We have measured electron-impact optical emission cross sections for selected resonance and nearby nonresonant levels of the neon ${2p}^{5}3d$ configuration at pressures from 2 to 70 mTorr. The enhanced fluorescence observed from nonresonant levels at high pressures is consistent with excitation transfer from highly populated resonance levels of the ${2p}^{5}3d$ configuration. We measured excitation-transfer cross sections of $540\pm 80\hspace{0.5em}{\mathrm{\AA }}^2,$ $1600\pm 500\hspace{0.5em}{\mathrm{\AA }}^2$, and $1100\pm 200\hspace{0.5em}{\mathrm{\AA }}^2$ for transfer from the ${3d}_5\to {3d}_6,$ ${3s}_1^{\prime }\to {3s}_1^{″},$ and ${3s}_1^{\prime }\to {3s}_1^{}$, respectively.

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov–de Gennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, extremely efficient in our implementation with parallel fast Fourier transform methods, and produces highly accurate results. For high dimensionality or low symmetry the time-dependent approach is a more practical computational scheme and produces accurate and reliable data. The method is suitable for general trap geometries, condensate flows and condensates permeated with defects and vortex structures.

A path-integral approach for δ-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale-invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the δ-function bound state. The well-known singular character of the two-dimensional δ-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.

It is proposed that superoscillations play an important role in the interferences that give rise to superluminal effects. To exemplify that, we consider a toy model that a wave packet to travel in zero time and negligible distortion, a distance arbitrarily larger than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Similar reasoning applies to the dwell time.

We present a two-active-electron (TAE) approach for solving the time-dependent Schrödinger equation (TDSE) for the interaction of a multi-electron system with an ultrashort, intense, and linearly polarized laser pulse [Lagmago Kamta and Starace, Phys. Rev. Lett. 86, 5687 (2001)]. A technique for obtaining angular distributions for double ionization by such pulses is also described. The approach for solving the TDSE in the TAE approximation is full dimensional and accounts for correlations between the two electrons, as well as the polarization of the core. It is based on a configuration-interaction expansion of the time-dependent wave function in terms of one-electron atomic orbitals. Applying the method to the lithium negative ion $\left({\mathrm{Li}}^{-}\right),$ we display the time-dependent dynamics of the photodetachment process. For low intensities, our results for the detachment yield follow expectations from lowest-order perturbation theory and agree satisfactorily with $\mathcal{R}$-matrix calculations. Our results for angular distributions indicate that following multiphoton double ionization by an intense laser field, electrons are predominantly ejected along the laser polarization axis; however, a significant number are ejected perpendicularly to this axis. An angular momentum-based analysis of these angular distributions indicates that, in the dipole approximation and for an initial ${}^1{S}^e$ state interacting with a linearly polarized laser field, double ejection of both electrons along the direction perpendicular to the laser polarization axis can only occur following absorption of an even number of photons, whereas multiphoton absorption of an odd number of photons does not lead to double ejection at these angles.

The different behavior of first-order interferences and second-order correlations are investigated for the case of two coherently excited atoms. For intensity measurements this problem is in many respects equivalent to Young’s double-slit experiment and was investigated in an experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)] and later analyzed in detail by Itano et al. [Phys. Rev. A 57, 4176 (1998)]. Our results show that in cases where the intensity interferences disappear the intensity-intensity correlations can display an interference pattern with a visibility of up to 100%. The contrast depends on the polarization selected for the detection and is independent of the strength of the driving field. The nonclassical nature of the calculated intensity-intensity correlations is also discussed.

We study the energy eigenvalue problem and the yrast states for a harmonically trapped two-component weak-interacting Bose-Einstein condensate (BEC) using an analytical method. The yrast states and energy eigenvalues for $L=0,1,2,3\mathrm{}$ are given in a special case. We illustrate the different eigenstate behaviors between even L and odd L for the two-component BEC. The odd-even effect of the yrast spectrum in the two-component BEC is also pointed out.

We propose a variable impact energy E algorithm within an optimized scattering angle ${\theta }_m$ given by $\sin {\theta }_m=1/(2E/\omega -1),$ at each E, with $\omega$ the excitation energy, for reliable small-angle electron differential cross-section measurements. Normalization of the measured data to the optical oscillator strength ${(G}_0)$ is ensured through an appropriate interpolation-extrapolation procedure. Our variable energy optimized method yields an excellent extrapolated $G_0$ value when applied to $e-H$ scattering data.

In a previous publication [J. Kempe et al., Quantum Computation and Information (Rinton Press, Princeton, NJ, 2001), Vol. 1, special issue, p. 33] we showed that it is possible to implement universal quantum computation with the anisotropic XY-Heisenberg exchange acting as a single interaction. To achieve this we used encodings of the states of the computation into a larger Hilbert space. This proof is nonconstructive, however, and did not explicitly give the trade-offs in time that are required to implement encoded single-qubit operations and encoded two-qubit gates. Here we explicitly give the gate sequences needed to simulate these operations on encoded qubits and qutrits (three-level systems) and analyze the trade-offs involved. We also propose a possible layout for the qubits in a triangular arrangement.

Using the generalized Bell states and controlled-NOT gates, we introduce an entanglement-based quantum key distribution (QKD) of d-level states (qudits). In case of eavesdropping, Eve’s information gain is zero and a quantum error rate of $\left(d-1\right)/d$ is introduced in Bob’s received qudits, so that for large d, comparison of only a tiny fraction of received qudits with the sent ones can detect the presence of Eve.

