We propose a feasible Gaussian version of the Schrödinger-cat state. We consider it as a robust Gaussian state of an oscillator prepared in a low-energy Gaussian quantum state entangled with another oscillator which was initially in a quantum state at thermal equilibrium with an arbitrary large energy (macroscopic oscillator). To generate it, we suggest two-mode squeezing as the best candidate. We test that the Gaussian version of the Schrödinger-cat state can be also used to remotely prepare a squeezed state of the macroscopic oscillator.

Precision tests with the hydrogen molecule are presently limited by unknown higher-order quantum electrodynamical effects. These corrections are represented by matrix elements of some effective operators, most of which are singular. The evaluation of matrix elements of singular operators puts high demands on the quality of the representation of the nonrelativistic wave functions. The basis of fully correlated exponential functions is well suited for representing the H${}_2$ wave function, as it has the correct properties both at coalescent points and at asymptotic distances. Moreover, the matrix elements of all operators can be conveniently obtained in this basis via integration or differentiation with respect to nonlinear parameters. In this work we develop an approach that paves the way to practical calculations with this basis.

Atomic properties of the 24 low-lying $ns$, $n{p}_j$, $n{d}_j$, $n{f}_j$, and $n{g}_j$ states in Th$$iv ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states ($5f_j$, $6d_j$, $7p_j$, and $7s$), and tensor polarizabilities of the $5f_j$, $6d_j$, and $7p_{3/2}$ states of Th$$iv are evaluated. The uncertainties of the recommended values are estimated. These calculations provide recommended values critically evaluated for their accuracy for a number of Th$$iv atomic properties for use in theoretical modeling as well as planning and analysis of various experiments including development of an ultraprecise nuclear clock and resonant excitation Stark ionization spectroscopy studies of actinide ions.

We use the soft-photon approximation to extract the Wigner time delay from atomic two-color photoionization experiments. Unlike the strong-field approximation, the present method does not require introduction of the Coulomb-laser coupling corrections and enables one to extract the Wigner time delay directly from attosecond time delay measurements.

We discuss the possibility of emitting vector solitons from a two-component elongated BEC by manipulating in time the inter- or intraspecies scattering lengths with Feshbach resonance tuning. We present different situations which do not have an analog in the single species case. In particular, we show vector soliton outcoupling by tuning the interspecies forces, how the evolution in one species is controlled by tuning the dynamics of the other, and how one can implement the so-called supersolitons. The analysis is performed by numerical simulations of the one-dimensional Gross-Pitaevskii equation. Simple analytic arguments are also presented in order to give a qualitative insight.

We address the stability of superfluid currents in a system of interacting lattice bosons. We consider various Gutzwiller trial states for the quantum phase model which provides a good approximation for the Bose-Hubbard model in the limit of large interactions and boson populations. We thoroughly analyze the current-carrying stationary states of the dynamics ensuing from a Gaussian ansatz, and derive analytical results for the critical lines signaling their modulational and energetic instability, as well as the maximum of the carried current. We show that these analytical results are in good qualitative agreement with those obtained numerically in previous works on the Bose-Hubbard model, and in the present work for the quantum phase model.

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system and study their stability. In most cases, the VA provides good accuracy and correctly predicts the stability by means of the Vakhitov-Kolokolov criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes.

In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter and could evolve into a “cavity glass microscope” for frustrated quantum systems out of equilibrium. Here we develop the nonequilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low-temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class, however, is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin-glass physics onto the photon subsystem realizes a “photon glass” state and makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function $g^{\left(2\right)}\left(\tau \right)$.

We calculate the third-order susceptibility ${\chi }^{\left(3\right)}$ of a pair of two-level atoms that interact via the exchange of photons. QED corrections to second order in coupling to vacuum field modes yield collective two-photon absorption resonances, which can be observed in transmission spectroscopy of shaped broadband pulses. While some collective effects can be obtained by introducing an effective interatomic coupling using a quantum master equation, the predicted signals contain distinct features that are missed by that level of theory and require a full diagrammatic QED treatment.

