Following evolution of an open quantum system one requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is “uncertain.” In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for $\Omega ,$ and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the x quadrature, homodyne of the y quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about $\Omega ,$ variance in $\Omega ,$ long-time system purity, and short-time system purity).

We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell’s inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.

Dynamical evolution is described as a parallel section on an infinite-dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the generators of the relativity group acting on the base manifold. In the case of Galilean transformations we show that the property that the curvature for the fundamental connection must be zero is just the Heisenberg equations of motion and the canonical commutation relation in geometric language. We then consider linear and circular accelerating frames and show that pseudoforces must appear naturally in the Hamiltonian.

The global rotational degrees of freedom in the Schrödinger equation for an N-body system are completely separated from the internal ones. After removing the motion of the center of mass, we find a complete set of $(2\mathrm{}\mathcal{l}+1)$ independent base functions with angular momentum $\mathcal{l}.$ These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only $\left(3N-6\right)$ internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.

The two-atom correlation scheme originally proposed by Davidovich, Brune, Raimond, and Haroche for measuring the decoherence of a mesoscopic superposition of coherent states of a QED cavity field is shown to be equivalent to a quantum computer solving Deutsch’s problem. Using the existing analysis of decoherence in the Master equation formalism, and other important losses in this system, the final probability for obtaining the correct result for the computation is found in terms of the time period between atom traversals, the number of photons in the cavity, and the precision of the atomic velocity. The error due to decoherence in this system amounts to a phase error, and in the Master equation approach is a linear effect at small time scales. By explicitly considering the dynamics of the decoherence process when the system is coupled to a bath of oscillators with finite mode cutoff the error due to decoherence is found to decrease significantly and becomes a quadratic effect at short-time scales.

We present the Schmidt decomposition for arbitrary wave functions of two indistinguishable bosons, extending the recent studies of entanglement or quantum correlations for two fermion systems [J. Schliemann et al., Phys. Rev. B 63, 085311 (2001) and quant-ph/0012094]. We point out that the von Neumann entropy of the reduced single-particle density matrix remains to be a good entanglement measure for two identical particles.

A nonperturbative theory for calculating time-resolved photoelectron angular distributions in linear molecules [J. Chem. Phys. 107, 7859 (1997)] is extended to nonlinear systems and reformulated so as to expose and utilize the underlying electronic and rotational symmetries. A sequence of approximations is next introduced, systematically reducing the formally exact expression to cruder forms that are applicable to systems of increasing complexity. As an example of the potential applications of time-resolved photoelectron angular distributions in polyatomic dynamics we examine the information they convey about an ultrafast internal conversion.

The hyperfine (hf) transition rates for muonic atoms have been remeasured for select light nuclei, using neutron detectors to evaluate the time dependence of muon capture. For ${}^{19}\mathrm{F}{\Lambda }_h=5.6\mathrm{}\left(2\right)\mathrm{}\hspace{0.5em}\mu {\mathrm{s}}^{-1}$ for the hf transition rate, a value that is considerably more accurate than previous measurements. Results are also reported for Na, Al, P, Cl, and K.

