Time-dependent density functionals depend in principle on the initial state of a system, but this is ignored in functional approximations presently in use. For one electron, it is shown that there is no initial-state dependence: for any density, only one initial state produces a well-behaved potential. For two noninteracting electrons with the same spin in one dimension, an initial potential that makes an alternative initial wave function evolve with the same density and current as a ground state is calculated. This potential is well-behaved, and can be made arbitrarily different from the original potential.

The partial and total photoionization cross sections from the initial ${}^2{P}_{3/2}$ ground state of atomic Br to the final ${\mathrm{Br}}^{+}{}^3{P}_J$ components across the ${4p}^4{(}^1{D}_2{)6d,8s(}^2{P,}^2{D,}^2{F,}^{2}S)$ autoionization resonances are presented. The multiconfiguration Hartree-Fock (MCHF) method has been used to calculate both bound and continuum wave functions in the nonrelativistic limit. The Breit-Pauli approximation is applied to determine the effect of spin-orbit interactions in the photoionization of atomic Br with the MCHF wave function as input. Our calculated results are compared with experimental data.

Surface diffusion and desorption of ${\mathrm{Li}}^{+}$ from the outer surface of ${\mathrm{C}}_{60}$ are explored by quasiclassical trajectory calculations. The dynamics of exohedral ${\mathrm{Li}}^{+},$ initially at the center of a ring on the outer cage of ${\mathrm{C}}_{60},$ is followed as a function of time. Ring hopping between adjacent rings is the major diffusion mechanism but 12–20 % of the ions, depending on the temperature, leave the ring, orbit the molecule, and fall back on a nonadjacent ring. There can be a sequence of hopping and orbiting before total desorption takes place. The average lifetime of an orbit is independent of the temperature, while the exohedral complex lifetime decreases with temperature. Rate coefficients for ring hopping and desorption are reported as a function of temperature. The average kinetic energy removed from the ${\mathrm{C}}_{60}$ by the desorbing ion increases with temperature and it is independent of the lifetime of the complex. Kinetic-energy release distributions at various temperatures are reported.

The critical behavior of collective modes and the collapsing dynamics of trapped Bose-Einstein condensates with attractive interactions are studied analytically and numerically. The time scales of these dynamics both below and above the critical point of the collapse are found to obey power laws with a single parameter of ${N/N}_c-1,$ where N is the number of condensate atoms and $N_c$ is the critical number. The collapsing condensate eventually undergoes rapid implosion, which occurs several times intermittently, and then the implosion turns to an explosion. The release energy of the explosion is found to be proportional to the square of the interaction strength, inversely proportional to the three-body recombination rate, and independent of the number of condensate atoms and the trap frequency.

A semiclassical theoretical framework is presented to describe the essential features of the excess quantum noise that occurs in systems with nonorthogonal eigenmodes. Excess noise is shown to be always spectrally colored, instead of white, so that the Petermann excess noise factor is best written as $K\left(\omega \right)$ instead of K. The consequences of this spectral coloring are analyzed for lasers, both below and above the lasing threshold.

We introduce a simple, experimentally realizable, entanglement manipulation protocol for exploring mixed-state entanglement. We show that for both nonmaximally entangled pure, and mixed polarization-entangled two-qubit states, an increase in the degree of entanglement and purity, is achievable.

We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined by an absorbing boundary. Trajectories that reach the absorbing wall are instantaneously terminated and their probability is discounted from the population of the surviving trajectories. This gives rise to a unidirectional absorption current at the boundary. We calculate the survival probability as a function of time. Several applications are given: the calculation of the absorption current in the slit experiment with a totally absorbing screen, the calculation of the survival probability of a particle between two totally absorbing walls, and the calculation of the survival probability and of the reflection coefficient of a Gaussian wave packet incident on a totally absorbing wall. The survival probability of a one-dimensional particle between two totally absorbing walls exhibits decay with beats.

Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to provide foundations of joint statistics of local general measurements on entangled systems in a general theoretical framework, the question is answered as to under what condition the outputs of two measuring apparatuses satisfy the joint probability formula for simultaneous measurements of their observables. For this purpose, all the possible state changes caused by measurements of an observable are characterized, and the notion of disturbance in measurement is formalized in terms of operations derived by the measuring interaction.

Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically nonzero rate and relative distance.

We show how to compute or at least to estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, the entanglement-assisted classical capacity, the one-shot classical capacity, and a quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation or amplification and classical noise.

We present a task that can be faithfully solved with finite resources only when aided by particles prepared in a particular entangled state: the singlet state. The task consists of identifying the mutual parallelity or orthogonality of weak distant magnetic fields whose absolute directions are completely unknown.