We investigate analytically and numerically the propagation properties of dark solitons in nonlocal media with competing nonlinearities. We obtain analytical relations for soliton parameters for an arbitrary degree of nonlocality. In particular, we show that the velocity of dark solitons can be affected by the degree of nonlocality of competing nonlinearities. The analytical results are confirmed by direct numerical simulations of the full model describing propagation of dark solitons in nonlocal media with competing nonlinearities.

We use the three-dimensional time-dependent Schrödinger equation (3 D-TDSE) to calculate angular electron momentum distributions and photoelectron spectra of atoms driven by spatially inhomogeneous fields. An example for such inhomogeneous fields is the locally enhanced field induced by resonant plasmons, appearing at surfaces of metallic nanoparticles, nanotips, and gold bow-tie shaped nanostructures. Our studies show that the inhomogeneity of the laser electric field plays an important role on the above-threshold ionization process in the tunneling regime, causing significant modifications on the electron momentum distributions and photoelectron spectra, while its effects in the multiphoton regime appear to be negligible. Indeed, through the tunneling above-threshold ionization (ATI) process, one can obtain higher energy electrons as well as a high degree of asymmetry in the momentum space map. In this study we consider near infrared laser fields with intensities in the mid- ${10}^{14}$ W/cm${}^2$ range and we use a linear approximation to describe their spatial dependence. We show that in this case it is possible to drive electrons with energies in the near-keV regime. Furthermore, we study how the carrier envelope phase influences the emission of ATI photoelectrons for few-cycle pulses. Our quantum mechanical calculations are fully supported by their classical counterparts.

Complex scattering potentials can admit scattering states that behave exactly like a zero-width resonance. Their energy is what mathematicians call a spectral singularity. This phenomenon admits optical realizations in the form of lasing at the threshold gain, and its time-reversal is responsible for antilasing. We study spectral singularities and whispering gallery modes (WGMs) of a cylindrical gain medium. In particular, we introduce a class of WGMs that support a spectral singularity and, as a result, have a divergent quality factor. These singular gallery modes (SGMs) are excited only if the system has a positive gain coefficient, but typically the required gain is extremely small. More importantly, given any amount of gain, there are SGMs requiring smaller gain than this amount. This means that, in principle, the system lacks a lasing threshold. Furthermore, the abundance of these modes allows for configurations where a particular value of the gain coefficient yields an effective excitation of two distant SGMs. This induces lasing at two different wavelengths.

We use frequency comb interferometry to simultaneously obtain the optical impulse responses and wide-band transmission spectra of silica microspheres, as they together provide a more complete description of light dynamics inside the resonator. The grouping of periodic cavity ring-down pulses in the impulse response provides confirmation that small asphericities give rise to a precession of the orbit of the light pulse propagating along the inner surface of the microcavity. This effect also strongly depends on coupling conditions. Moreover, we notice the presence of secondary pulses associated with modes of higher radial quantum number. All these features bring valuable information on the optical properties of microspheres.

We describe a version of the Zeno effect where the monitored physical property cannot be represented by a standard operator in the system space and the evolution to be prevented by observation is not unitary. This is the case of quantum-state purity of a spin-1/2 system, which is equivalent to the degree of polarization of a single photon. By a suitable embedding of the system (say, a single photon) in an enlarged space of a pair of photons, pure and fully mixed components lead to orthogonal subspaces, with lack of purity becoming equivalent to entanglement. By imposing desirable properties the representation of the system in the enlarged space is unique. We show that the Zeno effect is possible, and experimentally feasible, in the enlarged space. The peculiarity that photons in identical polarization states are involved in pairs to observe the dynamics of each photon allows us to refer it as the self-Zeno effect or Narcissus effect.

We show that a weak projective measurement of photon arrival time can be realized by controllable two-photon interferences with photons from short-time reference pulses at a polarization beam splitter. The weak value of the projector on the arrival time defined by the reference pulse can be obtained from the coincidence rates conditioned by a specific output measurement. If the weak measurement is followed by a measurement of frequency, the coincidence counts reveal the complete temporal coherence of the single-photon wave function. Significantly, the weak values of the input state can also be obtained at higher measurement strengths, so that correlations between weak measurements on separate photons can be observed and evaluated without difficulty. The method can thus be used to directly observe the nonclassical statistics of time-energy entangled photons.

