We compare decoherence induced in a simple quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We find that even a relatively compact oscillator bath (with the effective number of degrees of freedom of order ten), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that by a macroscopic, thermal environment, except possibly at singularities of the environment’s specific heat (critical points). In the latter case, the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the qubit with the environment.

Crossed beams of electrons and ${\mathrm{Al}}^{2+}$ ions combined with fluorescence detection were used to measure the absolute cross section for electron-impact excitation of the ions to yield 186.3 nm and 185.5 nm photons from the $3s-3p$ transition. The measured cross section near the 6.7 eV threshold energy is about $16\times {10}^{-16}{\mathrm{cm}}^2,$ and some resonance structure near threshold is indicated. Total relative uncertainties $\left(1\mathrm{}\sigma \right)$ are typically about 6%, to be combined with an 11% absolute calibration uncertainty. Total uncertainties at high confidence level (90%) are around 20%, using a coverage factor of 1.7. Comparisons made with various theoretical calculations, specifically distorted wave and nine-state close coupling, show better agreement of experimental values with distorted wave calculations, with the measured values being higher near threshold than the most recent close-coupling calculations.

Absolute cross sections for electron-impact excitation of the ${3s}^2\overrightarrow{S}{3p}^{2}P$ transition in ${\mathrm{Al}}^{2+}$ were measured near threshold using the merged electron-ion beams energy-loss technique. Although the present results are lower than the previous crossed-beams fluorescence measurements of Dunn et al. [Phys. Rev. A 66, 032706 (2002)] by about 30%, these two experimental excitation cross sections at threshold are in agreement when the energy resolutions and total expanded uncertainties are considered. The present results are in excellent agreement with the published close-coupling calculations, but lie about 30% lower than the distorted-wave predictions.

In this paper, we generalize and improve the derivation of photoionization rate formula for one-electron atoms proposed by Keldysh [Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)]]. More exact expressions of the photoionization rate in the tunneling regime have been obtained. In addition, we extend the derivation to photoionization rates of randomly oriented diatomic molecules.

We compute the photon creation inside a perfectly conducting, three-dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and (generalized) Neumann type, we analyze as a preliminary step the dynamical Casimir effect for a scalar field satisfying generalized Neumann boundary conditions. We show that particle production is enhanced with respect to the case of Dirichlet boundary conditions. Then we consider the transverse electric and transverse magnetic polarizations of the electromagnetic field. For resonant frequencies, the total number of photons grows exponentially in time for both polarizations, the rate being greater for transverse magnetic modes.

Measures of entanglement, fidelity, and purity are basic yardsticks in quantum-information processing. We propose how to implement these measures using linear devices and homodyne detectors for continuous-variable Gaussian states. In particular, the test of entanglement becomes simple with some prior knowledge that is relevant to current experiments.

We have calculated energy levels and lifetimes of ${4f}^7$ and ${4f}^{6}5d$ configurations of Gd IV using Hartree-Fock and configuration-interaction methods. This allows us to reduce significantly the uncertainty of the theoretical determination of the electron electric dipole moment (EDM) enhancement factor in this ion and, correspondingly, in gadolinium-containing garnets for which such measurements were recently proposed. Our new value for the EDM enhancement factor of ${\mathrm{Gd}}^{3+}$ is $-2.2\pm \mathrm{0.5.}$ Calculations of energy levels and lifetimes for Eu III are used to control the accuracy.

We propose an all-geometric implementation of quantum computation using neutral atoms in cavity QED. We show how to perform generic single- and two-qubit gates, the latter by encoding a two-atom state onto a single, many-level atom. We compare different strategies to overcome limitations due to cavity imperfections.

We consider a model of a dilute Bose-Einstein condensed gas at finite temperatures, where the condensate coexists in a trap with a cloud of thermal excitations. Within the Zaremba, Nikuni, and Griffin formalism, the dynamics of the condensate is described by a generalized Gross-Pitaevskii equation, while the thermal cloud is represented by a semiclassical kinetic equation. Our numerical approach simulates the kinetic equation using a cloud of representative test particles, while collisions are treated by means of a Monte Carlo sampling technique. A full three-dimensional split-operator fast Fourier transform method is used to evolve the condensate wave function. We give details regarding the numerical methods used and discuss simulations carried out to test the accuracy of the numerics. We use this scheme to simulate the monopole mode in a spherical trap. The dynamical coupling between the condensate and thermal cloud is responsible for frequency shifts and damping of the condensate collective mode. We compare our results to previous theoretical approaches, not only to confirm the reliability of our numerical scheme, but also to check the validity of approximations which have been used in the past.

The effective-action formalism is applied to a gas of bosons. The equations describing the condensate and the excitations are obtained using the loop expansion for the effective action. For a homogeneous gas, the expansion in terms of the diluteness parameter is identified in terms of the loop expansion. The loop expansion and the limits of validity of the well-known Bogoliubov [J. Phys. (Moscow) 11, 23 (1947)] and Popov, (Zh. Éksp. Teor. Fiz. 47, 1759 (1964) [Sov. Phys. JETP 20, 1185 (1965)]) equations are examined analytically for a homogeneous dilute Bose gas and numerically for a gas trapped in a harmonic-oscillator potential. The expansion to one-loop order, and hence the Bogoliubov equation, is shown to be valid for the zero-temperature trapped gas as long as the characteristic length of the trapping potential exceeds the s-wave scattering length.

