We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU($d$) unitaries, quantum superpositions stored in the decoherence-free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one-photon loss and can be demonstrated with photon quadruplets using currently available technology.

Excitation energies of the [Xe]$4f^{14}5d^{10}ns$, [Xe]$4f^{14}5d^{10}n{p}_j$, [Xe]$4f^{14}5d^{10}n{d}_j$, [Xe]$4f^{14}5d^{10}{n}^{\prime }{f}_j$, and [Xe]$4f^{14}5d^{10}{n}^{\prime }{g}_j$ states in Hg${}^{+}$ are evaluated ($n\le 10$, $n^{\prime }\le 9$, and $\left[\mathrm{Xe}\right]=1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{6}4d^{10}5s^{2}5p^6$). First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, and transition rates are determined for electric-dipole transitions, including the $ns$ ($n=6$–11), $np$ ($n=6$–10), $nd$ ($n=6$–10), $nf$ ($n=5$–9), and $ng$ ($n=5$–9) states. Lifetime values are determined for all above-mentioned states. The ground state $E1$, $E2$, and $E3$ polarizabilities are evaluated. The hyperfine structure in ${}^{199}$Hg${}^{+}$ and ${}^{201}$Hg${}^{+}$ ions is investigated. The hyperfine $A$ and $B$ values are determined for the first low-lying levels up to $n$ $=$ 7. The quadratic Stark effect on hyperfine structure levels of ${}^{199}$Hg${}^{+}$ and ${}^{201}$Hg${}^{+}$ ground states is investigated. The calculated shift for the ${}^{199}$Hg${}^{+}$ ($F$ $=$ 1, $M$ $=$ 0) $\leftrightarrow$ ($F$ $=$ 0, $M$ $=$ 0) transition is $-$0.0597(2) Hz/(kV/cm)${}^2$, in agreement with previous theoretical result $-$0.060(3) Hz/(kV/cm)${}^2$. These calculations provide a theoretical benchmark for comparison with experiment and theory and provide values of blackbody radiation shifts for microwave frequency standards with ${}^{199}$Hg${}^{+}$ and ${}^{201}$Hg${}^{+}$ ions.

An analytically solvable three-body collision system ($s$ wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys. 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

We observe two-body loss of ${}^3{P}_0$ ${}^{87}$Sr atoms trapped in a one-dimensional optical lattice. We measure loss rate coefficients for atomic samples between 1 and 6 $\mu$K that are prepared either in a single nuclear-spin sublevel or with equal populations in two sublevels. The measured temperature and nuclear-spin preparation dependence of rate coefficients agree well with calculations and reveal that rate coefficients for distinguishable atoms are only slightly enhanced over those of indistinguishable atoms. We further observe a suppression of excitation and losses during interrogation of the ${}^1{S}_0$–${}^3{P}_0$ transition as density increases and Rabi frequency decreases, which suggests the presence of strong interactions in our dynamically driven many-body system.

We present a study of dissociative electron attachment and vibrational excitation processes in electron collisions with the ${\mathrm{CF}}_3\mathrm{Cl}$ molecule. The calculations are based on the two-dimensional nuclear dynamics including the C-Cl symmetric stretch coordinate and the ${\mathrm{CF}}_3$ symmetric deformation (umbrella) coordinate. The complex potential energy surfaces are calculated using the ab initio $R$-matrix method. The results for dissociative attachment and vibrational excitation of the umbrella mode agree quite well with experiment whereas the cross section for excitation of the C-Cl symmetric stretch vibrations is about a factor-of-three too low in comparison with experimental data.

We present a theoretical and experimental study of the resonant circularly-polarized-light-induced Hanle effect in the ground state of Cs vapor atoms in a paraffin-coated cell. The effect manifests itself as a narrow resonance (centered at $B=0$) in the dependence of the optical transmission coefficient of the vapor on the magnitude of an external magnetic field $\vec{B}$. We develop a theoretical model that yields an algebraic expression for the shape of these resonances for arbitrary field orientations and arbitrary angular momenta of the states coupled by the exciting light, provided that the light power is kept sufficiently small. An experimental procedure for assessing the range of validity of the model is given. Experiments were carried out on the laser-driven Cs $D_1$ transition both in longitudinal and transverse field geometries, and the observed line shapes of the corresponding bright and dark resonances give an excellent confirmation of the model predictions. The method is applied for determining the intrinsic longitudinal and transverse relaxation rates of the vector magnetization in the vapor and their dependence on light power.

