We use analytic (current) density-potential maps of time-dependent (current) density-functional theory [TD(C)DFT] to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schrödinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time-dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum not gate.

We present a comprehensive study of electron collisions with boron atoms by using the $B$-spline $R$-matrix method for electron energies ranging from threshold to 100 eV. Elastic, excitation, and ionization cross sections were obtained for all transitions between the lowest 11 states of boron. A multiconfiguration Hartree-Fock method with nonorthogonal term-dependent orbitals was employed to generate accurate wave functions for the target states. Close-coupling expansions including 13, 51, and 999 physical and pseudo-target states of boron were used to check the sensitivity of the results to changes in the theoretical model. The cross-section dataset obtained from the large-scale calculations is expected to be sufficiently accurate and comprehensive for most current modeling applications involving neutral boron.

A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for $J\to J,J-1$ transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the $J\to J-1$ case (i.e., $J^{\prime \prime }=1\to J^{\prime }=0$) and $J\to J$ case (i.e., $J^{\prime \prime }=1/2\to J^{\prime }=1/2$). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the ${\mathrm{C}}_2^{-}$ molecular anion as a typical example of the interplay between the two simple transitions $J\to J,J-1$.

The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of our recently proposed density-functional theory [B. P. van Zyl, W. Kirkby, and W. Ferguson, Phys. Rev. A 92, 023614 (2015)]. In each two-dimensional layer, the fermions interact via a repulsive, isotropic dipolar interaction. The presence of a second layer introduces an attractive interlayer interaction, thereby allowing the presence of inhomogeneous density phases which would otherwise be energetically unfavorable. For any fixed layer separation, we find an instability to a commensurate one-dimensional stripe phase in each layer, which always precedes the formation of a triangular Wigner crystal. However, at a certain fixed coupling, tuning the separation can lead to the system favoring a commensurate triangular Wigner crystal, or one-dimensional stripe phase, completely bypassing the Fermi liquid state. While other crystalline symmetries, with energies lower than the liquid phase can be found, they are never allowed to form owing to their high energetic cost relative to the triangular Wigner crystal and stripe phase.

The study of the spatiotemporal dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest. This system has been shown to exhibit a phenomenon of polarization attraction which can be used to achieve a complete polarization of an initially unpolarized beam, almost without any loss of energy. In previous works, a theoretical description of this phenomenon has been developed in the particular case where the underlying stationary system exhibits the important property of integrability. Our aim here is to provide a generalization of the theoretical description to nonintegrable stationary systems. The analysis reveals that the spatiotemporal dynamics of the system relaxes towards a stationary trajectory whose geometric structure is revealed by the stable and unstable manifolds of some singular fixed points of the stationary system. We illustrate the theory by considering the representative and concrete example of a weakly birefringent optical fiber system.

We investigate squeezing of the resonance fluorescence of a laser-driven quantum dot (QD) close to a graphene sheet. The coupling between the QD and the surface plasmon around the graphene sheet is frequency dependent in the terahertz region, which can be adjusted by the laser intensity. Distinct decay rates in different transition channels of dressed QDs can be achieved due to the tailored photon reservoir, which can be used to improve the squeezing. It is found that increases in both the dephasing rate and the environmental temperature are harmful to the squeezing. Meanwhile, an enhancement in the QD-plasmon coupling strength may reduce the fragility of squeezing against the decoherence process. Additionally, in the strong light-matter coupling region, squeezing can be largely enhanced by tuning the strength of the pump field and its detuning from the QD.

Suppose a quantum system starts to evolve under a Hamiltonian from some initial state. When, for the first time, will an observable attain a preassigned value? To answer this question, one method often adopted is to make instantaneous measurements periodically and note down the serial number for which the desired result is obtained for the first time. We apply this protocol to an interacting spin system at zero temperature and show analytically that the response of this system shows a nonanalyticity as a function of the parameter of the Hamiltonian and the time interval of measurement. In contrast to quantum phase transitions, this type of phase transition is not a property of the ground state and arises from the Hamiltonian dynamics and quantum-mechanical nature of the measurement. The specific system studied is the transverse Ising chain, and the measurement performed is whether the total transverse magnetic moment (per site) is not equal to 1. The results for some other types of measurement are also discussed.

We propose a protocol for the manipulation of a three-level artificial atom in Lambda ($\mathrm{\Lambda }$) configuration. It allows faithful, selective and robust population transfer analogous to stimulated Raman adiabatic passage ($\mathrm{\Lambda }$-STIRAP), in last-generation superconducting artificial atoms, where protection from noise implies the absence of a direct pump coupling. It combines the use of a two-photon pump pulse with suitable advanced control, operated by a slow modulation of the phase of the external fields, leveraging on the stability of semiclassical microwave drives. This protocol is a building block for manipulation of microwave photons in complex quantum architectures. Its demonstration would be a benchmark for the implementation of a class of multilevel advanced control procedures for quantum computation and microwave quantum photonics in systems based on artificial atoms.

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractional occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Finally, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.

