrational ($J=0$) levels of ${}^{16}\mathrm{O}_3$ and ${}^{18}\mathrm{O}_3$, both made of bosons with zero nuclear spin, cannot dissociate on the ground-state potential energy surface. Energies and wave functions of bound states of the ozone isotopologue ${}^{16}\mathrm{O}_3$ with rotational angular momentum $J=0$ and 1 up to the dissociation threshold were also computed. For bound levels, good agreement with experimental energies is found: The rms deviation between observed and calculated vibrational energies is 1 ${\mathrm{cm}}^{-1}$. Rotational constants were determined and used for a simple identification of vibrational modes of calculated levels.

Electron scattering with atomic oxygen has been studied using the $B$-spline $R$-matrix-with-pseudostates method. Cross sections for elastic scattering, excitation, emission, and ionization processes are presented. The excitation cross sections have been calculated for transitions between the $2s^{2}2p^4$ and $2s^{2}2p^{3}3l$ states of oxygen in the energy range from threshold to 200 eV. The present work differs from numerous previous studies due to the inclusion of a large number of pseudostates in the calculation. We included a total of 1116 spectroscopic bound, core-excited autoionizing, and target continuum states in the close-coupling expansion. The atomic oxygen structure model has been described by combining the multiconfiguration Hartree-Fock and the $B$-spline box-based multichannel methods. The inclusion of a large number of pseudostates representing the target continuum has a major impact, especially on the theoretical prediction of the excitation cross sections for many transitions at intermediate energies. A large reduction in excitation and emission cross sections has been noted due to the inclusion of coupling to the ionization continuum. The calculated cross sections are now in better agreement with available experimental results. The ionization cross sections for the ground $2s^{2}2p^4{}^{3}P$ and metastable $2s^{2}2p^4{}^{1}D$ and ${}^{1}S$ states are also presented. The electron-impact-induced emission cross sections for the $\left(2s^{2}2p^{3}3s\right){}^3{S}^o–\left(2s^{2}2p^4\right){}^{3}P$ (130.4 nm), $\left(2s^{2}2p^{3}3d\right){}^3{D}^o–\left(2s^{2}2p^4\right){}^{3}P$ (102.7 nm), $\left(2s^{2}2p^{3}3s^{\prime }\right){}^3{D}^o–\left(2s^{2}2p^4\right){}^{3}P$ (98.9 nm), and $\left(2s^{2}2p^{3}3s^{\prime \prime }\right){}^3{D}^o–\left(2s^{2}2p^4\right){}^{3}P$ (87.8 nm) transitions have been calculated and compared with the available experimental results.

We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw light, as in conventional optical pumping, we propose to use techniques for coherent population transfer (e.g., adiabatic fast passage) to arrange the atoms so as to increase the entropy removed from the system with each spontaneous decay from the upper state. This minimizes the number of spontaneous-emission events required to produce a stretched state, thus reducing the population loss due to decay to other states. To produce a stretched state in a manifold with angular momentum $J$, conventional optical pumping requires about $2J$ spontaneous decays per atom; one of our proposed methods reduces this to about ${log}_{2}2J$, while another of the methods reduces it to about one spontaneous decay, independent of $J$.

The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. In our experiments with a few cold Rb Rydberg atoms, we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the Förster resonances, since the population transfer at the resonances occurs on a time scale of $\sim 100$ ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted Förster resonances, while nonsharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances $\mathrm{Rb}\left(n{P}_{3/2}\right)+\mathrm{Rb}\left(n{P}_{3/2}\right)\to \mathrm{Rb}\left(n{S}_{1/2}\right)+\mathrm{Rb}\left([n+1]S_{1/2}\right)$ for two Rb Rydberg atoms interacting in a time-varying electric field.

We report the observation of nonsequential two-photon absorption from the $K$ shell of solid Zr (atomic number $Z=40)$ using intense x-ray pulses from the Spring-8 Angstrom Compact Free-Electron Laser (SACLA). We determine the generalized nonlinear two-photon absorption cross section at the two-photon threshold in the range of 3.9–57 $\times {10}^{-60}{\text{cm}}^4\text{s}$ bounded by the estimated uncertainty in the absolute intensity. The lower limit is consistent with the prediction of 3.1 $\times {10}^{-60}{\text{cm}}^4\text{s}$ from the nonresonant $Z^{-6}$ scaling for hydrogenic ions in the nonrelativistic, dipole limit.

We analyze the two-dimensional photoelectron momentum distribution of an Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below $2U_p$. By using a generalized quantum trajectory Monte Carlo simulation and comparing with the numerical solution of the time-dependent Schrödinger equation, we demonstrate that a profound ringlike pattern coming from the interplay between the intra- and the intercycle interferences of electron trajectories can be observed in the deep tunneling ionization regime. Moreover, we found that the rescattered electrons play a negligible role on the formation of a ringlike interference pattern, and the appearance of the ringlike interference pattern masks the holographic interference structure. Our results provide an appropriate experimental condition for the observation of the photoelectron holography and help to gain physical insight into the corresponding ultrafast electron dynamic process with attosecond temporal resolution.