We explore strong field molecular ionization with velocity map imaging of fragment ions produced by dissociation following ionization. Our measurements and ab initio electronic structure calculations allow us to identify various electronic states of the molecular cation populated during ionization, with multiple pathways to individual states highlighted by the pulse shape dependence. In addition, we show that relative populations can be reconstructed from our measurements. The results illustrate how strong field molecular ionization can be complicated by the presence and interaction of multiple cationic states during ionization.

We consider a generalization of the two-dimensional (2D) quantum Hall insulator to a noncompact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered three-dimensional (3D) insulator with nontrivial topology. We further show that nontrivial combinations of quantized transverse conductivities can be engineered with the help of a staggered potential. We investigate the robustness and topological nature of this conductivity and connect it to the surface modes of the system. We also propose a simple experimental realization with ultracold atoms in 3D confined to a 2D square lattice with the third dimension being mapped to a gauge coordinate.

We propose a realization of the one-dimensional random dimer model and certain $N$-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the symmetry properties of the corresponding Hamiltonian, and we provide analytical and numerical results for the localization length as a function of energy. We demonstrate that the $N$-leg systems possess similarities with their one-dimensional ancestors but are demonstrably distinct. The existence of critical delocalization energies leads to dips in the momentum distribution that serve as a clear signal of the localization-delocalization transition. These momentum distributions are different for models with different group symmetries and are identical for those with the same symmetry.

A quantum theoretical description of photoemission by a single laser-driven electron wave packet is presented. Energy-momentum conservation ensures that the partial emissions from individual momentum components of the electron wave packet do not interfere when the driving field is unidirectional. In other words, light scattering by an electron packet is independent of the phases of the pure momentum states comprising the packet; the size of the electron wave packet does not matter. This result holds also in the case of high-intensity multiphoton scattering. Our analysis is first presented in the QED framework. Since QED permits the second-quantized entangled electron-photon final state to be projected onto pure plane-wave states, the Born probability interpretation requires these projections to be first squared and then summed to find an overall probability of a scattering event. The QED treatment indicates how a semiclassical framework can be developed to recover the key features of the correct result.

A quantum-field-theory description of photoemission by a laser-driven single-electron wave packet is presented. We show that, when the incident light is represented with multimode coherent states then, to all orders of perturbation theory, the relative phases of the electron's constituent momenta have no influence on the amount of scattered light. These results are extended using the Furry picture, where the (unidirectional) arbitrary incident light pulse is treated nonperturbatively with Volkov functions. This analysis increases the scope of our prior results in [Phys. Rev. A 84, 053831 (2011)], which demonstrate that the spatial size of the electron wave packet does not influence photoemission.

We report on the fabrication of high-$Q$, fused-quartz microresonators and the parametric generation of a frequency comb with 36-GHz line spacing using them. We have characterized the intrinsic stability of the comb in both the time and frequency domains to assess its suitability for future precision metrology applications. Intensity autocorrelation measurements and line-by-line comb control reveal near-transform-limited picosecond pulse trains that are associated with good relative phase and amplitude stability of the comb lines. The comb's 36-GHz line spacing can be readily photodetected, which enables measurements of its intrinsic and absolute phase fluctuations.

We experimentally demonstrate the high-efficiency reflection of a probe field in Λ-type three-level atoms of cesium vapor driven by two counterpropagating coupling fields. More than 60$\%$ of reflection efficiency is observed at the phase-matching angle. The underlying mechanism theoretically is investigated as the four-wave mixing is enhanced by the electromagnetically-induced transparency. Both of the two Doppler-free two-photon resonances (one for the probe and co-propagating fields, the other for the reflected and the counterpropagation fields) play an important role in satisfying the phase matching in the reflection direction. The phase compensation due to the anomalous dispersion and the decrease of effective absorption length in the atomic system allow the efficient reflection to be observed in a wide range of incident angles of the probe field and detunings of the coupling field.

We present a scheme that achieves negative refraction with low absorption in far-off resonant atomic systems. The scheme utilizes Raman resonances and does not require the simultaneous presence of an electric-dipole transition and a magnetic-dipole transition near the same wavelength. We show that two interfering Raman tran-sitions coupled to a magnetic-dipole transition can achieve a negative index of refraction with low absorption through magnetoelectric cross-coupling. We confirm the validity of the analytical results with exact numerical simulations of the density matrix. We also discuss possible experimental implementations of the scheme in rare-earth metal atomic systems.

We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.