We analyze atomic structures of plasma-embedded aluminum (Al) atom and its ions in the weak- and strong-coupling regimes. The plasma screening effects in these atomic systems are accounted for using the Debye and ion-sphere (IS) potentials for the weakly and strongly coupled plasmas, respectively. Within the Debye model, special attention is given to investigate the spherical and nonspherical plasma screening effects considering in the electron-electron interaction potential. The relativistic coupled-cluster (RCC) method has been employed to describe the relativistic and electronic correlation effects in the above atomic systems. The variations in the ionization potentials (IPs) and excitation energies (EEs) of the plasma-embedded Al ions are presented. It is found that the atomic systems exhibit more stability when the exact screening effects are taken into account. It is also shown that in the presence of a strongly coupled plasma environment, the highly ionized Al ions show blueshifts and redshifts in the spectral lines of the transitions between the states with the same and different principal quantum numbers, respectively. Comparison among the results obtained from the Debye and IS models are also carried out considering similar plasma conditions.

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum $J=0$ we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for $J>0$ we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF $\left(J=0\right)$ also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.

We consider two ultracold particles confined in a spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact pseudopotential with complex scattering length and investigate the properties of eigenenergies and eigenfunctions for different trap states as a function of the real and imaginary parts of the scattering length. In the analyzed case, the eigenenergies take complex values and their imaginary part can be interpreted in terms of decay rates. Then we introduce the model of a square well with absorbing boundary conditions that is later used to investigate the effects of the finite range of interaction on the properties of a reactive scattering in the trap. Finally, we analyze the decay rates for some reactive alkali dimer molecules assuming short-range probability of reaction equal to unity. In this case, the complex scattering length is given by the universal value related to the mean scattering length of the van der Waals interaction between molecules.

The polarization correlations in doubly differential cross sections are investigated for photoionization and ordinary bremsstrahlung. These correlations describe the polarization transfer between incident light and ejected photoelectrons as well as between an incoming electron beam and bremsstrahlung light, respectively. They are characterized by a set of seven real parameters $C_{ij}$. We show that the squares of these parameters are connected by simple “sum rules.” These sum rules can be applied for both one-electron systems and also for atoms, if the latter are described within the independent particle approximation. In particular, they are exact in their simplest form (i) for the photoionization of $K$-, $L_{I,II}$-, and $M_{I,II}$-atomic shells, as well as (ii) for bremsstrahlung in which the electron is scattered into $s_{1/2}$ or $p_{1/2}$ states, as in the tip (bremsstrahlung) region. Detailed calculations are performed to verify the derived identities and to discuss their possible applications for the analysis of modern photoionization and bremsstrahlung experiments. In particular, we argue that the sum rules may help to determine the entire set of (significant) polarization correlations in the case when not all $C_{ij}$ are available for experimental observation.

Selected features of nonsequential double ionization have been qualitatively reproduced by a multitude of different (quantum and classical) approaches. In general, however, the typical uncertainty of laser pulse parameters and the restricted number of observables measured in individual experiments leave room for adjusting theoretical results to match the experimental data. While this has been hampering the assessment of different theoretical approaches leading to conflicting interpretations, comprehensive experimental data that would allow such an ultimate and quantitative assessment have been missing so far. To remedy this situation we have performed a kinematically complete measurement of single-cycle multiple ionization of argon over a one order of magnitude range of intensity. The momenta of electrons and ions resulting from the ionization of the target gas are measured in coincidence, while each ionization event is tagged with the carrier-envelope phase and intensity of the 4-fs laser pulse driving the process. The acquired highly differential experimental data provide a benchmark for a rigorous test of the many competing theoretical models used to describe nonsequential double ionization.

Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling can exhibit hysteresis loops of atomic currents. Cold atoms in ring-shape potentials are thus promising for demonstrating rate-dependent hysteresis and its associated phenomena.

We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in present-day experiments with ultracold atoms and we show how to relate the work statistics to that of the population imbalance of the two modes.

Estimating the temperature of a cold quantum system is difficult. Usually one measures a well-understood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes minimal knowledge of the state of a system and is potentially nondestructive. Our method uses a universal temperature dependence of the quench dynamics of an initially thermal system coupled to a qubit probe that follows from the Tasaki-Crooks theorem for nonequilibrium work distributions. We provide examples for a cold-atom system, in which our thermometry protocol may retain accuracy and precision at subnano-Kelvin temperatures.

We investigate the dynamics following a global parameter quench for two one-dimensional models with variable-range power-law interactions: a long-range transverse Ising model, which has recently been realized in chains of trapped ions, and a long-range lattice model for spinless fermions with long-range tunneling. For the transverse Ising model, the spreading of correlations and growth of entanglement are computed using numerical matrix product state techniques, and are compared with exact solutions for the fermionic tunneling model. We identify transitions between regimes with and without an apparent linear light cone for correlations, which correspond closely between the two models. For long-range interactions (in terms of separation distance $r$, decaying slower than $1/r$), we find that despite the lack of a light cone, correlations grow slowly as a power law at short times, and that—depending on the structure of the initial state—the growth of entanglement can also be sublinear. These results are understood through analytical calculations, and should be measurable in experiments with trapped ions.