Tests of local hidden-variable theories using measurements with continuous-variable (CV) outcomes are developed, and a comparison of different methods is presented. As examples, we focus on multipartite entangled Greenberger-Horne-Zeilinger and cluster states. We suggest a physical process that produces the states proposed here, and investigate experiments both with and without binning of the continuous variable. In the former case, the Mermin-Klyshko inequalities can be used directly. For unbinned outcomes, the moment-based Cavalcanti-Foster-Reid-Drummond inequalities are extended to functional inequalities by consideration of arbitrary functions of the measurements at each site. By optimizing these functions, we obtain more robust violations of local hidden-variable theories than with either binning or moments. Recent inequalities based on the algebra of quaternions and octonions are compared with these methods. Since the prime advantage of CV experiments is to provide a route to highly efficient detection via homodyne measurements, we analyze the effect of noise and detection losses in both binned and unbinned cases. The CV moment inequalities with an optimal function have greater robustness to both loss and noise. This could permit a loophole-free test of Bell inequalities.

We propose Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found that the Lieb-Robinson speed is not always algebraic in the interaction strengths. We consider Hamiltonians with any finite number of bounded operators and also a certain class of unbounded operators. We obtain bounds and propagation speeds for quantum systems on lattices and also general graphs possessing a kind of homogeneity and isotropy. One area for which this formalism could be useful is the study of quantum phase transitions which occur when interactions strengths are varied.

A measurement scheme of atomic qubits pinned at given positions is studied by analyzing the interference pattern obtained when they emit photons spontaneously. In the case of two qubits, a well-known relation is revisited in which the interference visibility is equal to the concurrence of the state in the infinite spatial separation limit of the qubits. By taking into account the superradiant and subradiant effects, it is shown that a state tomography is possible when the qubit spatial separation is comparable to the wavelength of the atomic transition. In the case of three qubits, the relations between various entanglement measures and the interference visibility are studied, where the visibility is defined from the two-qubit case. A qualitative correspondence among these entanglement relations is discussed. In particular, it is shown that the interference visibility is directly related to the maximal bipartite negativity.

We constructed a cavity QED system with a diamagnetic atom of ${}^{171}\mathrm{Yb}$ and performed projective measurements on a single nuclear spin. Since Yb has no electronic spin and has $1/2$ nuclear spin, the procedure of spin polarization and state verification can be dramatically simplified compared with the pseudo-spin-$1/2$ system. By enhancing the photon emission rate of the ${}^1{S}_0$-${}^3{P}_1$ transition, projective measurement is implemented for an atom with the measurement time of $T_{\mathrm{meas}}=30\hspace{0.5em}\mathrm{\mu }\mathrm{s}$. Unwanted spin flip and dark counts of the detector lead to systematic error when the present technique is applied for the determination of diagonal elements of an unknown spin state, which is $\delta \left|\beta \right|{}^2⩽2\times {10}^{-2}$. Fast measurement on a long-lived qubit is key to the realization of large-scale one-way quantum computing.

An effective optimization strategy has been developed to construct highly accurate bound-state wave functions in various three-body systems. Our procedure appears to be very effective for computations of weakly bound states and various excited states, including rotationally excited states (i.e. states with $L⩾1$). The efficiency of our procedure is illustrated by computations of excited $P^{*}(L=1)-$ states in the $\mathit{dd}\mu$, $\mathit{dt}\mu$ and $\mathit{tt}\mu$ muonic molecular ions, $P(L=1)-$ states in the nonsymmetric $\mathit{pd}\mu$, $\mathit{pt}\mu$ and $\mathit{dt}\mu$ ions, and $2^{1}P(L=1)-$ and $2^{3}P(L=1)-$ states in He atoms.

Results from a joint experimental and theoretical investigation of electron impact excitation of the $(3d^{10}4s){}^2{S}_{1/2}\to (3d^{9}4s^2){}^2{D}_{5/2,3/2}$ transitions in copper atoms are presented. The experimental results were obtained with the laser-induced fluorescence technique, while the numerical calculations were performed in a variety of nonrelativistic, semirelativistic, and fully relativistic $R$-matrix (close-coupling) calculations. Whereas there is qualitative agreement between the measured and predicted energy dependence of the angle-integrated cross section, significant uncertainties remain regarding the position and the height of the near-threshold maximum of the excitation function for the $(3d^{9}4s^2){}^2{D}_{3/2}$ state. These uncertainties translate into difficulties regarding the absolute normalization of the relative experimental data to the theoretical predictions.