Double photoionization of the core $1s$ electrons in atomic beryllium is theoretically studied using a hybrid approach that combines orbital and grid-based representations of the Hamiltonian. The ${}^{1}S$ ground state and ${}^{1}P$ final state contain a double occupancy of the $2s$ valence shell in all configurations used to represent the correlated wave function. Triply differential cross sections are evaluated, with particular attention focused on a comparison of the effects of scattering the ejected electrons through the spherically symmetric valence shell with similar cross sections for helium, representing a purely two-electron target with an analogous initial-state configuration.

Photoassociation (PA) dynamics of ultracold cesium atoms steered by a modulated two-color laser field $E\left(t\right)=E_{0}f\left(t\right)\cos (\frac{2\pi }{T_p}-\phi )\cos \left({\omega }_{L}t\right)$ is investigated theoretically by numerically solving the time-dependent Schrödinger equation. The PA dynamics is sensitive to the phase of envelope (POE) $\phi$ and the period of the envelope $T_p$, which indicates that it can be controlled by varying POE $\phi$ and period $T_p$. Moreover, we introduce the time- and frequency-resolved spectrum to illustrate how the POE $\phi$ and the period $T_p$ influence the intensity distribution of the modulated laser pulse and hence change the time-dependent population distribution of photoassociated molecules. When the Gaussian envelope contains a few oscillations, the PA efficiency is also dependent on POE $\phi$. The modulated two-color laser field is available in the current experiment based on laser mode-lock technology.

The two-photon resonance ionization probability of atoms in strong extreme-ultraviolet free-electron laser (EUV FEL) pulses has been investigated by the model of time-dependent wave packet propagation of a light-coupled multilevel atom. Under the simulation within the model assuming single-mode FEL pulses, the ionization probability $P_{\mathrm{ion}}$ has shown characteristic dependences on the scaled coupling parameter $U_{gi}$ between two levels of the ground ($g$) and intermediate ($i$) resonance states, namely, $P_{\mathrm{ion}}\propto {\left(U_{gi}\right)}^n$, with $n$ being equal to ∼2, less than 1, and ∼1 for the small, medium, and large $U_{gi}$ regimes, respectively. This power dependence of the ionization probability has been interpreted due to Rabi oscillations between $g$ and $i$ states. To compare with recent experimental results on the same condition, the multimode nature of self-amplitude spontaneous emission (SASE) FEL pulses has been managed in the simulation. Then, the recent experimental laser-power dependence of the two-photon resonance ionization of He [Sato et al., J. Phys. B 44, 161001 (2011)] has been well described by that for the large $U_{gi}$ regime of the simulation, i.e., $n$ ∼ 1. Thus, the observed linear laser-power dependence has been rationalized as being caused by the strong Rabi oscillations between the (2$p$)–(1$s$) states.

In recent years it has become possible to align molecules in free space using ultrashort laser pulses. Here we explore two schemes for controlling molecule-surface scattering processes and which are based on laser-induced molecular alignment. In the first scheme, a single ultrashort nonresonant laser pulse is applied to a molecular beam hitting the surface. This pulse modifies the angular distribution of the incident molecules and causes the scattered molecules to rotate with a preferred sense of rotation (clockwise or counterclockwise). In the second scheme, two properly delayed laser pulses are applied to a molecular beam composed of two chemically close molecular species (isotopes, or nuclear-spin isomers). As the result of the double-pulse excitation, these species are selectively scattered to different angles after the collision with the surface. These effects may provide new means for the analysis and separation of molecular mixtures.

We report results of numerical and analytical studies of the spontaneous symmetry breaking in solitons, both two- and one-dimensional (2D and 1D), which are trapped in $\mathsf{H}$-shaped potential profiles built of two parallel potential troughs linked by a narrow rung in the transverse direction. This system can be implemented in self-attractive Bose-Einstein condensates (BECs), as well as in a nonlinear bulk optical waveguide. We demonstrate that the introduction of the transverse link changes the character of the symmetry-breaking bifurcation (SBB) in the system from subcritical to supercritical. (In terms of the corresponding phase transition, it is a change between the first and second kinds.) A noteworthy feature of the SBB in this setting is a nonmonotonous dependence of the soliton’s norm at the bifurcation point on the strength of the transverse link. In the full 2D system, the results are obtained in a numerical form. An exact analytical solution is found for the bifurcation in the 1D version of the model, with the transverse rung modeled by the local linear coupling between the parallel troughs with the $\delta$-functional longitudinal profile. By replacing the $\delta$ function by its finite-width Gaussian counterpart, similar results are obtained by means of the variational approximation (VA). The VA is also applied to the 1D system with a mixed linear and nonlinear transverse localized coupling. Comparison of the results produced by the different varieties of the system clearly reveals basic features of its the symmetry-breaking transition.