The influence of electromagnetic fields on the dielectronic recombination of ${\mathrm{O}}^{5+}$ ions has been measured at the Stockholm heavy ion storage ring CRYRING. The experimental energy range covered all $2\overrightarrow{s}2p$ $\Delta n=0\mathrm{}$ resonances. Electric fields up to 600 V/cm were applied and a noticeable enhancement of the dielectronic recombination cross section as a function of electric-field strength was observed. Field ionization of highly exited Rydberg states was used to investigate the enhancement of the recombination rate for two narrow bands of n states ranging from $n\approx 19–22$ and from $n\approx 23–25.$ The experimental data are compared to theory. After applying a field-ionization model to the calculations, the field-free spectra show good agreement with the experimental data. Although experiment and theory show the same trend of increasing strength of dielectronic recombination with increasing external electric field and with increasing n, quantitative discrepancies remain.

It is shown that certain unitary gauge operations that are normally of negligible importance in the theory of laser-atom interactions become significant for pulses containing only a few cycles, and it is discussed how to make gauge invariant predictions in general, and in particular in the velocity and length gauges, and in the Henneberger frame.

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-$T_c$ behavior of the system, and predicts a value of $T_c$ that is a significant fraction of the Fermi temperature. It is shown that this mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory, we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic ${}^6\mathrm{Li}.$

We find the exact solution to the three-state problem for a class of intuitive and counterintuitive sequences of delayed pulses of finite duration in terms of the Clausen’s generalized hypergeometric function, which reduces to simple analytic expressions, involving elementary functions only, for final occupation probabilities. These analytic results show that the sequence of delayed pulses, independently of the pulse order and applied detunings, can completely remove the population from the initially populated state (thus creating a quantum superposition of two other involved states). This conclusion extends the original result of Vitanov and Stenholm [Phys. Rev. A 55, 648 (1997)], to the case of nonzero two-photon detuning and more general pulse shapes.

In economics, duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called the “leader-follower” model. We give a quantum perspective on the Stackelberg duopoly that gives a backwards-induction outcome same as the Nash equilibrium in the static form of duopoly also known as the Cournot’s duopoly. We find the two-qubit quantum pure states required for this purpose.

We first construct a probabilistic and approximate quantum cloning machine (PACM) and then clarify the relation between the PACM and other cloning machines. After that, we estimate the global fidelity of the approximate cloning that improves the previous estimation for the deterministic cloning machine; and also derive a bound on the success probability of producing perfect multiple clones. Afterwards, we further establish a more generalized probabilistic and approximate cloning and deleting machine (PACDM) and discuss the connections of the PACDM to some of the existing quantum cloning and deleting machines. Finally the global fidelity and a bound on the success probability of the PACDM are obtained. Summarily, the quantum devices established in this paper improve and also greatly generalize some of the existing machines.

We investigate the excitation of atomic levels in a high-voltage discharge gap by studying the spectrum of the $2p-3d$ transitions of Li I atoms flowing in the gap. The Stark splitting of this transition, due to the gap electric field, enables resolving the lines originating from different magnetic sublevels of the $3d$ level. We show that the atomic level populations are dominated by excitations due to ions accelerated in the gap. The directionality of the ion beam induces magnetic sublevel populations that are remarkably different from the statistical distribution, where the major role is played by the relatively low-energy ions accelerated near the ion-emitting surface. By accounting for the polarization properties of the beam-induced level excitations we were able to obtain good agreement with observed populations of atomic levels with different $m_l$ values.

Ionization of hydrogen atoms by the impact of fast charged particles can be accurately treated theoretically using simple two-center wave functions to describe the scattering system both initially and finally. For the final state, we use a continuum distorted wave (CDW) that contains the product of three Coulombic distortion factors (one for each two-body interaction), hence it is called the 3C wave function. This CDW (3C) wave function is ideal for studying fast collisions since it is asymptotically correct in all asymptotic domains of momentum space for all configurations of the three particles in coordinate space [S. Jones and D. H. Madison, Phys. Rev. A $62,$ 42 701 (2000)]. Coulomb distortion in the entrance channel is provided by an eikonal initial state (EIS), and this CDW-EIS approximation, introduced by Crothers and McCann [J. Phys. B $16,$ 3229 (1983)], has proven to be the most accurate perturbative method ever devised within a two-state approximation. The first fully differential cross sections for ion-atom ionization in the CDW-EIS approximation are presented. In addition, by considering projectiles of different mass and charge, it will be shown that although the charge of the projectile is important, the mass of the projectile plays virtually no role in the vast majority of fast ionizing collisions.

We present a theoretical and experimental investigation of quantum fluctuations in vertical-cavity surface-emitting lasers (VCSELs) having one longitudinal and transverse linearly polarized mode above threshold. We develop the quantum version of the broadly used four-level spin-flip model to take into account the quantum statistics of the pumping process of the active atoms. Our theory allows for arbitrary pumping statistics varying from Poissonian to regular. We compare experimental results obtained with single-mode VCSELs with predictions of our theory and find very good agreement. We demonstrate that the quantum fluctuations of the subthreshold field component polarized orthogonally to the lasing mode have to be taken into account for adequate description of quantum fluctuations in VCSELs. In particular, we show that when the laser light passes through a polarizer, the two orthogonal polarization components of the light wave after passing through the polarizer can be strongly anticorrelated.