Using scaled-energy Stark spectroscopy, we report the observation of recurrences due to closed orbits, both geometric and diffractive, in the $\nu =0$, $R=1$, $\mathit{nd}$ Rydberg series of ${\mathrm{H}}_2$ ($16<n<26$) interacting with the $\nu =0$, $R=3$ series ($13<n<15$). The data support the molecular closed-orbit theory prediction of diffractive trajectories due to inelastic scattering of the excited electron on the molecular core. We have made similar measurements in He, and a comparison between the recurrence properties of ${\mathrm{H}}_2$ and its united atom equivalent is given.

We study the finite-temperature properties of two-component fermionic atoms trapped in a two-dimensional (2D) optical lattice. We apply the self-energy functional approach to the 2D Hubbard model with a harmonic-trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott-insulating and the metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusplike anomaly at lower temperatures, suggesting a second- or higher-order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.

We study the optimal focusing of two-level atoms with a near-resonant standing wave light, using both classical and quantum treatments of the problem in the thin- and thick-lens regimes. It is found that the near-resonant standing wave focuses the atoms with a reduced background in comparison with far-detuned light fields. For some parameters, the quantum atomic distribution shows even better localization than the classical one. Spontaneous emission effects are included via the technique of quantum Monte Carlo wave function simulations. We investigate the extent to which nonadiabatic and spontaneous emission effects limit the achievable minimal size of the deposited structures.

We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch representation. It is shown that an isolated steady state of the Bloch equation cannot be a center, i.e., that the existence of a unique steady state implies attractivity and global asymptotic stability. Necessary and sufficient conditions for the existence of a unique steady state are derived and applied to different physical models, including two- and four-level atoms, (truncated) harmonic oscillators, and composite and decomposable systems. It is shown how these criteria could be exploited in principle for quantum reservoir engineeing via coherent control and direct feedback to stabilize the system to a desired steady state. We also discuss the question of limit points of the dynamics. Despite the nonexistence of isolated centers, open quantum systems can have nontrivial invariant sets. These invariant sets are center manifolds that arise when the Bloch superoperator has purely imaginary eigenvalues and are closely related to decoherence-free subspaces.

The recombination of an electron with an (initially) hydrogenlike ion is investigated. The effect of the electron-electron interaction is treated rigorously to the first order in the parameter $1/Z$ and within the screening-potential approximation to higher orders in $1/Z$, with $Z$ being the nuclear charge number. The two-electron correction contains the dielectronic recombination part, which contributes to the process not only under the resonance condition for the projectile energy but also in the regions far from resonances. The mechanism of the off-resonant dielectronic recombination is studied in detail.

We suggest that the problem of single ionization of helium by electron impact, leaving the ion in the ground state, has been solved theoretically for the full range of kinematics and collision geometries of practical interest. Following the emphasis on the study of out-of-plane geometries where the cross sections are very small [Schulz et al., Nature 422, 48 (2003)], we find that the convergent close-coupling calculations, in either a frozen- or a multicore treatment of the target, are in excellent agreement with the available measurements. Curiously, some systematic discrepancies are identified for some in-plane cases where the cross sections are an order of magnitude larger. Further measurements are required to resolve these discrepancies. If subsequent measurements confirm the present calculations, then we would have a strong case that the problem has been solved.

Coherent anti-Stokes Raman scattering (CARS) microscopy has been a major tool of investigation of biological structures as it contains the vibrational signature of molecules. A quantum control method based on chirped pulse adiabatic passage was recently proposed for selective excitation of a predetermined vibrational mode in CARS microscopy [Malinovskaya and Malinovsky, Opt. Lett. 32, 707 (2007)]. The method utilizes the chirp sign variation at the peak pulse amplitude and gives a robust adiabatic excitation of the desired vibrational mode. Using this method, we investigate the impact of coupling between vibrational modes in molecules on controllability of excitation of the CARS signal. We analyze two models of two coupled two-level systems (TLSs) having slightly different transitional frequencies. The first model, featuring degenerate ground states of the TLSs, gives robust adiabatic excitation and maximum coherence in the resonant TLS for positive value of the chirp. In the second model, implying nondegenerate ground states in the TLSs, a population distribution is observed in both TLSs, resulting in a lack of selectivity of excitation and low coherence. It is shown that the relative phase and coupling between the TLSs play an important role in optimizing coherence in the desired vibrational mode and suppressing unwanted transitions in CARS microscopy.

