We consider the transport properties of multiple-particle quantum states in a class of one-dimensional systems with a single quantum impurity. In these systems, the local interaction at the quantum impurity induces strong and nontrivial correlations between the multiparticles. We outline an exact theoretical approach, based upon real-space equations of motion and the Bethe ansatz, that allows one to construct the full scattering matrix ($S$ matrix) for these systems. In particular, we emphasize the need for a completeness check upon the eigenstates of the $S$ matrix, when these states obtained from Bethe ansatz are used for describing the scattering properties. As a detailed example of our approach, we solve the transport properties of two photons incident on a single two-level atom, when the photons are restricted to a one-dimensional system such as a photonic crystal waveguide. Our approach predicts a number of nonlinear effects involving only two photons, including background fluorescence, spatial attraction and repulsion between the photons, as well as the emergence of a two-photon bound state.

We report on the Stark deceleration and electrostatic trapping of ${}^{14}\text{N}\text{H}$ $\left(a{}^1\Delta \right)$ radicals. In the trap, the molecules are excited on the spin-forbidden $A{}^3\Pi \leftarrow a{}^1\Delta$ transition and detected via their subsequent fluorescence to the $X{{}^3\Sigma }^{-}$ ground state. The $1∕e$ trapping time is $1.4\pm 0.1\text{s}$, from which a lower limit of 2.7 s for the radiative lifetime of the $a{}^1\Delta$, $v=0$, $J=2$ state is deduced. The spectral profile of the molecules in the trapping field is measured to probe their spatial distribution. Electrostatic trapping of metastable NH followed by optical pumping of the trapped molecules to the electronic ground state is an important step toward accumulation of these radicals in a magnetic trap.

The exactly solvable Lieb-Liniger model of interacting bosons in one dimension has attracted renewed interest as current experiments with ultracold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to 20 particles for attractive interactions. We discuss the features of the solutions, and how they deviate from the well-known string solutions [Thacker, Rev. Mod. Phys. 53, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive one-dimensional Bose gas on a ring.

We performed a comprehensive study of filamentation in xenon. Due to its high nonlinear refraction index, but relatively low ionization potential, xenon can support filamentation at peak powers lower than in air. In our experiments, we studied pulse shortening, spatial mode cleaning, and generation of terahertz radiation. We observed that in xenon, self-compression is easily obtainable and terahertz radiation generation efficiency is significantly stronger as compared to air.

Mandel’s $Q$ parameter, which is determined from single-event photon statistics, provides an alternative way to recognize single molecules with fluorescence detection, other than the second-order correlation function. It is shown that the $Q$ parameter of an assumed ideal double-molecule fluorescence with the same average photon number as that of the sample fluorescence can act as the criterion for single-molecule recognition. The influence of signal-to-background ratio and the error estimates for photon statistics are also presented. We have applied this method to ascertain single Cy5 dye molecules within hundreds of milliseconds.

By using principal minor method, which is developed from the Peres-Horodecki criterion for the separability of a quantum state, we derive the necessary and sufficient conditions for the entanglement sudden death of a two-qubit state under amplitude damping and phase damping.

We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on a probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high-fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high $(\sim 5\%)$. We demonstrate that with a reasonable time overhead our scheme can achieve deterministic nonlocal coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local unitary operation. We estimate the clock cycle and the effective error probability for implementation of quantum registers with ion traps or nitrogen-vacancy centers. Our scheme capitalizes on an efficient two-level pumping scheme that in principle can create Bell pairs with arbitrarily high fidelity. We introduce a Markov chain model to study the stochastic process of entanglement pumping and map it onto a deterministic process. Finally we discuss requirements for achieving fault-tolerant operation with our register-based hybrid scheme and also present an alternative approach to fault-tolerant preparation of Greenberger-Horne-Zeilinger states.

The relativistic coupled-cluster single-double method is used to calculate the dependence of frequencies of strong $E1$ transitions in many monovalent atoms and ions on the fine-structure constant $\alpha$. These transitions are used in the search for manifestations of the variation of the fine-structure constant in quasar absorption spectra. Results of the present calculations are in good agreement with previous calculations but are more accurate.

