Reported herein are measured absolute single, double, and triple charge exchange (CE) cross sections for the highly charged ions (HCIs) ${\mathrm{C}}^{q+}$ $(q=5,6)$, ${\mathrm{O}}^{q+}$ $(q=6,7,8)$, and ${\mathrm{Ne}}^{q+}$ $(q=7,8)$ colliding with the molecular species ${\mathrm{H}}_2\mathrm{O}$, CO, and $\mathrm{C}{\mathrm{O}}_2$. Present data can be applied to interpreting observations of x-ray emissions from comets as they interact with the solar wind. As such, the ion impact energies of $7.0q\mathrm{keV}$ $(1.62–3.06\mathrm{keV}∕\mathrm{amu})$ are representative of the fast solar wind, and data at $1.5q\mathrm{keV}$ for ${\mathrm{O}}^{6+}$ $(0.56\mathrm{keV}∕\mathrm{amu})$ on CO and $\mathrm{C}{\mathrm{O}}_2$ and $3.5q\mathrm{keV}$ for ${\mathrm{O}}^{5+}$ $(1.09\mathrm{keV}∕\mathrm{amu})$ on CO provide checks of the energy dependence of the cross sections at intermediate and typical slow solar wind velocities. The HCIs are generated within a $14\mathrm{GHz}$ electron cyclotron resonance ion source. Absolute CE measurements are made using a retarding potential energy analyzer, with measurement of the target gas cell pressure and incident and final ion currents. Trends in the cross sections are discussed in light of the classical overbarrier model (OBM), extended OBM, and with recent results of the classical trajectory Monte Carlo theory.

Using matter waves that are trapped in a deep optical lattice, dissipationless directed transport is demonstrated to occur if the single-band quantum dynamics is periodically tilted on one half of the lattice by a monochromatic field. Most importantly, the directed transport can exist for almost all system parameters, even after averaged over a broad range of single-band initial states. The directed transport is theoretically explained within ac-scattering theory. Total reflection phenomena associated with the matter waves traveling from a tilting-free region to a tilted region are emphasized. The results are of relevance to ultracold physics and solid-state physics, and may lead to powerful means of selective, coherent, and directed transport of cold particles in optical lattices.

Experiments in dense, ultracold gases of rubidium Rydberg atoms show a considerable decrease of the radiative excited state lifetimes compared to dilute gases. This accelerated decay is explained by collective and cooperative effects, leading to superradiance. A formalism to calculate effective decay times in a dense Rydberg gas shows that for these atoms the decay into nearby levels increases by up to three orders of magnitude. Excellent agreement between theory and experiment follows from this treatment of Rydberg decay behavior.

A method for nondestructive characterization of a dipole-trapped atomic sample is presented. It relies on a measurement of the phase shift imposed by cold atoms on an optical pulse that propagates through a free-space Mach-Zehnder interferometer. Using this technique we are able to determine, with very good accuracy, relevant trap parameters such as the atomic sample temperature, trap oscillation frequencies, and loss rates. Another important feature is that our method is faster than conventional absorption or fluorescence techniques, allowing the combination of high-dynamical range measurements and a reduced number of spontaneous emission events per atom.

We study the validity of the entanglement parameter introduced in a recent publication by Guangqiang et al. [Phys. Rev. A 73, 012314 (2006)] for detecting Eve, the eavesdropper. We have found that Eve can be detected using this parameter only if Alice establishes a quantum correlation between the Einstein-Podolsky-Rosen (EPR) pair. This quantum correlation is related to the possibility of an apparent violation of the Heisenberg inequality for the quadrature components of the EPR pair.

We present a theoretical study of the pathway of harmonic generation in bichromatic linearly polarized laser fields. A “harmonic-collapse” phenomenon is observed in the power spectrum for a particular value of the amplitude ratio of two components of the external field. We employ an offset frequency shift to the additional field to distinguish the harmonic pathway and then to explain the harmonic-collapse phenomenon. The harmonic intensity as a function of the relative amplitude ratio and, furthermore, the fine structure of the harmonic spectrum can be well understood on the basis of a pathway analysis.

Quantum feedback control is a technology that can be used to drive a quantum system into a predetermined eigenstate. In this article, sufficient conditions for the experiment parameters of a quantum feedback control process of a homodyne measurement are given to guarantee feedback control of a spin-$1∕2$ quantum system in case of imperfect detection efficiency. For the case of pure states and perfect detection efficiency, time scales of feedback control processes are calculated.

The subsystem compatibility problem, which concerns the question of whether a set of subsystem states are compatible with a state of the entire system, has received much study. Here we attack the problem from a new angle, utilizing the ideas of convexity that have been successfully employed against the separability problem. Analogously to an entanglement witness, we introduce the idea of a compatibility witness, and prove a number of properties about these objects. We show that the subsystem compatibility problem can be solved numerically and efficiently using semidefinite programming, and that the numerical results from this solution can be used to extract exact analytic results, an idea which we use to disprove a conjecture about the subsystem problem made by Butterley et al. [Found. Phys. 36, 83 (2006)]. Finally, we consider how the ideas can be used to tackle some important variants of the compatibility problem; in particular, the case of identical particles (known as $N$-representability in the case of fermions) is considered.

The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. As an example, we consider the $XY$ spin chain dephasingly coupled to a qubit. The geometric phase induced in the qubit is presented and discussed. The results show that the geometric phase might be used to signal the critical points of a many-body system, and it tends to zero as the parameters of the many-body system go away from the critical points.

