We have measured and calculated doubly differential cross sections for ionization of atomic hydrogen using $75$-keV proton impact for fixed projectile energy losses as a function of scattering angle. This collision system represents a pure three-body system and thus offers an accurate test of the theoretical description of the few-body dynamics without any complications presented by electron correlation in many-electron targets. Comparison between experiment and several theoretical models reveals that the projectile-target nucleus interaction is best described by the operator of a second-order term of the transition amplitude. Higher-order contributions in the projectile-electron interaction, on the other hand, are more appropriately accounted for in the final-state wave function.

We report calculations of Born-Oppenheimer potential energy curves of the chromium-rubidium heteronuclear molecule (${}^{52}\mathrm{Cr}$${}^{87}\mathrm{Rb}$), and the long-range dispersion coefficient for the interaction between ground state Cr and Rb atoms. Our calculated van der Waals coefficient ($C_6=1770$ a.u.) has an expected error of $3\%$. The ground state ${}^6{\Sigma }^{+}$ molecule at its equilibrium separation has a permanent electric dipole moment of $d_e(R_e=3.34Å)=2.90\hspace{0.5em}D$. We investigate the hyperfine and dipolar collisions between trapped Cr and Rb atoms, finding elastic to inelastic cross section ratio of ${10}^2$–${10}^3$.

We investigate the combined effects of weak disorder and a two-dimensional (2D) optical lattice on the collective excitations of a harmonically trapped Bose-Einstein condensate (BEC) at zero temperature. Accordingly, we generalize the hydrodynamic equations of superfluid for a weakly interacting Bose gas in a 2D optical lattice to include the effects of weak disorder. Our analytical results for the collective frequencies beyond the mean-field approximation reveal the peculiar role of disorder, interplaying with the 2D optical lattice and interatomic interaction, on elementary excitations along the 3D to 1D crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.

We perform a numeric study (Worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two- and three-dimensional optical lattices. At strong enough interactions and low enough temperatures the system features magnetic ordering. We compute critical temperatures and entropies for the disappearance of the Ising antiferromagnetic and the $\mathit{xy}$-ferromagnetic order and find that the largest possible entropies per particle are $~0.5k_B$. We also estimate (optimistically) the experimental hold times required to reach equilibrium magnetic states to be on a scale of seconds. Low critical entropies and long hold times render the experimental observations of magnetic phases challenging and call for increased control over heating sources.

We study fluctuations in the atom number difference between two halves of a harmonically trapped Bose gas in three dimensions. We solve the problem analytically for noninteracting atoms. In the interacting case we find an analytical solution in the Thomas-Fermi and high temperature limit in good agreement with classical field simulations. In the large system size limit, fluctuations in the number difference are maximal for a temperature $T\simeq 0.7T_c$ where $T_c$ is the critical temperature, independently of the trap anisotropy. The occurrence of this maximum is due to an interference effect between the condensate and the noncondensed fields.

We study the spectral properties of stationary laser solitons (LSs) generated in two broad-area vertical cavity surface emitting lasers coupled to each other in face-to-face configuration [P. Genevet et al., Phys. Rev. Lett. 101, 123905 (2008)]. We demonstrate experimentally that LS emission occurs on a single longitudinal mode frequency of the compound cavity. Multistability is reported among differently “colored” LSs. We also develop a theoretical model beyond the single longitudinal mode approximation whose numerical simulation results are in good agreement with the experimental observations.

Metal-dielectric stacks can be designed to support resonant transmission modes for certain evanescent field components of an incident electromagnetic field. Here we show that when combined with an appropriate subwavelength pitch grating the amplified Fourier components coincide with different diffraction orders at different frequencies. It thereby becomes possible to collect a wide range of evanescent Fourier components by performing measurements at different optical frequencies. For a typical anisotropic metal-dielectric stack, we find that for a source emitting at wavelengths $400$–$500$ nm, imaging with a resolution of $\approx 20$ nm becomes possible. Although the reconstructed image contains ringing effects due to gaps in the measured Fourier spectrum, the final resolution achievable is a significant improvement over other fast near-field imaging techniques. The presented technique may find applications in fast super-resolution surface imaging of objects that emit over a wider optical frequency range.

We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second-order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse bandwidth. Our approach goes beyond the usual coupled wave description of ${\chi }^{(2)}$ phenomena and provides an accurate modeling of the evolution of ultra-broadband pulses also when the separation into different coupled frequency components is not possible or not profitable.

We theoretically study the effect of atomic nonlinearity on the tunneling time in the case of an atomic Bose-Einstein condensate (BEC) traversing the laser-induced potential barrier. The atomic nonlinearity is controlled to appear only in the region of the barrier by employing the Feshbach resonance technique to tune interatomic interaction in the tunneling process. Numerical simulation shows that the atomic nonlinear effect dramatically changes the tunneling behavior of the BEC matter wave packet and results in the violation of the Hartman effect and the occurrence of negative tunneling time.

Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, “magic” optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias $B$ field along a circularly polarized trapping laser field. We map out these $B$ fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.

We investigate the dynamical relations among entanglement, mixedness, and nonlocality, quantified by concurrence $C$, purity $P$, and maximum Bell function $B$, respectively, in a system of two qubits in a common structured reservoir. To this aim we introduce the $C$-$P$-$B$ parameter space and analyze the time evolution of the point representative of the system state in such a space. The dynamical interplay among entanglement, mixedness, and nonlocality strongly depends on the initial state of the system. For a two-excitation Bell state the representative point draws a multibranch curve in the $C$-$P$-$B$ space and we show that a closed relation among these quantifiers does not hold. By extending the known relation between $C$ and $B$ for pure states, we give an expression among the three quantifiers for mixed states. In this equation we introduce a quantity, vanishing for pure states, which in general does not have a closed form in terms of $C$, $P$ and $B$. Finally, we demonstrate that for an initial one-excitation Bell state, a closed $C$-$P$-$B$ relation instead exists and the system evolves, remaining always a maximally entangled mixed state.