We have observed a reduction in the amount of positronium emitted from an atomically clean Al(111) surface that depends on the incident positron beam density. We interpret this as evidence for the formation of molecular positronium, created following interactions between two pseudopositronium atoms trapped in a surface state. We find that this process is highly sensitive to the condition of the surface and is easily suppressed by changes thereupon. The implications of our data for planned spectroscopic studies of molecular positronium are discussed, as well as improvements to the experimental procedure that will allow more detailed measurements of the thermodynamics of the formation of this molecule from metal surfaces.

Perturbation theory is examined in analytic density-functional theory (ADFT), for which $V$ representability means slightly more than in conventional density-functional theory because the potential is fitted. There is synergism between variationality and $V$ representability. Together they redirect the object of perturbation theory from the set of occupied virtual orbital rotations to the change in the fit to the Kohn-Sham potential, which is called the Sambe-Felton potential. This reduces the dimensionality of perturbation theory from order $N^2$ to order $N$, where $N$ is the number of basis functions. With variational fitting, no fractional or negative powers of the density appear when using the Slater exchange kernel, which is proportional to the cube root of the spin density. Requiring the Fock matrix and density matrix to commute through each order of perturbation theory determines the role of fractional occupation numbers in density-functional perturbation theory, which are treated via the corresponding nonintegral differences between the occupation numbers of orbitals. This theory is tested by removing a tenth or twentieth of an electron from the highest occupied molecular orbital for a standard set of small molecules, in which case the first- and second-order perturbed energies are accurate to 70%, when compared to the energy difference of the two corresponding self-consistent-field (SCF) calculations. For an all-electron ADFT calculation on a $C_{4v}$-symmetric ${\mathrm{Zr}}_6{\mathrm{O}}_{12}$ cluster, the timing for all SCF coupled perturbed iterations is not significant compared to the single required $N^4$ sum over occupied and virtual orbitals.

Large discrepancies exist between measurements [Brown et al., Phys. Rev. Lett. 96, 253201 (2006)] and previous calculations [Chen and Pradhan, Phys. Rev. Lett. 89, 013202 (2002)] for electron impact excitation (EIE) cross sections in 3C $\left(\lambda 15.015\text{Å}\right)$ and 3D $\left(\lambda 15.262\text{Å}\right)$ of Fe XVII. A converged Dirac $R$-matrix calculation of EIE in Fe XVII with an accuracy of $\approx 5\%$ (from theory estimate) in 3C and 3D cross sections is reported. We carry out five sets of Dirac $R$-matrix calculations to establish the convergence in our calculations. Full relativistic effects are included and the convergence of both the correlation and channel coupling effects and the combined effects of interacting Rydberg resonance series in EIE of Fe XVII is achieved. The intrinsic oscillatory features of 3C and 3D effective cross sections convolved with electron distributions are further demonstrated. Compared with recent electron beam ion trap (EBIT) measurements, there is still an $\approx 20\%$ difference. I give one possible reason for this puzzling difference.

We present an analysis of atomic diffraction due to the interaction of an atomic beam with a pair of Gaussian light pulses. We derive a simple analytical expression for the populations in different diffraction orders. The validity of the obtained solution extends beyond the Raman-Nath regime, where the kinetic energy associated with different diffraction peaks is neglected, into the so-called channeling regime where accurate analytical expressions have not previously been available for the diffraction. Comparison with experimental results and exact numerical solutions demonstrate the validity of our analytical formula.

We consider the characterization of entanglement from the perspective of a Heisenberg formalism. We derive a two-party generalized separability criterion, and from this describe a physical understanding of entanglement. We find that entanglement may be considered as fundamentally a local effect, and therefore as a separate computational resource from nonlocality. We show how entanglement differs from correlation physically, and explore the implications of this concept of entanglement for the notion of classicality. We find that this understanding of entanglement extends naturally to multipartite cases.

