In continuation of our earlier works, we present results concerning the computation of matrix elements of the multipolar Hamiltonian (MPH) between extended wave functions that are obtained numerically. The choice of the MPH is discussed in connection with the broader issue of the form of radiation-atom (or -molecule) interaction that is appropriate for the systematic solution of various problems of matter-radiation interaction. We derive analytic formulas, in terms of the sine-integral function and spherical Bessel functions of various orders, for the cumulative radial integrals that were obtained and calculated by Komninos, Mercouris, and Nicolaides [Phys. Rev. A 71, 023410 (2005)]. This development allows the much faster and more accurate computation of such matrix elements, a fact that enhances the efficiency with which the time-dependent Schrödinger equation is solved nonperturbatively, in the framework of the state-specific expansion approach. The formulas are applicable to the general case where a pair of orbitals with angular parts $|{\ell }_1,m_1\rangle$ and $|{\ell }_2,m_2\rangle$ are coupled radiatively. As a test case, we calculate the matrix elements of the electric field and of the paramagnetic operators for on- and off-resonance transitions, between hydrogenic circular states of high angular momentum, whose quantum numbers are chosen so as to satisfy electric dipole and electric quadrupole selection rules. Because of the nature of their wave function (they are nodeless and the large centrifugal barrier keeps their overwhelming part at large distances from the nucleus), the validity of the electric dipole approximation in various applications where the off-resonance couplings must be considered becomes precarious. For example, for the transition from the circular state with $n$ = 20 to that with $n$ = 21, for which $〈r〉\approx 400$ a.u., the dipole approximation starts to fail already at XUV wavelengths ($\lambda <125\mathrm{nm}$).

We develop a dissipative quantum state preparation scheme for the creation of phase- and number-squeezed states. It utilizes ultracold atoms in a double-well configuration immersed in a background Bose-Einstein condensate, with the latter consisting of an atom species different from the atoms in the double well and acting as a dissipative quantum reservoir. We derive a master equation for this system starting from microscopic physics and show that squeezing develops on a time scale proportional to $1/N$, where $N$ is the number of particles in the double well. This scaling, caused by bosonic enhancement, allows us to make the time scale for the creation of squeezed states very short. The lifetime of squeezed states is limited by dephasing arising from the intrinsic structure of the setup. However, the dephasing can be avoided by stroboscopically switching the driving off and on. We show that this approach leads to robust stationary squeezed states. Finally, we provide the necessary ingredients for a potential experimental implementation by specifying a parameter regime for rubidium atoms that leads to squeezed states.

Using a time-dependent density matrix renormalization group (TDMRG) approach we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian. It is observed that the motion is essentially periodic with the clouds bouncing elastically, at least on the time scale of the first few oscillations that can be resolved with high accuracy. This is in agreement with the results of the “quantum Newton cradle” experiment of Kinoshita et al. [Nature (London) 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description, or generalized nonlinear Schrödinger equation, with the pressure term taken from the Bethe ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). In the case of the clouds' collision TDMRG alone allows one to extract the oscillation period which is found to be measurably different from the breathing mode period. Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics.

We investigate the properties of parity-time ($\mathcal{PT}$)-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain or loss contrast parameter. For unbounded $\mathcal{PT}$ lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of $\mathcal{PT}$ symmetry in energy transport problems occurring in such $\mathcal{PT}$-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples.

It has been shown by numerical simulation that the nonlinear interaction between a laser soliton and an injected monochromatic cw results in their phase locking. As a consequence, the velocity of the soliton begins to depend on the amplitude and frequency of the injected radiation. It has been found that if the frequency of the external signal coincides with the frequency of the dispersive waves emitted by solitons in a laser cavity with lumped intracavity elements, a mechanism for controlling long-range soliton interaction occurs. This mechanism is related to the interference between the injected wave and the dispersive waves involved in the strong long-range interaction between solitons. We have demonstrated the mechanism of soliton-soliton repulsion and, as its consequence, the occurrence of harmonic passive mode locking (multipulse generation with an equidistant arrangement of identical solitons in the laser cavity).

Analytical light-bullet solutions of a ($3+1$)-dimensional nonlinear Schrödinger equation with inhomogeneous diffraction or dispersion and nonlinearity in the presence of the harmonic and parity-time-symmetric potentials are explored. Diffraction or dispersion and nonlinearity play important roles in the evolutional characteristics such as amplitude, width, and phase. The compression and broadening behaviors of light bullets are discussed and compared in the exponential, Gaussian and hyperbolic diffraction or dispersion decreasing media and the periodic distributed amplification system. Moreover, phase changes of light bullets in different systems are also illustrated.

