Homogenization protocols model the quantum mechanical evolution of a system to a fixed state independently from its initial configuration by repeatedly coupling it with a collection of identical ancillas. Here we analyze these protocols within the formalism of “relaxing” channels providing an easy-to-check sufficient condition for homogenization. In this context we describe mediated homogenization schemes where a network of connected qudits relaxes to a fixed state by only partially interacting with a bath. We also study configurations which allow us to introduce entanglement among the elements of the network. Finally we analyze the effect of having competitive configurations with two different baths and we prove the convergence to dynamical equilibrium for Heisenberg chains.

We present attacks that show that unconditionally secure two-party classical computation is impossible for many classes of function. Our analysis applies to both quantum and relativistic protocols. We illustrate our results by showing the impossibility of oblivious transfer.

The hyperfine transitions in the 399 nm ${{}^{1}S}_0\leftrightarrow {{}^{1}P}_1$ line in ${}^{173}\text{Y}\text{b}$ overlap with the transition in ${}^{172}\text{Y}\text{b}$. We use transverse laser cooling on this line to selectively deflect ${}^{173}\text{Y}\text{b}$ atoms from a thermal beam containing both isotopes. We then use an acousto-optic modulator to span the frequency difference between the hyperfine transitions, and hence measure hyperfine structure in the ${{}^{1}P}_1$ state. Our precise values for the hyperfine constants, $A_{173}=57.693\pm 0.006\text{MHz}$ and $B_{173}=609.028\pm 0.056\text{MHz}$, improve previous values significantly.

We present a compact ${}^{87}\text{R}\text{b}$ atomic source for high precision dual atom interferometers. The source is based on a double-stage magneto-optical trap (MOT) design, consisting of a two-dimensional (2D) -MOT for efficient loading of a 3D-MOT. The accumulated atoms are precisely launched in a horizontal moving molasses. Our source generates a high atomic flux $\left(>{10}^{10}\text{atoms}∕\text{s}\right)$ with precise and flexibly tunable atomic trajectories as required for high resolution Sagnac atom interferometry. We characterize the performance of the source with respect to the relevant parameters of the launched atoms, i.e., temperature, absolute velocity, and pointing, by utilizing time-of-flight techniques and velocity selective Raman transitions.

We calculate the interaction induced inhomogeneous broadening of spectral lines in a trapped Bose gas as a function of the depth of a three-dimensional cubic optical lattice. As observed in recent experiments, we find that the terraced “wedding-cake” structure of Mott plateaus splits the spectrum into a series of discrete peaks. The spectra are extremely sensitive to density corrugations and trap anharmonicities. For example, even when the majority of the cloud is superfluid the spectrum displays discrete peaks.

We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and for general product measurements at the output, can efficiently simulate Shor’s factoring algorithm. This is done by using the notion of the semiclassical Fourier transform due to Griffith and Niu, and further discussed in the context of Shor’s algorithm by Browne.

It is known that the entanglement present in the transverse spatial properties of photon pairs generated by spontaneous parametric down-conversion depends explicitly on the characteristics of the pump laser beam. Here we show that, for pump beams described by a Hermite-Gaussian mode, the entanglement depends on the beam width as well as the order of the beam. The amount of entanglement generally increases with the order of the beam and is less dependent on the beam width for higher orders. We propose a method to measure the spatial entanglement directly, independent of the dimension of the subsystems.

Recent work to include $R$-matrix data within a larger model comprised mostly of distorted-wave and plane-wave Born data has resulted in the general spectral modeling (GSM) code. It employs a quasistatic approximation, a standard, low-density methodology that assumes the ionization balance is separable from a determination of the excited-state populations that give rise to the spectra. GSM further allows for some states to be treated statistically as contributions to effective rates, instead of being included explicitly in the kinetics model. While these two approximations are known to be valid at low densities, this work investigates using such methods to model high-density, non-LTE emission spectra and determines at what point the approximations break down by comparing to spectra produced by the Los Alamos National Laboratory code ATOMIC which makes no such approximations. As both approximations are used by other astrophysical and low-density modeling codes, the results should be of broad interest. He-like $K\alpha$ emission spectra are presented for three elements, Ni, Fe, and Ca, in order to gauge the effect of both the statistical methods and the ground-state-only, quasistatic approximation employed in GSM. This work confirms that at and above the temperature of maximum abundance of the He-like ionization stage, the range of validity for both approximations is sufficient for modeling the low- and moderate-density regimes one typically finds in astrophysical and magnetically confined fusion plasmas. However, a breakdown does occur for sufficiently high densities; we obtain quantitative limits that are significantly higher than previous works. Additionally, this work demonstrates that, while the range of validity for both approximations is sufficient to accurately predict the density-dependent quenching of the $z$ line, the approximations begin to break down at higher densities. Thus, these approximations should be used with greater care when modeling high-density plasmas such as those found in laser-driven inertial confinement fusion and electromagnetic pinch devices.

A procedure for systematically evaluating the long-range dispersion interaction between two homonuclear atoms in arbitrary $LS$ coupled states is outlined. The method is then used to generate dispersion coefficients for a number of the low-lying states of the Na and Mg dimers.