Supersolid phases as a result of a coexistence of superfluid and density ordered checkerboard phases are predicted to appear in ultracold Fermi molecules confined in a bilayer array of two-dimensional square optical lattices. We demonstrate the existence of these phases within the inhomogeneous mean-field approach. In particular, we show that tuning the interlayer separation distance at a fixed value of the chemical potential produces different fractions of superfluid, density ordered, and supersolid phases.

Deterministic preparation of an ultracold harmonically trapped one-dimensional Fermi gas consisting of a few fermions has been realized by the Heidelberg group. Using Floquet formalism, we study the time dynamics of two- and three-fermion systems in a harmonic trap under an oscillating magnetic field. The oscillating magnetic field produces a time-dependent interaction strength through a Feshbach resonance. We explore the dependence of these dynamics on the frequency of the oscillating magnetic field for noninteracting, weakly interacting, and strongly interacting systems. We identify the regimes where the system can be described by an effective two-state model and an effective three-state model. We find an unbounded coupling to all excited states at the infinitely strong interaction limit and several simple relations that characterize the dynamics. Based on our findings, we propose a technique for driving transition from the ground state to the excited states using an oscillating magnetic field.

Following up on previous studies on parity-time-symmetric gain-loss bilayers, and inspired by formal analogies with plasmonic waveguides, we study non-Hermiticity-induced wave confinement and guiding phenomena that can occur in loss-gain-loss three-layers. By revisiting previous well-established “gain-guiding” concepts, we investigate analytically and numerically the dispersion and confinement properties of guided modes that can be supported by this type of structures, by assuming realistic dispersion models and parameters for the material constituents. As key outcomes, we identify certain modes with specific polarization and symmetry that exhibit particularly desirable characteristics, in terms of quasireal propagation constant and subwavelength confinement. Moreover, we elucidate the effects of material dispersion and parameters and highlight the potential advantages by comparison with the previously studied gain-loss bilayer configurations. Our results provide additional perspectives on light control in non-Hermitian optical systems and may find potentially intriguing applicability to reconfigurable nanophotonic platforms.

We investigate the behavior of two quantum emitters (two-level atoms) embedded in a linear waveguide, in a quasi-one-dimensional configuration. Since the atoms can emit, absorb, and reflect radiation, the pair can spontaneously relax towards an entangled bound state, under conditions in which a single atom would instead decay. Exploiting the resolvent formalism, we analyze the properties of these bound states, which occur for resonant values of the interatomic distance, and discuss their relevance with respect to entanglement generation. The stability of such states close to the resonance is studied, as well as the properties of nonresonant bound states, whose energy is below the threshold for photon propagation.

We study exact solutions of the steady-state behavior of several nonlinear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planck equations in the generalized $P$ representation, we investigate the analytical solutions of two fundamental models. First, we solve for the steady-state response of a linear cavity that is coupled to an approximate transmon qubit and use this solution to study both the weak and strong driving regimes, using analytical expressions for the moments of both cavity and transmon fields, along with the Husimi $Q$ function for the transmon. Second, we revist exact solutions of a quantum Duffing oscillator, which is driven both coherently and parametrically while also experiencing decoherence by the loss of single photons and pairs of photons. We use this solution to discuss both stabilization of Schrödinger cat states and the generation of squeezed states in parametric amplifiers, in addition to studying the $Q$ functions of the different phases of the quantum system. The field of superconducting circuits, with its strong nonlinearities and couplings, has provided access to parameter regimes in which returning to these exact quantum optics methods can provide valuable insights.

Superradiant lasers based on atomic ensembles exhibiting ultranarrow optical transitions can emit light of unprecedented spectral purity and may serve as active atomic clocks. We consider two frequency-detuned active atomic clocks, which are coupled in a cascaded setup, i.e., as master and slave lasers, and study the synchronization of the slave to the master clock. In a setup where both atomic ensembles are coupled to a common cavity mode, such synchronization phenomena have been predicted by Xu et al. [M. Xu, D. A. Tieri, E. C. Fine, J. K. Thompson, and M. J. Holland, Phys. Rev. Lett. 113, 154101 (2014).] and experimentally observed by Weiner et al. (J. M. Weiner et al., arXiv:1503.06464). Here we demonstrate that synchronization still occurs in cascaded setups but exhibits distinctly different phase diagrams. We study the characteristics of synchronization in comparison to the case of coupling through a common cavity. We also consider synchronization through a classical channel where light of the master laser is measured phase sensitively and the slave laser is injection locked by feedback and compare to the results achievable by coupling through quantum channels.

The hypothesis of a discrete fabric of the universe, the “Planck scale,” is always on stage since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here, we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e., the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.