We report a theoretical study showing that rogue waves can emerge in whispering-gallery-mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. The nonlinear dynamics of the propagation of light in a whispering-gallery-mode resonator is investigated using the Lugiato-Lefever equation, and we give evidence of a range of parameters where rare and extreme events associated with non-Gaussian statistics of the field maxima are observed.

We present a general formalism for characterizing 2-time quantum states, describing pre- and postselected quantum systems. The most general 2-time state is characterized by a “density vector” that is independent of measurements performed between the preparation and postselection. We provide a method for performing tomography of an unknown 2-time density vector. This procedure, which cannot be implemented by weak or projective measurements, brings new insight to the fundamental role played by Kraus operators in quantum measurements. Finally, after showing that general states and measurements are isomorphic, we show that any measurement on a 2-time state can be mapped to a measurement on a preselected bipartite state.

We extend several measurement-based definitions of effective superposition size to coherent state superpositions with branches composed of either single coherent states or tensor products of coherent states. These measures of superposition size depend on determining the maximal quantum distinguishability of certain states associated with the superposition state: e.g., in one measure, the maximal distinguishability of the branches of the superposition is considered as in quantum binary decision theory; in another measure, the maximal distinguishability of the initial superposition and its image after a one-parameter evolution generated by a local Hermitian operator is of interest. The scaling of the size of the superposition with the number of modes and mode intensity (i.e., photon number) is compared to the scaling of certain geometric properties of the Wigner function of the superposition and also to the superposition size estimated experimentally from decoherence. We also apply earlier comparison-based methods for determining macroscopic superposition size that require a reference Greenberger-Horne-Zeilinger (GHZ) state. The case of a hierarchical Schrödinger cat state with branches composed of smaller superpositions is also analyzed from a measurement-based perspective.

We investigate high-fidelity quantum driving in a nonlinear two-level system and find that nonlinear atomic interaction can break the speed limit of the linear model. We show that repulsive atomic interaction can decrease the minimal time requested for reaching target state even to zero, while attractive atomic interaction tends to increase the minimal time. There exists a critical attractive interaction beyond which the target state cannot be reached with high fidelity. Possible experimental observation of the nonlinear effects using a Bose-Einstein condensate in an accelerating optical lattice is discussed.

The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families of gates which are able to give maximum entangling power for all values of purity. It is notable that one of this gates coincides with a maximum discording one. We give analytical proof that such gate is indeed a perfect entangler at all purities and give numerical evidence for the existence of the second one. Furthermore, we find that there are other gates, many in fact, which are perfect entanglers for a restricted range of purities. This highlights the fact that many perfect entangler gates could in principle be found if a thorough analysis of the full parameter space is performed.

We develop a framework that allows a description of measurements in Hilbert spaces that is smaller than their natural representation. This description, which we call a “squashing model,” consists of a squashing map that maps the input states of the measurement from the original Hilbert space to the smaller one, followed by a targeted prescribed measurement on the smaller Hilbert space. This framework has applications in quantum key distribution, but also in other cryptographic tasks, as it greatly simplifies the theoretical analysis under adversarial conditions.

A two-step, two-color laser spectroscopy technique has been used to measure the hyperfine splitting of the $7p_{1/2}$ excited state in ${}^{203}$Tl and ${}^{205}$Tl, as well as the isotope shift within the $7s_{1/2}$-$7p_{1/2}$ transition. Our measured values for the hyperfine splittings, 2153.2(7) MHz (in ${}^{203}$Tl) and 2173.3(8) MHz (in ${}^{205}$Tl), each differ by 20 MHz from previously published values which quoted comparable precision. The transition isotope shift of ${}^{203}$Tl relative to ${}^{205}$Tl was measured to be 534.4(9) MHz. In our experiment, one laser was locked to the thallium $6p_{1/2}$-$7s_{1/2}$ 378-nm transition, while a second, spatially overlapping laser was scanned across the $7s_{1/2}(F=1)$-$7p_{1/2}(F=0,1)$ infrared transitions. To facilitate accurate frequency calibration, radio-frequency modulation of the laser was used to create sidebands in the absorption spectrum.