We derive an analytic solution for pulsed frequency conversion based on electromagnetically induced transparency or maximum coherence in resonant atomic vapors. In particular, drive-field and coherence depletion are taken into account. The solutions are obtained with the help of a Hamiltonian approach, which in the adiabatic limit allows one to reduce the full set of Maxwell-Bloch equations to simple canonical equations of Hamiltonian mechanics for the field variables. Adiabatic integrals of motion can be obtained and general expressions for the spatiotemporal evolution of field intensities derived. Optimum conditions for maximum conversion efficiency are identified and the physical mechanism of nonlinear conversion in the limit of drive-field and coherence depletion discussed.

Laser diodes subject to a delayed optical feedback may exhibit high-frequency oscillating intensities as a result of a beating between two external-cavity-modes (ECMs). We analyze the conditions for the stability of these microwave oscillations in the framework of the Lang-Kobayashi equations for a single-mode edge-emitting semiconductor laser [R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980)]. We show that two different scenarios are possible. If the linewidth enhancement factor is relatively large $(\alpha =2\mathrm{}-5),$ the beating occurs between a stable ECM (mode) and an unstable ECM (antimode). The stability of the time-periodic solution is then limited in parameter space. But if the linewidth enhancement factor is sufficiently low $(\alpha <~{\alpha }_c\simeq 1),$ a beating between two stable modes is possible allowing stable high-frequency oscillating outputs.

The physics of guided nonlinear propagation of ultrashort pulses with an arbitrary polarization state is investigated down to the few-cycle regime. The electric field of the pulse is described in terms of monochromatic circularly polarized waves; numerical simulations for the propagation of ultrashort pulses with elliptical and circular polarization are presented and discussed. The theoretical results can be applied to the compression of high-energy laser pulses with an arbitrary polarization state. An experimental demonstration of the compression of circularly polarized pulses is presented.

We calculate nuclear-polarization energy shifts in muonic ${}^{208}\mathrm{Pb}.$ We employ a relativistic field-theoretical calculation and evaluate the ladder, cross, and seagull terms of the two-photon exchange diagrams in both the Feynman and Coulomb gauges. Gauge independence is very well satisfied with the calculated nuclear-polarization energies. Using these results, we analyze fine-structure splitting energies of muonic ${}^{208}\mathrm{Pb}$ because of the presence of the persisting discrepancies between experiment and calculation. The present nuclear-polarization energies explain about half of the anomaly in the $\Delta 2p$ fine-structure splitting energy, and only one-fourth of the anomaly in the $\Delta 3p$ fine-structure splitting energy.

We study (by an exact numerical scheme) the single-particle density matrix of $\sim {10}^3$ ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to the interpretation and further development of the recent pioneering experiment by Greiner et al., Nature, (London) $415,$ 39 (2002). In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid–Mott-insulator transition.

Analytic solutions to the time-dependent Schrödinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential barrier opacity $\alpha ,$ we find that the probability density exhibits two evolving structures. One refers to the propagation of a forerunner related to a time domain resonance [Phys. Rev. A 64, 0121907 (2001)], while the other consists of a semiclassical propagating wave front. We find a regime where the forerunners are absent, corresponding to positive time delays, and show that this regime is characterized by opacities $\alpha <{\alpha }_c.$ The critical opacity ${\alpha }_c$ is derived from the analytical expression for the delay time, which reflects a link between transient effects in tunneling and the delay time.

Quantum-mechanical entanglement is essential for certain forms of quantum communication, and occurs as a consequence of some operations in quantum computation. The ability to quantify this resource correctly has thus become of great interest to those working in the field of quantum information theory. In this paper, we show that all existing entanglement measures but one fail important tests of fitness when applied to n-particle m-site states of indistinguishable particles, where n, $m>~2.$ The accepted method of measuring the entanglement of a bipartite system of distinguishable particles is to use the von Neumann entropy of the reduced density matrix of one half of the system. We show that expressing the full density matrix using a site-spin occupation number basis, and reducing with respect to that basis, gives an entanglement that meets all currently known fitness criteria for systems composed of either distinguishable or indistinguishable particles. We consider an output state from a previously published thought experiment, a state that is entangled in both spin and spatial degrees of freedom, and show that the site entropy measure gives the correct total entanglement. We also show how the spin-space entanglement transfer occurring within the apparatus can be understood in terms of the transfer of probability from single-occupancy to double-occupancy sectors of the density matrix.

Homodyne detection is considered as a way to improve the efficiency of communication near the single-photon level. The current lack of commercially available infrared photon-number detectors significantly reduces the mutual information accessible in such a communication channel. We consider simulating direct detection via homodyne detection. We find that our particular simulated direct detection strategy could provide limited improvement in the classical information transfer. However, we argue that homodyne detectors (and a polynomial number of linear optical elements) cannot simulate photocounters arbitrarily well, since otherwise the exponential gap between quantum and classical computers would vanish.

We discuss techniques for producing, manipulating, and measuring qubits encoded optically as vacuum- and single-photon states. We show that a universal set of nondeterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.

The remarkable transmission of two bits of information via a single qubit entangled with another at the destination is presented as an expansion of the unremarkable classical circuit that transmits the bits with two direct qubit-qubit couplings between the source and destination.