Collective operations on a network of spatially separated quantum systems can be carried out using local quantum operations, classical communication (CC), and shared entanglement (SE). Such operations can also be used to communicate classical information and establish entanglement between distant parties. We show how these facts lead to measures of the inseparability of quantum operations, and we argue that a maximally inseparable operation on two qubits is the SWAP operation. The generalization of our argument to N-qubit operations leads to the conclusion that permutation operations are maximally inseparable. For even N, we find the minimum SE and CC resources which are sufficient to perform an arbitrary collective operation. These minimum resources are $2\left(N-1\right)$ units of entanglement and $4\left(N-1\right)$ bits, and these limits can be attained using a simple teleportation-based protocol. We also obtain lower bounds on the minimum resources for the odd case. For all $N>~4,$ we show that the SE and CC resources required to perform an arbitrary operation are strictly greater than those that any operation can establish or communicate.

Collisions between free electrons and the molecular anion ${\mathrm{F}}_2^{-}$ have been studied in a merged beams experiment at the heavy ion storage ring ASTRID. Absolute cross sections for detachment ${(e}^{-}+{\mathrm{F}}_2^{-}\to {\mathrm{F}}_2^0{+2e}^{-}$ or ${\mathrm{F}}^0+{\mathrm{F}}^0{+2e}^{-})$ and dissociation ${(e}^{-}+{\mathrm{F}}_2^{-}\to {\mathrm{F}}^0+{\mathrm{F}}^{-}{+2e}^{-})$ are reported in the energy range 0–27 eV. Branching ratios between the two detachment channels are also given. Dissociation is found to be the dominating reaction and the dissociation cross section is about an order of magnitude larger than the detachment cross section in the investigated energy range. The threshold for detachment is as high as 10 eV, and the branching into the channel with a molecular fragment amounts to less than 20% over most of the energy range. The results are compared to previously measured cross sections for other anions and the importance of nuclear dynamics in the processes is discussed.

The relative electron-impact cross sections for exciting the $3\overrightarrow{d}2p{}^1{P}_1$ resonance and ${}^3{D}_1$ intercombination lines have been measured in nine neonlike ions between ${\mathrm{Cr}}^{14+}$ and ${\mathrm{Kr}}^{26+}.$ The ratio drops from about 4.4 for ${\mathrm{Cr}}^{14+}$ to less than unity for ${\mathrm{Kr}}^{26+}$ in response to an increase in relativistic effects. A measurement of the dependence of this ratio on electron energy is presented for ${\mathrm{Fe}}^{16+}.$ No dependence on electron energy is found. The measured ratios are generally lower than theory, showing that the relative intensity of the intercombination line is larger than predicted and illustrating the difficulty to predict electron-impact excitation cross sections in the intermediate coupling regime at the level needed for spectral diagnostics.

We study the Autler-Townes spectrum of a V-type atom coupled to a single-mode, frequency-tunable cavity field at finite temperature, with a pre-selected polarization in the bad cavity limit, and show that, when the mean number of thermal photons $N\gg 1$ and the excited sublevel splitting is very large (of the same order as the cavity linewidth), probe gain may occur at either sideband of the doublet, depending on the cavity frequency, due to cavity-induced quantum interference. It is also possible to choose the cavity detuning so that one of the Autler-Townes sidebands vanishes.

We demonstrate production of cold lead monoxide (PbO) molecules by laser ablation in a cryogenic cell filled with helium buffer gas and cooled by a cryostat to a temperature of 4 K. The molecules are probed by laser-induced fluorescence excited in the $\overrightarrow{X}B$ band. The molecules thermalize with the buffer gas, both translationally and rotationally, in less than 30 ms after the ablation pulse. A single ablation pulse fired at the solid PbO sample yields about ${10}^{12}$ cold molecules. We present an analysis indicating that buffer-gas cooled PbO molecules excited to either the a or B state could be effectively used to search for the permanent electric dipole moment of the electron.

Using a simple stability argument for the entropy production we find the conditions for a state to remain pure under certain dissipative dynamics. We also calculate the time scales for the onset of decoherence when these conditions are not satisfied.

We solve numerically the time-dependent Dirac equation for a quantum wave packet tunneling through a potential barrier. We analyze the spatial probability distribution of the transmitted wave packet in the context of the possibility of effectively superluminal peak and front velocities of the electron during tunneling. Both the Dirac and Schrödinger theories predict superluminal tunneling speeds. However, in contrast to the Dirac theory the Schrödinger equation allows a possible violation of causality. Based on an analysis of the tunneling process in full temporal and spatial resolution, we introduce an instantaneous tunneling speed that can be computed inside the potential barrier.

Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general $K\times M$ problem and characterize the set of effectively different states (which cannot be related by local transformations). Thus, we generalize earlier results obtained for the simplest $2\times 2$ system, which lead to a stratification of the six-dimensional set of $N=4\mathrm{}$ pure states. We define the concept of absolutely separable states, for which all globally equivalent states are separable.

In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.