Remote state preparation (RSP) provides an indirect way of transferring quantum information based on the nonlocal effect of quantum measurement. Although RSP has been demonstrated in recent years to remotely prepare multiphoton states, quantum measurement on the same number of additional photons was required, i.e., to prepare $N$-photon states via RSP, quantum measurement on the other $N$-photons was required, hence significantly limiting practicality and applicability of RSP. Here we report an experimental demonstration of remote preparation of three-photon entangled states by measuring only a single-photon entangled with the three photons. We further generalize our protocol to prepare multiphoton entangled states with arbitrary photon number and purity and to prepare a genuinely three-partite entangled state, both via single-photon measurement. As our RSP scheme relies on the nonlinearity induced by single-photon measurement, it enables quantum state engineering of multiphoton entangled states beyond the linear optical limit. Our results are expected to have significant impacts on quantum metrology and quantum information processing.

We introduce two tangle-based four-party entanglement measures $t_1$ and $t_2$, and two negativity-based measures $n_1$ and $n_2$, which are derived from the monogamy relations. These measures are computed for three four-qubit maximally entangled and $W$ states explicitly. We also compute these measures for the rank-2 mixture ${\rho }_4=p|{\text{GHZ}}_4\rangle \langle {\text{GHZ}}_4|+(1-p)|W_4\rangle \langle W_4|$ by finding the corresponding optimal decompositions. It turns out that $t_1\left({\rho }_4\right)$ is trivial and the corresponding optimal decomposition is equal to the spectral decomposition. Probably, this triviality is a sign of the fact that the corresponding monogamy inequality is not sufficiently tight. We fail to compute $t_2\left({\rho }_4\right)$ due to the difficulty in the calculation of the residual entanglement. The negativity-based measures $n_1\left({\rho }_4\right)$ and $n_2\left({\rho }_4\right)$ are explicitly computed and the corresponding optimal decompositions are also derived explicitly.

We present a general method to derive entanglement breaking (EB) conditions for continuous-variable quantum gates. We start with an arbitrary entanglement witness and reach an EB condition. The resultant EB condition is applicable not only for quantum channels but also for general quantum operations; namely, the trace-non-increasing class of completely positive maps. We illustrate our method associated with a quantum benchmark based on the input ensemble of Gaussian distributed coherent states. We also exploit our idea for channels acting on finite-dimensional systems and present a Schmidt-number benchmark based on input states of two mutually unbiased bases and measurements of generalized Pauli operators.

We discuss the characteristics of the dependence of attosecond transient-absorption spectra on the angle between the molecular alignment axis and the polarization of the pump and probe fields. We show how the dipole couplings and therefore the spectra can efficiently be controlled by exploiting the sensitivity of the transition dipoles on this relative orientation. The possibility to tune the dipole coupling by molecular alignment allows a detailed analysis of the complex structures of molecular attosecond transient-absorption spectra.

The surface plasmon in silver clusters is red shifted with respect to standard jellium random-phase approximation (RPA) predictions that work well for simple metal clusters. The reason for the deviation arises primarily from the non-negligible polarization interaction between the valence electrons and ionic cores. In order to quantify this effect in the jellium approximation we introduce a modified RPAE (RPA with exact exchange). The jellium background of Ag cores is treated as a polarizable sphere. This model predicts a dipole surface resonance in excellent agreement with published experimental data. Moreover it yields the blue shift (red shift) with decreasing sizes for cationic (anionic) Ag clusters as observed experimentally.

We present a theory for the diffraction of large molecules or nanoparticles at a standing light wave. Such particles can act as a genuine photon absorbers due to their numerous internal degrees of freedom effecting fast internal energy conversion. Our theory incorporates the interplay of three light-induced properties: the coherent phase modulation due to the dipole interaction, a nonunitary absorption-induced amplitude modulation described as a generalized measurement, and a coherent recoil splitting that resembles a quantum random walk in steps of the photon momentum. We discuss how these effects show up in near-field and far-field interference schemes, and we confirm our effective description by a dynamic evaluation of the grating interaction, which accounts for the internal states.

The scattering matrix $S$ obeys the symmetry property $\mathcal{PT}S\mathcal{PT}=S^{-1}$ in a parity-time $\left(\mathcal{PT}\right)$ symmetric system and the unitary relation $S^{†}S=1$ in the absence of gain and loss. Here we report a different symmetry relation of $S$ in a one-dimensional heterostructure, which is given by the amplitude ratio of the incident waves in the scattering eigenstates. It originates from the optical reciprocity and holds independently of the presence of gain and loss in the system. Guided by this symmetry relation, we probe the remnant of the spontaneous symmetry breaking of a $\mathcal{PT}$-symmetric $S$ matrix, when the system does not have exact $\mathcal{PT}$ symmetry due to unbalanced gain and loss and even in the absence of gain. We show that the additional symmetry relation provides clear evidence of a quasitransition, even when all previously found signatures of the $\mathcal{PT}$-symmetry breaking of $S$ are completely erased.