Time-dependent Fröhlich transformations can be used to derive an effective Hamiltonian for a class of quantum systems with time-dependent perturbations. We use such a transformation for a system with time-dependent atom-photon coupling induced by the classical motion of two atoms in an inhomogeneous electromagnetic field. We calculate the entanglement between the two atoms resulting from their motion through a cavity as a function of their initial position difference and velocity.

We propose a general scheme to measure the concurrence of an arbitrary two-qubit pure state in atomic systems. The protocol is based on one- and two-qubit operations acting on two available copies of the bipartite system, and followed by a global qubit readout. We show that it is possible to encode the concurrence in the probability of finding all atomic qubits in the ground state. Two possible scenarios are considered: atoms crossing three-dimensional microwave cavities and trapped ion systems.

I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the nonunique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distribution is generic), and a no-cloning theorem. Two particular theories are then investigated in detail, for the sake of comparison with the classical and quantum cases. One of these includes states that can give rise to arbitrary nonsignaling correlations, including the superquantum correlations that have become known in the literature as nonlocal machines or Popescu-Rohrlich boxes. By investigating these correlations in the context of a theory with well-defined dynamics, I hope to make further progress with a question raised by Popescu and Rohrlich, which is why does quantum theory not allow these strongly nonlocal correlations? The existence of such correlations forces much of the dynamics in this theory to be, in a certain sense, classical, with consequences for teleportation, cryptography, and computation. I also investigate another theory in which all states are local. Finally, I raise the question of what further axiom(s) could be added to the framework in order to identify quantum theory uniquely, and hypothesize that quantum theory is optimal for computation.

We analyze the class of single-qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that $\frac{3}{8}$ of the generalized depolarizing channels can be simulated by the one-qubit mixed-state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli channel cannot be simulated by a one-qubit mixed-state environment.

The relaxation processes of rotational angular momentum of polar diatomic molecules diluted in simple liquids are analyzed by applying a non-Markovian relaxation theory to the study of the binary time autocorrelation function of the angular momentum. This non-Markovian theory was previously applied to the study of the infrared and Raman spectroscopy, and also to the analysis of the rotational energy relaxation processes. We have obtained non-Markovian evolution equations for the two-time $j$-level angular momentum correlation components involved in the angular momentum correlation function. In these equations, the time-dependent angular momentum transfer rates and the pure orientational angular transfer rates are given in terms of the binary time autocorrelation function of the diatomic-solvent anisotropic interaction. The non-Markovian evolution equations converge to Markovian ones in the long time limit, reaching the angular momentum transfer rates in the usual time-independent form. Alternative time scales for the angular relaxation processes, relative to the individual rotational processes as well as to the global decay correlations, are introduced and analyzed. The theory is applied to the study of the angular momentum relaxation processes of HCl diluted in liquid $\mathrm{S}{\mathrm{F}}_6$, a system for which rotational energy relaxation and infrared and Raman spectroscopy was previously analyzed in the scope of the same theory.

Usually, variational calculations for the second-order reduced density matrix are performed subject to the constraint that the “$P$” and “$Q$” matrices are positive semidefinite, which only constrains the lowest eigenvalue of these matrices. We characterize the highest eigenvalue of these matrices and discuss how the associated constraint (which is related to the ground-state energy of the Hamiltonians $H=-P$ and $H=-Q$) can be implemented in practical calculations. This necessary condition for $N$-representability should help ensure that the second-order reduced density matrix is not “overcorrelated.”

The valence shell excitations of argon were investigated by an angle-resolved fast-electron energy-loss spectrometer at an incident electron energy of $2500\mathrm{eV}$, and the transition multipolarities for the excitations of $3p\to 3d$, $4d$, $5s$, and $5p$ were elucidated with the help of the calculated intermediate coupling coefficients using the COWAN code. The generalized oscillator strengths for the excitations to $3p^5(3d,3d^{\prime })$, $3p^5(5p,5p^{\prime })$, and $3p^5(5s,4d)$ were measured, and the profiles of these generalized oscillator strength were analyzed. Furthermore, although the present experimental positions of the maxima for the electric-monopole and electric-quadrupole excitations in $3p\to 5p$ are in agreement with the theoretical calculations [Amusia et al., Phys. Rev. A 67, 022703 (2003)], the generalized oscillator strength profiles show obvious differences. In addition, the experimental generalized oscillator strength ratios for the electric-octupole transitions in $3p\to 3d$ are different from the theoretical prediction calculated by the COWAN code.

We investigate the tunneling dynamics of Bose-Einstein condensates (BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunneling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poincaré section method that visualizes the motions of BECs in a reduced phase plane.

The subwavelength localization of an ensemble of atoms concentrated to a small volume in space is investigated. The localization relies on the interaction of the ensemble with a standing wave laser field. The light scattered in the interaction of the standing wave field and the atom ensemble depends on the position of the ensemble relative to the standing wave nodes. This relation can be described by a fluorescence intensity profile, which depends on the standing wave field parameters and the ensemble properties and which is modified due to collective effects in the ensemble of nearby particles. We demonstrate that the intensity profile can be tailored to suit different localization setups. Finally, we apply these results to two localization schemes. First, we show how to localize an ensemble fixed at a certain position in the standing wave field. Second, we discuss localization of an ensemble passing through the standing wave field.

Our analytical solution shows that the number of atoms continuously injected into Bose-Einstein condensate from the reservoir depends on the linear gain/loss coefficient, and cannot be controlled by applying the external magnetic field via Feshbach resonance reported by Yuce and Kilic [Phys. Rev. A 74, 033609 (2006)].