Exchange-only Kohn-Sham (KS) theory is developed based on a physically motivated common energy denominator approximation for the orbital Green’s function $G_{i\sigma }.$ An explicit expression for the exchange potential $v_{x\sigma }$ in terms of the occupied KS orbitals is obtained via the analytical inverse of the resulting density response function ${\chi }_{s\sigma },$ with $v_{x\sigma }$ being subdivided into the Slater potential $v_{S\sigma }$ and the “response” potential $v_{\mathrm{resp}\sigma }.$ The latter exhibits a characteristic orbital structure with “diagonal” contributions from the densities $|{\psi }_{i\sigma }{|}^2$ of the occupied KS orbitals as well as “off-diagonal” ones from the occupied-occupied orbital products ${\psi }_{i\sigma }{\psi }_{j\sigma }^{*}.$ An expression for the response part $f_{\mathrm{resp}\sigma }$ of the exchange kernel is derived. It is established for the case of a symmetric molecular chain in an applied electric field that the kernel derived from the Krieger-Li-Iafrate potential with the Sharp-Horton approximation for $G_{i\sigma }$ fails to produce the field-counteracting potential $\delta v_{\mathrm{resp}\sigma },$ which is lacking in local-density and generalized-gradient approximations but which is required to obtain realistic (hyper)polarizabilities. On the contrary, as is shown in the case of ${\mathrm{He}}_2,$ the present kernel $f_{\mathrm{resp}\sigma }$ generates a field-counteracting potential $\delta v_{\mathrm{resp}\mathrm{\sigma }}^{\left(\mathrm{f}\mathrm{c}\right)}.$ The field-counteracting exchange effect is seen to arise from the spatial dependence of the cross product ${\psi }_g{\psi }_u{\rho }^{-1}$ of the symmetric and antisymmetric orbitals which is coupled with an integral over itself times δρ. Similar “self-coupling” terms are indicated in the general case of a symmetric molecular chain.

We report scattering lengths for the ${}^1{\Sigma }_g^{+},$ ${}^3{\Sigma }_u^{+},$ and ${}^5{\Sigma }_g^{+}$ adiabatic molecular potentials relevant to collisions of two metastable $2{}^{3}S$ helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections, and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.

A modified perturbation theory, previously introduced for the construction of asymptotic states accounting for a general class of long-range angle-dependent multipole potentials is developed in further detail. The threshold behavior of these states is presented in explicit form and these results are used, with the aid of a modified effective-range formulation, to determine the threshold energy dependence of the multichannel transition matrix. Unitarity properties are established formally and verified in the low-energy limit. A variational procedure for determining the parameters appearing in the modified effective-range expansion is described. The same procedure accounts for the presence of zero-energy bound states leading to resonant behavior that alters the threshold energy dependence.

K x rays have been observed in electron capture processes of H-like ${\mathrm{Si}}^{13+},$ ${\mathrm{S}}^{15+},$ and ${\mathrm{Ar}}^{17+}\mathrm{}\left(1s\right)\mathrm{}$ ions colliding with various atom and molecule gas targets over the collision energy of $1–70$ $\mathrm{keV}/u.\mathrm{}$ These K x rays are the final results of cascade-down to the ground ${(1s}^2)$ state from highly excited states formed through electron capture. It has been found that at low energies $(<\mathrm{}10\mathrm{}$ $\mathrm{keV}/u)$ the cross sections for the production of K x rays are nearly constant, and decrease slowly when the collision energy is increased. The cross sections also have been found to increase roughly with the inverse square of the ionization energy of the targets. It is also noted that the intensity ratios of the $K\beta$ line to the $K\alpha$ line increase slightly as the ionization energy of the target increases, suggesting that an electron is captured in different $\mathrm{}(n/)\mathrm{}$ states in different targets. These ratios are found to decrease slightly as the collision energy increases. The measured K x-ray production cross sections also have been compared with total electron-capture cross sections based upon an empirical formula, and it has been found that, on average, roughly two-third of total electron capture processes result in K x-ray emission, with the remaining one-third ending at the metastable state level after electron capture without emitting K x rays.

Photoionization cross sections for ionization to ${\mathrm{Be}}^{+}(2s,2p,3s,$ and $3p)$ states from the excited $2s2p{}^{1,3}{P}^o$ states of atomic beryllium have been calculated using a noniterative eigenchannel R-matrix method. All associated partial photoionization cross sections are also presented. The cross sections contain a number of autoionizing Rydberg series of resonances converging to the ${\mathrm{Be}}^{+}(2p,3s,3p,$ and $3d)$ states. Lower members of the Rydberg series of resonances with $n<~12$ are identified and resonance positions $E_r,$ effective quantum numbers $n^{*},$ and widths $\Gamma$ are presented. Excellent agreement between length and velocity gauge results is found, along with overall good agreement with previous work.