I consider the interaction of a small quantum system (a qubit) with a structured environment consisting of many levels. The qubit will experience a decoherence process, which implies that part of its initial information will be encoded into correlations between system and environment. I investigate how this information is distributed on a given subset of levels as a function of its size, using the mutual information between both entities, in the spirit of the partial-information plots studied by Zurek and co-workers. In this case we can observe some differences, which arise from the fact that I am partitioning just one quantum system and not a collection of them. However, some similar features, like redundancy (in the sense that a given amount of information is shared by many subsets), which increases with the size of the environment, are also found here.

We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension.

State preparation, qubit rotation, and high fidelity readout are demonstrated for two different ${}^{137}\mathrm{Ba}{}^{+}$ qubit types. First, an optical qubit on the narrow $6S_{1/2}$ to $5D_{5/2}$ transition at 1.76 $\mu$m is implemented. Then, leveraging the techniques developed there for readout, a ground-state hyperfine qubit using the magnetically insensitive transition at 8 GHz is accomplished.

We propose a method that employs functionals of the one-electron reduced density matrix (density matrix) to capture long-range effects of electron correlation. The complementary short-range regime is treated with density functionals. In an effort to find approximations for the long-range density-matrix functional, a modified power functional is applied to the homogeneous electron gas with Coulomb interactions replaced by their corresponding long-range counterparts. For the power $\beta =1/2$ and the range-separation parameter $\omega =1/r_s$, the functional reproduces the correlation and the kinetic correlation energies with a remarkable accuracy for intermediate and large values of $r_s$. Analysis of the Euler equation corresponding to this functional reveals correct $r_s$ expansion of the correlation energy in the limit of large $r_s$. The first expansion coefficient is in very good agreement with that obtained from the modified Wigner-Seitz model.

We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely, an energy-flux-driven quantum $\mathit{XX}$ chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux-carrying steady state.

The technique of stimulated Raman adiabatic passage (STIRAP) is a highly efficient tool for coherent population transfer in a chainwise-connected three-state quantum system. It is widely accepted that the two-photon resonance between the two end states of the chain is a crucial condition for STIRAP. This assumption is indeed correct when the two driving fields, pump and Stokes, produce nearly equal couplings for their respective transitions. We show analytically, supported by numeric examples, that when the pump and Stokes couplings differ significantly, the two-photon population transfer profile is distorted and its center is shifted away from the two-photon resonance; hence, the optimal operation of STIRAP demands a two-photon detuning. We derive simple analytic estimates for the center and the width of the two-photon profile. The results are of potential importance in situations when the pump and Stokes fields are of different physical natures (e.g., laser and cavity fields) or when two-photon resonance is unwanted (e.g., in the presence of residual light).

Absolute photoionization measurements were performed for a mixture of ${}^2{P}_{3/2}^o$ ground-state and ${}^2{P}_{1/2}^o$ metastable-state Ca${}^{3+}$ ions over the photon energy range $65.7$–$104.6$ eV by merging an ion beam with a beam of monochromatized synchrotron radiation. The ionization threshold energy of the ${}^2{P}_{3/2}^o$ ground state was measured to be $67.063$ $\pm$ $0.015$ eV, which is $0.207$ eV lower than the value tabulated in the NIST database. Most of the observed resonances associated with multiple Rydberg series of autoionizing states have been assigned spectroscopically using the quantum defect form of the Rydberg formula, guided by relativistic Hartree-Fock calculations of resonance energies and oscillator strengths. Intermediate coupling $R$-matrix calculations performed using the semi-relativistic Breit-Pauli approximation are in suitable agreement with measured absolute photoionization cross section in the energy range studied for this complex Cl-like ion species.

This is the first of two papers that develop theories and numerical methods for photoionization microscopy of hydrogen atoms in strong electric fields, in semiclassical and quantum-mechanical frameworks, respectively. In this paper, semiclassical open-orbit theory is presented to describe the propagation of outgoing electron waves to macroscopic distances. Spatial distributions of electron probability densities and current densities are predicted. The open-orbit theory, based on an assumption that electron waves propagate along classical paths from a pointlike source to a detector, provides a clear and intuitive physical picture to interpret structures of observed geometrical interference patterns in photoionization microscopy. We calculate photoelectron ejection of hydrogen atoms in electric fields, and comparison is made with quantum-mechanical results, which will be detailed in the second paper [Zhao and Delos, Phys. Rev. A 81, 053418 (2010)]. A strong quantum tunneling effect has been found. Such a tunneling effect should be visible in the experiment.

Complementary to the semiclassical method developed in the preceding paper, here we develop a quantum-mechanical approach to characterize propagation of electron waves to large distances in photoionization microscopy of hydrogen atoms in uniform external electric fields. A formula for outgoing electron waves from the atomic source produced in photoionization has been derived. Spatial distributions of electron probability densities can be determined using the obtained formula. The electron waves that propagate to a large distance due to photoionization from the $n=2$ initial state of hydrogen atoms in electric fields has been calculated and the resulting probability densities are presented. Comparison with semiclassical results is made, and they are found to be in good agreement. A detailed analysis is given of strong quantum tunneling effects found in our calculations.