We report on photoassociation of cold ${}^{87}\mathrm{Rb}$ atoms providing the spectroscopy of $(5s_{1∕2}+5p_{1∕2})0_u^{+}$ long-range molecular states, in the energy range of [$-12.5$, $-0.7{\mathrm{cm}}^{-1}$] below the dissociation limit. A Lu-Fano approach coupled to the LeRoy-Bernstein formula is used to analyze the data. The Lu-Fano graph exhibits the coupling of the molecular series with the $(5s_{1∕2}+5p_{3∕2})0_u^{+}$ one, which is due to spin effects in the molecule. A two-channel model involving an improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize $(5s_{1∕2}+5p_{3∕2})0_u^{+}$ levels, to evaluate the coupling, and to predict the energy and width of the first predissociated level of $(5s_{1∕2}+5p_{3∕2})0_u^{+}$ series. An experimental spectrum confirms the prediction.

We perform monocentric close-coupling calculations to obtain partial and total cross sections for excitation and electron loss in bare $A^{q+}+\mathrm{H}\left(1s\right)$ collisions, with $1⩽q⩽6$, for intermediate $(E=40\mathrm{keV}∕\mathrm{amu})$ to high $(E=7000\mathrm{keV}∕\mathrm{amu})$ impact energies. We use underlying basis sets of even-tempered Slater-type orbitals and confined spherical Bessel functions and compare the accuracy of the cross sections derived from these two implementations. Scaling rules are then established for the partial excitation cross sections of interest in fusion plasma research. We also undertake impact parameter first-Born calculations using the spherical Bessel underlying set to compare in the course of collision the close-coupling and perturbative descriptions of the ionization process.

Stochastic resonance (SR) is experimentally demonstrated in an atomic optical bistable system consisting of three-level atoms in $\Lambda$-type configuration confined in an optical ring cavity. The optical bistable system with enhanced Kerr nonlinearity due to atomic coherence is driven by a periodic signal and a Gaussian white noise source with variable amplitude, and displays an improved output signal-to-noise ratio, a characteristic signature of SR. The measured results match qualitatively with the theoretical predictions of the generic model for the SR phenomenon.

We investigate the propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems using an iterative predictor-corrector finite-difference time-domain method. It is shown that when the initial effective area is equal to $2\pi$, the effective area will remain invariant during the course of propagation, and a complete Rabi oscillation can be achieved. However, for an elliptically polarized few-cycle ultrashort laser pulse, polarization conversion can occur. Eventually, the laser pulse will evolve into two separate circularly polarized laser pulses with opposite helicities.

An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical transition probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the transition probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent (i.e., they have no solution) for any control field that produces a transition probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the transition probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a transition probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a transition probability of unit value is shown to have an extensive null space and only a finite number of negative eigenvalues. Collectively, these findings show that (a) the transition probability landscape extrema consists of values corresponding to no control or full control, (b) approaching full control involves climbing a gentle slope with no false traps in the control space and (c) an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory.

The coincidence rate between x rays reflected and refracted from a silicon crystal after a high-resolution monochromator was measured at the long undulator beam line of SPring-8. The data show excess coincidences relative to the random background, which vanish when the detectors of the reflected and refracted beams probe widely separated parts of the incoming x-ray wave front. The measured coincidence rate with different detector sizes and distances between the probed wave front positions, perpendicular to the scattering plane, agree well with fitting functions derived for the present experimental conditions. Furthermore, it is shown that the coincidence rate measured between probing positions in the scattering plane depends strongly on the angular spread of reflected and refracted x rays. Small angular spread is obtained by detuning from the exact Bragg condition, which results in good quantitative agreement of the coincidence data and theoretical predictions.

Several convenient formulas for the entanglement of two indistinguishable delocalized spin-$1∕2$ particles are introduced. These generalize the standard formula for concurrence, valid only in the limit of localized or distinguishable particles. Several illustrative examples are given.

In perturbation conditions, a theoretical approach based on Coulomb-Volkov states has proved to accurately describe the process of above-threshold ionization induced by short laser pulses. When a target can be ionized with a single photon, this approach has been successfully extended beyond perturbation conditions by taking into account, throughout the interaction, the initial state population, which is easily determined by means of a reduced set of coupled state equations. It is shown here that solving this latter set of equations for the population of the continuum is a very simple way to reproduce accurately single-photon transitions in the case of highly saturated ionization.