The classical microcanonical ensemble approach to high-harmonic generation (HHG) in rare gases subjected to intense laser fields is studied. We show that the ensemble spectrum is a “sampled” version of the single trajectory spectrum. Unlike the radiation of the single ensemble member, the total ensemble radiation possesses all the basic HHG features: odd laser harmonics, plateau, and cutoff. The sampling theorem for uniform grids is used to explain why the ensemble spectrum can be computed accurately with a very small number of ensemble members compared to the Monte Carlo method. Furthermore, The phase space relevant to harmonic generation is found to be significantly smaller than the field free microcanonical ensemble. In addition we demonstrate the seeding effect that was predicted and observed in quantum simulation. For circular polarization, we verify that the harmonic generation is highly suppressed even when the argument of the three-step model does not apply. All the findings are numerically calculated for the xenon atom.

Ionization, excitation, and de-excitation to the ground state are studied theoretically for the first excited singlet state $B^1{\Sigma }_u{}^{+}$ of ${\mathrm{H}}_2$ exposed to intense laser fields with photon energies between about 3 and $13$ eV. A parallel orientation of a linear polarized laser and the molecular axis is considered. Within the dipole and the fixed-nuclei approximations the time-dependent Schrödinger equation describing the electronic motion is solved in full dimensionality and compared to simpler models. A dramatic breakdown of the single-active-electron approximation is found and explained to be due to the inadequate description of the final continuum states.

A closed-form analytic formula describing high-order harmonic generation (HHG) in a two-color field of frequencies $\omega$ and $2\omega$ is derived quantum mechanically in the low-frequency (tunneling) limit for an electron bound by a short-range potential and generalized to the case of an active electron in a neutral atom. The HHG rates are presented as a product of an electron wave packet describing the ionization of an active electron and its propagation in a laser field up to the recombination event and an atom-specific cross section of the electron’s photorecombination. In contrast to the case of a monochromatic laser pulse [Frolov et al., Phys. Rev. Lett. 102, 243901 (2009)], the two-color wave packet involves the interference of two terms (involving the Airy function) that describe the emission of harmonics during the first and second half-cycles of the fundamental laser cycle and give rise to the two-plateau structures in the HHG spectra. For the case of the H atom, we show that our analytic results are in good agreement with those obtained from a numerical solution of the three-dimensional time-dependent Schrödinger equation. The factorization formula is used for describing the dependence of HHG rates for inert gases on the relative phase and intensities of the $\omega$ and $2\omega$ components of a laser field. It is shown that atomic structure (including electron correlation) effects can modify substantially the two-color HHG spectra of inert gases.

We design magnetic traps for atoms based on the average magnetic field of vortices induced in a type-II superconducting thin film. This magnetic field is the critical ingredient of the demonstrated vortex-based atom traps, which operate without transport current. We use Bean’s critical-state method to model the vortex field through mesoscopic supercurrents induced in the thin strip. The resulting inhomogeneous magnetic fields are studied in detail and compared to those generated by multiple normally conducting wires with transport currents. Various vortex patterns can be obtained by programing different loading-field and transport-current sequences. These variable magnetic fields are employed to make versatile trapping potentials.

We argue that ultracold atoms in strongly shaken optical lattices can be subjected to conditions similar to those experienced by electrons in laser-irradiated crystalline solids, but without introducing secondary polarization effects. As a consequence, one can induce nonperturbative multiphoton-like resonances due to the mutual penetration of ac-Stark-shifted Bloch bands. These phenomena can be detected with a combination of currently available laboratory techniques.

We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero-density fixed point. Moreover, we find that the $T=0$ thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.

We study the quantum (zero-temperature) critical behaviors of confined particle systems described by the one-dimensional (1D) Bose-Hubbard model in the presence of a confining potential, at the Mott insulator to superfluid transitions, and within the gapless superfluid phase. Specifically, we consider the hard-core limit of the model, which allows us to study the effects of the confining potential by exact and very accurate numerical results. We analyze the quantum critical behaviors in the large trap-size limit within the framework of the trap-size scaling (TSS) theory, which introduces a new trap exponent $\theta$ to describe the dependence on the trap size. This study is relevant for experiments of confined quasi-1D cold atom systems in optical lattices. At the low-density Mott transition, TSS can be shown analytically within the spinless fermion representation of the hard-core limit. The trap-size dependence turns out to be more subtle in the other critical regions, when the corresponding homogeneous system has a nonzero filling $f$, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the $n=1$ Mott transition, this gives rise to a modulated TSS: The TSS is still controlled by the trap-size exponent $\theta$, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.