A systematic study of the ionization of atomic hydrogen by electron impact from 0.3 eV to a few eV above the ionization threshold has been carried out using a semiclassical-quantal calculation. Differential and integrated cross sections are presented at 0.3 eV above the energy threshold. Triple-differential cross sections (TDCS) are presented at constant ${\theta }_{12}$ geometry where ${\theta }_{12}=180\mathrm{}°$ and $150°.$ Good agreement is achieved with the measurement [Röder et al., Phys. Rev. Lett. 79, 1666 (1997)] and calculations based on exterior complex scaling at 2 eV and 4 eV above threshold. Results of triple-differential cross sections are also presented at 0.3, 0.5, and 1.0 eV above threshold at both ${\theta }_{12}=180\mathrm{}°$ and $150°.$ At ${\theta }_{12}=180\mathrm{}°$ the small local maximum in the TDCS around ${\theta }_1=90\mathrm{}°$ reported by Pan and Starace [Phys. Rev. A 45, 4588 (1992)] at 0.5 eV above threshold is not observed in our calculation at energies down to 0.3 eV above threshold. The shape of our double differential cross sections seems to disagree qualitatively with the available calculations as we found two local maxima around $15°$ and $165°$ in our calculation. Single differential cross sections in our formulation appear naturally as a function of total excess energy E and, therefore, constant for all combinations of individual electron energies $E_1$ and $E_2$ with ${E=E}_1{+E}_2.$ Total ionization cross sections are also compared with measurement and available theoretical calculations and found to be in reasonably good agreement up to 10 eV above ionization threshold.

A quantum electrodynamical approach for the calculation of the nuclear spin-spin coupling tensor of nuclear-magnetic-resonance spectroscopy is given. Quantization of radiation fields within the molecule is considered and expressions for the magnetic field in the neighborhood of a nucleus are calculated. Using a generalization of time-dependent response theory, an effective spin-spin interaction is obtained from the coupling of nuclear magnetic moments to a virtual quantized magnetic field. The energy-dependent operators obtained reduce to usual classical-field expressions at suitable limits.

The phase damping induced in the cyclotron mode of a trapped electron by the coupling to the axial fluctuations is studied analytically. This system, described as a nonlinear oscillator stochastically driven in frequency, allows testing the generality of some elements present in the phenomenology of decoherence. In our approach, the reduced density matrix is obtained by performing a statistical average from the propagator for each noise realization. For short times, the decay of the coherences presents a nonexponential form, rooted in the non-Gaussian character of the stochastic driving. For large times, the decay becomes purely exponential, the rate showing a complex dependence on the difference between the Fock indices. As the populations do not change, the asymptotic state corresponds to a nonthermalized statistical mixture.

We present a method to generate qubits of the vibrational motion of an ion. The method is developed in the non-rotating-wave-approximation regime, therefore we consider regimes where the dynamics has not been studied. Because the solutions are valid for a more extended range of parameters we call them generalized qubits.

Coherence properties of atomic Bose-Einstein condensates determine the performance of waveguide atom interferometers. We analyze the expansion of a Bose-Einstein condensate from a magnetic microtrap into a waveguide. We derive analytical expressions to describe the expansion, show how the expanded cloud maps onto transverse linear eigenfunctions of the guide, and calculate the dependence of the modal decomposition coefficients on the chemical potential of the cloud and the anisotropy of the trap. Analytical results are compared with three-dimensional numerical simulations of the expansion.

We propose a technique, called quantum-optical coherence tomography (QOCT), for carrying out tomographic measurements with dispersion-cancelled resolution. The technique can also be used to extract the frequency-dependent refractive index of the medium. QOCT makes use of a two-photon interferometer in which a swept delay permits a coincidence interferogram to be traced. The technique bears a resemblance to classical optical coherence tomography (OCT). However, it makes use of a nonclassical entangled twin-photon light source that permits measurements to be made at depths greater than those accessible via OCT, which suffers from the deleterious effects of sample dispersion. Aside from the dispersion cancellation, QOCT offers higher sensitivity than OCT as well as an enhancement of resolution by a factor of two for the same source bandwidth. QOCT and OCT are compared using an idealized sample.

We propose a scheme for conditional generation of two-mode N-photon path-entangled states of traveling light field. These states may find applications in quantum optical lithography and they may be used to improve the sensitivity of interferometric measurements. Our method requires only single-photon sources, linear optics (beam splitters and phase shifters), and photodetectors with single-photon sensitivity.