We present a calculation of the shot noise in a ballistic electron waveguide $\sqrt{\mathrm{NOT}}$ gate. A general expression for the shot noise in the leads connected to these types of gates is shown. We then parametrize an $S$-matrix which qualitatively describes the action of a $\sqrt{\mathrm{NOT}}$ gate previously found through numerical methods for $\mathrm{GaAs}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ based waveguide systems. Using this $S$-matrix, the shot noise in a single output lead and across two output leads is calculated. We find that the measurement of the shot noise across two output leads allows for the determination of the fidelity of the gate itself.

The atomic xenon laser is among the most efficient and powerful of the near-infrared gas lasers, especially when pumped by molecular ions in an $\mathrm{Ar}\text{−}\mathrm{Xe}$ mixture. Accurate transition probabilities for the laser transitions are critical in developing a fundamental understanding of the inversion dynamics, gain, and power extraction of this device. We compare results from several methods of calculating transition probabilities for six laser lines ranging in wavelength from $1.733$ to $3.508\mathrm{\mu }\mathrm{m}$. In some cases, our recommended values differ considerably from those employed in previous work.

We present total and partial electron-capture cross sections for ${\mathrm{Ne}}^{10+}+\mathrm{H}\left(1s\right)$ collisions at energies from $0.01\mathrm{eV}\text{to}1\mathrm{keV}$ using the hyperspherical close-coupling method. Good agreements with the previous calculations by the classical-trajectory Monte-Carlo method are found for total capture cross section, but not for partial cross sections, especially below about $200\mathrm{eV}∕\mathrm{amu}$. We found that the total cross section is mainly due to the population of $n=7$ channels and only at energies above $50\mathrm{eV}∕\mathrm{amu}$ $n=5,6$ channels begin to contribute to the total cross section.

An optical spring effect has been observed in the motion of a Fabry-Pérot cavity suspended in the Low-Frequency Facility, R&D experiment of the VIRGO Collaboration. The experimental setup consists of a 1-cm-long cavity hanging from a mechanical isolation system, conceived to suppress seismic noise transmission to the optical components of the interferometer. The observed radiation pressure effect corresponds to an optical stiffness $k_{opt}$ ranging between $2.5\times {10}^4$ and $6.5\times {10}^4\mathrm{N}∕\mathrm{m}$. This paper reports several measurements of the mirror relative displacement carried out in different working conditions. The measured error signal spectra show broad resonances at frequencies compatible with the optomechanical system. In other runs cavity detuning oscillations have been observed at subhertz frequencies. In these cases the power spectrum of the control loop error signal exhibited a broad resonance with superimposed uniformly spaced peaks. These observations, validated by a simple model, prove that the fluctuations of the optical spring effect can become so large as to exhibit nonlinear features.

The response to a probe laser beam of a suspended, misaligned, and detuned optical cavity is examined. A five degree of freedom dynamical model of the fluctuations of the longitudinal and transverse mirror coordinates is presented. Classical and quantum mechanical effects of radiation pressure are studied with the help of the optical stiffness coefficients and the signals provided by an FM sideband technique and a quadrant detector, for generic values of the product $\varpi \tau$ of the fluctuation frequency times the cavity round trip. A simplified version is presented for the case of small misalignments. Mechanical stability, mirror position entanglement, and ponderomotive squeezing are accommodated in this model. Numerical plots refer to cavities under test at the so-called Pisa LF facility. The presented model can describe radiation pressure effects recently appeared in the VIRGO antenna and give a framework for designing the next generation of gravitational wave antennas where such effects would be of critical relevance.

A scheme based on photonic crystal technology is proposed as an ultrabright source of entangled photons on a miniaturized scale. The geometry consists of a multilayer microcavity, excited by a resonant pump frequency, such that the emitted photons are guided transversally to the direction of the incident pump. The entanglement occurs in direction, frequency, and polarization, and the bandwidth of the emitted photons is of the order of $1\mathrm{nm}$. We propose a feasible design based on ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ structures and predict an emission rate ${10}^5\text{pairs}\text{per}\text{second}$ with $100\mathrm{mW}$ pump power. These results are promising for realization of chip and future quantum computer applications.