Quantum, in contrast to classical, information theory, allows for different incompatible types (or species) of information which cannot be combined with each other. Distinguishing these incompatible types is useful in understanding the role of the two classical bits in teleportation (or one bit in one-bit teleportation), for discussing decoherence in information-theoretic terms, and for giving a proper definition, in quantum terms, of “classical information.” Various examples (some updating earlier work) are given of theorems which relate different incompatible kinds of information, and thus have no counterparts in classical information theory.

We present a scheme for robust and efficient projection measurement of a qubit consisting of the two magnetic sublevels in the electronic ground state of alkaline-earth-metal ions. The scheme is based on two stimulated Raman adiabatic passages involving four partially coherent laser fields. We show how the efficiency depends on experimentally relevant parameters: Rabi frequencies, pulse widths, laser linewidths, one- and two-photon detunings, residual laser power, laser polarization, and ion motion.

We give a microscopic derivation of the Clausius-Mossotti relations for a homogeneous and isotropic magnetodielectric medium consisting of radiatively broadened atomic oscillators. To this end the diagram series of electromagnetic propagators is calculated exactly for an infinite bicubic lattice of dielectric and magnetic dipoles for a small lattice constant compared to the resonance wavelength $\lambda$. Modifications of transition frequencies and linewidth of the elementary oscillators are taken into account in a self-consistent way by a proper incorporation of the singular self-interaction terms. We show that in radiatively broadened media sufficiently close to the free-space resonance the real part of the index of refraction approaches the value $-2$ in the limit of $\rho {\lambda }^3⪢1$, where $\rho$ is the number density of scatterers. Since at the same time the imaginary part vanishes as $1∕\rho$, local field effects can have important consequences for realizing low-loss negative index materials.

To implement a positive-operator-valued measurement (POVM), which is defined on the $d_S$-dimensional Hilbert space of a physical system, one has to extend the Hilbert space to include $d_A$ additional dimensions (called the ancilla). This is done via either the tensor product extension (TPE) or the direct sum extension (DSE). The implementation of a POVM utilizes the available resources more efficiently if it requires fewer additional dimensions. To determine how to implement a POVM with the least additional dimensions is, therefore, an important task in quantum information. We have determined the necessary and sufficient (hence minimal) number of the additional dimensions needed to implement the same POVM by the TPE and the DSE, respectively. If the POVM has $n$ elements and $r_i$ is the rank of the $i$th element, then the dimension of the minimal ancilla is $d_A={\sum }_{i=1}^n{r}_i-d_S$ for the DSE implementation, and this represents a lower bound for the added dimensions in the TPE implementation. In the proof, we explicitly construct the DSE implementation of a general POVM with elements of arbitrary rank. As an example, we determine $d_A$ for the unambiguous discrimination of $N$ linearly independent states and provide the full DSE implementation of a state-discriminating POVM for $N=2$.

We have combined the idea of renormalization group and quantum-information theory. We have shown how the entanglement or concurrence evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. Moreover, we introduce how the renormalization-group approach can be implemented to obtain the quantum-information properties of a many-body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one-dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length.

We present measurements of the internal state distribution of electrostatically guided formaldehyde. Upon excitation with continuous tunable ultraviolet laser light the molecules dissociate, leading to a decrease in the molecular flux. The population of individual guided states is measured by addressing transitions originating from them. The measured populations of selected states show good agreement with theoretical calculations for different temperatures of the molecule source. The purity of the guided beam as deduced from the entropy of the guided sample using a source temperature of $150\mathrm{K}$ corresponds to that of a thermal ensemble with a temperature of about $30\mathrm{K}$.

We report measurements of both the phase and intensity of high-order harmonic emission from aligned ${\mathrm{CO}}_2$ molecules, using a mixture of a molecular and an atomic gas. The molecules are transiently aligned using an ultrashort pulse, and a subsequent stronger pulse is used to generate high-order harmonics from a mixed $\mathrm{Kr}∕{\mathrm{CO}}_2$ sample. The high-order harmonic emission from the molecules interferes with the reference emission from the atoms. By monitoring the change in harmonic emission as a function of gas mixture and molecular alignment, we can retrieve the orientational dipole that has general features consistent with a two-center emission model.