We analyze a model for spin squeezing based on the so-called countertwisting Hamiltonian, including the effects of dissipation and finite system size. We discuss the conditions under which the Heisenberg limit, i.e., phase sensitivity $\propto 1/N,$ can be achieved. A specific implementation of this model based on atom-atom interactions via quantized photon exchange is presented in detail. The resulting excitation corresponds to the creation of spin-flipped atomic pairs and can be used for fast generation of entangled atomic ensembles, spin squeezing, and applications in quantum information processing. The conditions for achieving strong spin squeezing with this mechanism are also analyzed.

An alternative fidelity measure between two states of a qunit, an N-state quantum system, is proposed. It has a hyperbolic geometric interpretation, and it reduces to the Bures fidelity in the special case when $N=2.\mathrm{}$

A recent examination of the properties of an extension of the strong-field approximation (SFA) yielded excellent results for the prediction of ion yields in an intermediate range of intensities. The implication that other predictions of the SFA can also be extended to this moderate domain of intensities is shown to be unwarranted.

We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement outcomes are associated with distinct interference effects in a sample weakly coupled to an environment.

We study a physical implementation of an entanglement purification protocol using a cavity quantum electrodynamics based proposal, in both the microwave and the optical domain. The protocol consists of local quantum operations of each particle of an entangled system with one auxiliary particle (ancilla). After the above interaction a measurement on ancillas is carried out. In the microwave region the quantum information is stored in field states inside two distant cavities. We also give a procedure for quantifying the degree of entanglement between quantum fields, which allows verifying the efficiency of the purification process. In the optical domain, we study a setup of cold trapped ions inside cavities, where quantum bits are defined by two electronic levels of ions. This latter proposal is extended to create multiparticle entangled states among distant quantum systems. Entanglement is achieved through a set of local measurements on pairs of entangled particles.

In a recent paper [D. A. Meyer, Phys. Rev. Lett. 82, 1052 (1999)], it has been shown that a classical zero-sum strategic game can become a winning quantum game for the player with a quantum device. Nevertheless, it is well known that quantum systems easily decohere in noisy environments. In this paper, we show that if the handicapped player with classical means can delay his action for a sufficiently long time, the quantum version reverts to the classical zero-sum game under decoherence.

The translation of Grover’s search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are expectation values of observables on individual qubits, is described in detail. A filtering scheme, which effectively determines expectation values on a limited portion of the quantum state, is presented and used to locate a single item for searches involving more than one marked item. A truncated version of Grover’s algorithm, requiring fewer steps than the translated standard version but locating marked items just as successfully, is proposed. For quantum computational devices that only return expectation values, the truncated version is superior to its standard counterpart. This indicates that it is possible to modify quantum algorithms so as to reduce the required temporal resources by using the ensemble’s spatial resources.

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To search a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a complex phase in its amplitude. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel are also studied.

Nearly 100 low-, moderately high-, and high-lying singly and doubly excited states of He, Li, and Be have been calculated using a nonvariational, work-function-based exchange potential within the nonrelativistic Hohenberg-Kohn-Sham density-functional theory (DFT). The nonlinear gradient included in the Lee-Yang-Parr correlation functional is used to incorporate the correlation potential. The generalized pseudospectral method is used for nonuniform and optimal spatial grid discretization and solution of the Kohn-Sham equation to obtain accurate eigenvalues, expectation values, and radial densities for both ground and excited states. The results are compared with the available theoretical and experimental data. The discrepancy in the calculated singly excited state energies is within about 0.01% for He (for other atoms, it is less than 0.2%), while that for the doubly excited states of He is well within 3.6%. The deviations in the calculated single- and double-excitation energies for 31 selected states are in the error ranges 0.009–0.632 % and 0.085–1.600 %, respectively. The overall agreement of the present results is quite gratifying, especially in the light of DFT’s difficulties in dealing with excited states. The exchange-only results are practically of Hartree-Fock quality, and the correlation-included results are usually slightly overestimated. The present method offers a simple, computationally efficient and general scheme for accurate calculation of multiply excited Rydberg states within DFT.

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.

Noise reduction effects in two spatially coupled $\mathrm{Nd}:{\mathrm{YVO}}_4$ microchip lasers are studied theoretically in the case of similar intensity pump beams. We demonstrate that the synchronization phenomena commonly observed in spatially coupled unstable lasers applies to the quantum-noise-driven dynamics in steady-state stable lasers. We observe a complete suppression of the relaxation oscillation peaks in the intensity difference noise spectrum, and this is well described by linearized rate equations. The influence of both gain and index guiding is considered, together with that of relative frequency detuning.

We study the process of squeezing of an ensemble of cold atoms in a pulsed optical lattice. The problem is treated both classically and quantum mechanically under various thermal conditions. We show that a dramatic compression of the atomic density near the minima of the optical potential can be achieved with a proper pulsing of the lattice. Several strategies leading to the enhanced atomic squeezing are suggested, compared, and optimized.