For helium, long-range interaction coefficients $C_3$, $C_6$, $C_8$, $C_9$, and $C_{10}$ for all $S\text{−}S$ and $S\text{−}P$ pairs of the energetically lowest five states $(1{}^{1}S,2{}^{3}S,2{}^{1}S,2{}^{3}P,$ and $2{}^{1}P)$ are calculated precisely using correlated wave functions in Hylleraas coordinates. Finite nuclear isotope mass effects are included.

The Tani transformation is used for the representation of the Hamiltonian to a decaying system with bound states. We considered the Liouvillean Green function and self-energy for a system far from equilibrium. Then we express the many-body Green function in terms of expectation values of decaying system operators. Next we considered that the solutions obtained from the variational stabilization process with functional derivative correspond to the resonant poles for the decaying system. This adapted variation of the procedure is applied to our model potential of three-dimensional $\delta$ barriers. We evaluated the poles for $S$ states and the corresponding initial-state wave functions for this potential.

Collisions between electrons and a ${\mathrm{H}}_2\mathrm{O}$ vapor target at projectile energies ranging from $600\mathrm{eV}\text{to}4\mathrm{keV}$ have been investigated experimentally and theoretically, in order to determine cross sections for the production of a $K$-shell vacancy of the ${\mathrm{H}}_2\mathrm{O}$ molecule. The electrons originating from direct ionization and from autoionization were detected at angles in the range 30°–130° with respect to the incident beam direction. From the spectra, cross sections for the emission of a target electron following the production of a $K$-shell vacancy in oxygen are determined as a function of the projectile energy. The present experimental results are compared with semiempirical formula that have been extensively used previously for electron-atom collisions, and with model calculations using plane wave Born approximation. The ratio between $K$-shell and total ionization cross sections is found to be similar to that determined for an O atomic target, except at the highest projectile energies, for which it is equivalent to that determined for Ne. We show that this ratio is essentially governed, for sufficiently high collision energies, by the ratio between the outer- and inner-shell ionization potentials.

We consider the transfer of excitation in fast symmetric atom-atom collisions. We show that the process can be very strongly influenced by the resonance coupling to the radiation field and that the reason for this lies in the very long range of the latter. Further, we demonstrate that, because of the Doppler effect, the role of this channel in the transfer of excitation in symmetric collisions decreases when the collision energy increases. Since the resonance coupling represents an effect, which does not appear in the nonrelativistic treatment, we observe in such collisions the interesting situation: relativistic effects can be very profound at nonrelativistic collision velocities $v$, where $(v∕c{)}^2\ll 1$ ($c$ is the speed of light), but tend to disappear in the extreme relativistic limit $v\to c$.

We present spectral modeling results for neutral helium. Our underlying atomic data contains radiative transition rates that are generated from atomic structure calculations and electron-impact excitation rates, that are determined from both the standard $R$-matrix method and the $R$-matrix with pseudostates (RMPS) method. In this paper, we focus on transitions of particular importance to diagnostic line ratios. For example, our calculated rate coefficient for the electron-impact transition $1s3s{}^{1}S\to 1s3p{}^{1}P$, which has a pronounced effect on the $728.1\mathrm{nm}$ diagnostic spectral line, is found to be in good agreement with previous experimental measurements. We also consider transitions from the $1s^2{}^{1}S$ ground and $1s2s{}^{3}S$ terms to terms of the $n=4$ shell. They are found to be affected significantly by coupling of the bound states to the target continuum (continuum coupling), which is included in our RMPS calculation, but not in our standard $R$-matrix calculation. We perform collisional-radiative calculations to determine spectral line intensity ratios for three ratios of particular interest, namely the $504.8\mathrm{nm}∕471.3\mathrm{nm}$, $492.2\mathrm{nm}∕471.3\mathrm{nm}$, and $492.2\mathrm{nm}∕504.8\mathrm{nm}$ line ratios. Comparing our results determined from the RMPS excitation rates with those from the standard $R$-matrix excitation rates, we find that continuum coupling affects the rate coefficients significantly, leading to different values for all three line ratios. We also compare our modeling results with spectral measurements taken recently on the Auburn Helicon plasma device, finding that the ground and metastable populations are not in equilibrium, and that the experimental measurements are more consistent with the $1s2s{}^{3}S$ metastable term populations being short lived in the plasma.