The interaction of high-energy electrons, positrons, and photons with intense laser pulses is studied in head-on collision geometry. It is shown that electrons and/or positrons undergo a cascade-type process involving multiple emissions of photons. These photons can consequently convert into electron-positron pairs. As a result charged particles quickly lose their energy developing an exponentially decaying energy distribution, which suppresses the emission of high-energy photons, thus reducing the number of electron-positron pairs being generated. Therefore, this type of interaction suppresses the development of the electromagnetic avalanche-type discharge, i.e., the exponential growth of the number of electrons, positrons, and photons does not occur in the course of interaction. The suppression will occur when three-dimensional effects can be neglected in the transverse particle orbits, i.e., for sufficiently broad laser pulses with intensities that are not too extreme. The final distributions of electrons, positrons, and photons are calculated for the case of a high-energy e-beam interacting with a counterstreaming, short intense laser pulse. The energy loss of the e-beam, which requires a self-consistent quantum description, plays an important role in this process, as well as provides a clear experimental observable for the transition from the classical to quantum regime of interaction.

Local unitary stabilizer subgroups constitute powerful invariants for distinguishing various types of multipartite entanglement. In this paper, we show how stabilizers can be used as a basis for entanglement verification protocols on distributed quantum networks using minimal resources. As an example, we develop and analyze the performance of a protocol to verify membership in the space of Werner states, that is, multiqubit states that are invariant under the action of any one-qubit unitary applied to all the qubits.

We study the atomic ionization process in high-frequency laser pulses by the Bohmian-trajectory scheme. Combined with the analysis of the trajectories of Bohmian particles and the time-dependent potential well based on the Kramers-Henneberger transformation, we find that there are two kinds of forces that act on each Bohmian particle (BP): the classical force from the combined potential of the atomic Coulomb potential and the laser field and the quantum force. By investigating the forces acting on different BPs, we find that the quantum force plays an important role in the atomic ionization process in the laser pulse.

I perform lattice Monte Carlo studies of universal four-component fermion systems in one spatial dimension. Continuum few-body observables (i.e., ground-state energies and integrated contact densities) are determined for both unpolarized and polarized systems of up to eight fermions confined to a harmonic trap. Estimates of the continuum energies for four and five trapped fermions show agreement with exact analytic calculations to within approximately one percent statistical uncertainties. Continuum many-body observables are determined for unpolarized systems of up to 88 fermions confined to a finite box, and 56 fermions confined to a harmonic trap. Results are reported for universal quantities such as the Bertsch parameter, defined as the energy of the untrapped many-body system in units of the corresponding free-gas energy, and its subleading correction at large but finite scattering length. Two independent estimates of these quantities are obtained from thermodynamic limit extrapolations of continuum extrapolated observables. A third estimate of the Bertsch parameter is obtained by combining estimates of the untrapped and trapped integrated contact densities with additional theoretical input from a calculation based on Thomas-Fermi theory. All estimates of the Bertsch parameter and its subleading correction are found to be consistent to within approximately one percent statistical uncertainties. Finally, the continuum restoration of virial theorems is verified for both few- and many-body systems confined to a trap.

We discuss the thermodynamic signatures for the topological phase transitions into Majorana and Weyl superfluid phases in ultracold Fermi gases in two and three dimensions (2D and 3D) in the presence of Rashba spin-orbit coupling and a Zeeman field. We analyze the thermodynamic properties exhibiting the distinct nature of the topological phase transitions linked with the Majorana fermions (2D Fermi gas) and Weyl fermions (3D Fermi gas) which can be observed experimentally, including pressure, chemical potential, isothermal compressibility, entropy, and specific heat, as a function of the interaction and the Zeeman field at both zero and finite temperatures. We conclude that among the various thermodynamic quantities, the isothermal compressibility and the chemical potential as functions of the artificial Zeeman field have the strongest signatures of the topological transitions in both two and three dimensions.