We measured singly charged fullerenelike fragment ions by high-resolution time-of-flight (TOF) mass spectroscopy in collisions of 10 MeV ${\mathrm{He}}^{2+}$ with ${\mathrm{C}}_{60}.$ The experimental TOF spectrum was compared with Monte Carlo simulations based on the statistical ${\mathrm{C}}_2$ emission model using two different combinations of transition states and activation energies of fullerene ions. When a very loose transition state and high activation energy of fullerene ions (9.5 eV for ${\mathrm{C}}_{60}^{+})$ are used, the simulation successfully reproduces the experimental spectrum. This indicates that the dominant process of production of singly charged fullerenelike fragments is sequential ${\mathrm{C}}_2$ emission, clearly supporting the combination of higher activation energies and a very loose bound transition state.

Simple and versatile traps for neutral atoms can be built using the magnetic potentials created by a current-carrying wire and a homogeneous bias field. These traps exhibit favorable scaling properties and can achieve parameters required for Bose-Einstein condensation traps at very low power consumption.

We study the propagation effects of phase-controlled two-color lasers in a two-level medium under a weak pumping condition. By solving the coupled equations for atoms and fields simultaneously, it is found that the propagation effects significantly modify the atom-field interactions. A time-dependent analysis is also undertaken to explain the numerical results.

An ideal atom laser would produce an atomic beam with highly stable flux and energy. In practice, the stability is likely to be limited by technical noise and nonlinear dynamical effects. We investigate the dynamics of an atom laser using a comprehensive one-dimensional, mean-field numerical model. We fully model the output beam and experimentally important physics such as three-body recombination. We find that at high-pump rates, the latter plays a role in suppressing the high-frequency dynamics, which would otherwise limit the stability of the output beam.

The dynamics of localized excitations in an array of Bose-Einstein condensates (BECs) is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distribution localized on very few lattice sites (intrinsic localized modes), as well as atomic population distributions involving many lattice sites (envelope solitons), is studied both numerically and analytically. The origin and properties of these modes are shown to be inherently connected with the interplay between macroscopic quantum tunneling and nonlinearity-induced self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of these excitations is studied both for zero and nonzero backgrounds. We find that in a definite range of parameters, homogeneous distributions can become modulationally unstable. We also show that bright solitons and excitations of shock-wave type can exist in BEC arrays even in the case of positive scattering length. Finally, we argue that a BEC array with negative scattering length in the presence of linear potentials can display collapse.

An electro-optical feedback loop can make in-loop light (squashed light) which produces a photocurrent with noise below the standard quantum limit (such as squeezed light). We investigate the effect of squashed light interacting with a three-level atom in the cascade configuration and compare it to the effects produced by squeezed light and classical noise. It turns out that one master equation can be formulated for all three types of light and that this unified formalism can also be applied to the evolution of a two-level atom. We show that squashed light does not mimic all aspects of squeezed light, and in particular, it does not produce the characteristic linear intensity dependence of the population of the upper-most level of the cascade three-level atom. Nevertheless, it has nonclassical transient effects in the de-excitation.

Homodyne statistics of light generated by an atomic system exhibiting optical bistability are analyzed. Using the dynamical equations of motion for a single atom in a coherently driven cavity in the good cavity limit, we show that the homodyne field can be described in terms of two independent real Gaussian stochastic processes and a coherent component. By making a Karhunen-Loève expansion of the field variables we derive the generating function for the photoelectron statistics. From this generating function photoelectron-counting distribution, factorial moments, and waiting-time distribution are obtained analytically. These quantities are directly measurable in photon-counting experiments. We show that the homodyne field exhibits many interesting nonclassical features including nonclassical effects in higher-order factorial moments.