Fluorescence yields are one of the fundamental parameters in atomic physics and related areas. Despite the increase of experimental work in the last decade, to obtain values of $K$-shell fluorescence yields available data are scarce or outdated for many elements. The available theoretical results cannot fill the gap since quite often they are derived from semi-empirical calculations based on old models. This is the case of Ge that has many applications in science. In this work, we present the results of a collaboration between an experimental and a theoretical group to obtain the decay rates and fluorescence yields for Ge. The calculations were performed within the Dirac-Fock method, including relativistic and QED corrections, using a state-of-the-art approach. The experimental work was carried out at the SOLEIL synchrotron and the fluorescence yields were measured by two distinct methods: the reflection geometry method and the escape peak method. The results show a very good agreement between the experiment and theory (1.1%), well within the experimental uncertainty (2.4%).

We investigate numerically parametrically driven coupled nonlinear Schrödinger equations modeling the dynamics of coupled wave fields in a periodically oscillating double-well potential. The equations describe, among other things, two coupled periodically curved optical waveguides with Kerr nonlinearity or Bose-Einstein condensates in a double-well potential that is shaken horizontally and periodically in time. In particular, we study the persistence of equilibrium states of the undriven system due to the presence of the parametric drive. Using numerical continuations of periodic orbits and calculating the corresponding Floquet multipliers, we find that the drive can (de)stabilize a continuation of an equilibrium state indicated by the change in the (in)stability of the orbit, showing that parametric drives can provide a powerful control to nonlinear (optical- or matter-wave-) field tunneling. We also discuss the appearance of chaotic regions reported in previous studies that is due to destabilization of a periodic orbit. Analytical approximations based on an averaging method are presented. Using perturbation theory, the influence of the drive on the symmetry-breaking bifurcation point is analyzed.

In quantum information, quantum systems and their properties offer unprecedented opportunities. Being able to harness additional degrees of freedom adds power and flexibility to quantum algorithms and protocols. In this work, we demonstrate that the radial transverse mode of a single photon constitutes one such degree of freedom. We do so by showing that we can tune the two-photon interference, a quintessential quantum effect and the basic constituent of many quantum protocols, by manipulating its radial transverse modal profiles. Our work, in addition to allowing for greater versatility of existing protocols and significantly increasing the information channel capacity, can inspire novel quantum information tasks.

Correlations between uncoupled particles induced by the interaction with different types of light are investigated using a superoperator formalism. We derive compact expressions for the doubly-excited-state distributions of noninteracting multilevel atoms excited by classical laser light, classical stochastic light, and quantum light. We find that the $g_2$ function of the incoming light can be directly related to its ability to induce correlations in the matter. Unlike coherent light, quantum light can induce entanglement between the atoms. The photon coincidence signal created by classical fields may be factorized into a product of single photon counting rates. This is not the case for quantum light.

We discuss the detrimental effect of small rapid random fluctuations of laser-field amplitude and phase upon the efficiency of stimulated Raman adiabatic passage (STIRAP). Such fluctuations typically accompany the laser stabilization procedures that produce nearly monochromatic light on top of a much broader bandwidth Lorentz-profile pedestal which may carry only a few percent or less of the total power. As we will show, their effects differ qualitatively from the fluctuations that have hitherto been considered (for example, phase diffusion). We present analytic expressions for the population transfer efficiency of STIRAP when limited by stochastic fluctuations of this type. These expressions show, in contrast to situations discussed in the past in which population transfer improves with increasing peak Rabi frequencies, that for the weak broadband noise that accompanies a strong narrow-spectral component, there is an optimum value for the peak Rabi frequency and that the effect of fluctuations, although small, cannot be entirely eliminated in practice. The mission of the current work is to point out that, under the given circumstances, efforts in experiments trying to overcome the detrimental consequences of fluctuations by increasing the intensity, which is the intuitively proper approach, will not be successful.

We study the properties of energy eigenstates in open quantum systems in which clockwise and counterclockwise traveling waves are weakly coupled. We show that under rather general conditions the energy eigenstates of such systems can appear in pairs of nonorthogonal, copropagating traveling-wave states. The relation to exceptional points of the effective non-Hermitian Hamiltonian is discussed.

We investigate quantum measurements on a complex Hilbert space spanned by binary optical coherent states. We derive that arbitrary quantum measurement with finite detection operators can be implemented on this space, which is not constrained to be projective, by using just a beam splitter, a local coherent light source, a photon detector, and a feedback circuit.