The charge states of fragment ions were measured for $1\text{−}\mathrm{MeV}$/atom $\mathrm{C}_3{}^{+}$ cluster ions penetrating a carbon foil of $2.4\text{−}\mu \mathrm{g}∕{\mathrm{cm}}^2$ thickness. Those ions were detected by event-by-event mode with a fluorescent screen detector monitored by a charge-coupled device camera. The detected ion signals were traced by Coulomb explosion imaging technique, which enables us to classify charge states of each fragment ion and spatial arrangements of aligned cluster ions after emerging from the foil. Using this technique, we found the reduction of the average charge per ion. We also found that (i) the measured average charges of the aligned fragment ions in a linear-chain arrangement are larger than those in a triangular arrangement, and (ii) the edge-position ions in a linear-chain arrangement have the average charges greater than the middle-position ion. These experimental results are well supported by a recent refined theory on the cluster average charge.

We present optimal control, using femtosecond laser pulses in a closed-loop experiment, of the ionization process of ultracold rubidium molecules formed in a magneto-optical trap. The resulting spectrum of the optimally shaped pulse exhibits two frequency bands, which drive a resonantly enhanced three-photon ionization. The obtained data reveals the ionization process where only the electronic states corresponding to the $5s5d$-asymptote are utilized for the second excitation step.

We describe an efficient technique for calculating cross sections for two-photon single and double ionization of an atom without the use of the final-state continuum wave function. We present results of an application to helium over the photon energy range $25-54\text{eV}$, and we compare our results to a representative sample of results obtained by others.

The time-correlation function of ultracold atomic gas is theoretically investigated. Atoms are initially confined in an optical lattice and in a Mott insulator regime. We consider the effect of gravity on the time correlation among atomic wave functions when the atomic cloud is released from the optical lattice. The time-correlation function in this process displays sharp peaks, a feature that is analogous to the spatial-normalized correlation observed in recent experiments. The origin and properties of the interference pattern are theoretically investigated in detail. Similar to the spatial correlation, the time correlation in expanding atomic clouds reveals the ordering of indistinguishable particles in an optical lattice. Experimental detection scheme and its potential use in the measurement of gravitational acceleration are briefly discussed.

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement. We offer a fully analytical explanation of the observed parametric resonance, based on a Mathieu-type analysis of the non-polynomial Schrödinger equation. The theoretical prediction for the pattern periodicity versus the driving frequency is directly compared to the experimental data, yielding good qualitative and quantitative agreement between the two. These results are corroborated by direct numerical simulations of both the one-dimensional non-polynomial Schrödinger equation and of the fully three-dimensional Gross-Pitaevskii equation.

We derive an effective low-dimensional Hamiltonian for strongly interacting ultracold atoms in a transverse trapping potential near a wide Feshbach resonance. The Hamiltonian includes crucial information about transverse excitations in an effective model with renormalized interaction between atoms and composite dressed molecules. We fix all the parameters in the Hamiltonian for both one- and two-dimensional cases.

Contributions to the fifth-order nonlinear optical susceptibility ${\chi }^{\left(5\right)}$ of a collection of homogeneously broadened two-level atoms that scale as $N^2{\left({\gamma }_{\mathrm{at}}^{\left(3\right)}\right)}^2$ and $N^2{\mid {\gamma }_{\mathrm{at}}^{\left(3\right)}\mid }^2$, where ${\gamma }_{\mathrm{at}}^{\left(3\right)}$ is the lower-order atomic hyperpolarizability and $N$ is the atomic number density, are predicted theoretically. These “cascaded” contributions are a consequence of local-field effects. We determine them from a fifth-order solution of the Lorentz-Maxwell-Bloch equations. They are missing from a straightforward generalization of Bloembergen’s result for the local field correction to the second order nonlinearity, but are recovered by a careful application of his general approach. We find that at high atomic densities $(N>{10}^{15}{\mathrm{cm}}^{-3})$ the value of the cascaded third-order contribution can be as large as the “direct” fifth-order term in the expression for the fifth-order susceptibility.

The traversal times for an electromagnetic pulse traversing a slab of dispersive and dissipative material with negative dielectric permittivity $\left(ϵ\right)$ and magnetic permeability $\left(\mu \right)$ have been calculated by using the average flow of electromagnetic energy in the medium. The effects of bandwidth of the pulse and dissipation in the medium have been investigated. While both large bandwidth and large dissipation have similar effects in smoothening out the resonant features that appear due to Fabry-Pérot resonances, large dissipation can result in very small or even negative traversal times near the resonant frequencies. We have also investigated the traversal times and Wigner delay times for obliquely incident pulses and evanescent pulses. The coupling to slab plasmon-polariton modes in frequency ranges with negative $ϵ$ or $\mu$ is shown to result in large traversal times at the resonant conditions. We also find that the group velocity mainly contributes to the delay times for pulses propagating across a slab with $n=-1$. We have checked that the traversal times are positive and subluminal for pulses with sufficiently large bandwidths.

We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Gröbner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled $\mid n,0⟩+\mid 0,n⟩$ (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.

We present the propagation-dependent polarization vector fields by use of an isotropic microchip laser with the longitudinal-transverse coupling and the entanglement of the polarization states. With the coherent superposition of orthogonal circularly polarized vortex modes which are made up of two Laguerre-Gaussian modes with different order, the experimental three-dimensional vector fields can be reconstructed analytically. From the theoretical analyses, the generalized structures of singularities such as $V$ points, $C$ lines, and $L$ surfaces can be clearly demonstrated. Importantly, the projections of $C$ lines on the transverse plane are found to form the intriguing petal structures.

By employing a recent proposal [R. Filip, P. Marek, and U.L. Andersen, Phys. Rev. A 71, 042308 (2005)] we experimentally demonstrate a universal, deterministic, and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward, and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a continuous variable quantum computer.