The generation of harmonics by atoms or ions in a two-color, coplanar field configuration with commensurate frequencies is investigated through both an analytical calculation based on the Lewenstein model and the numerical ab initio solution of the time-dependent Schrödinger equation of a two-dimensional model ion. Through the analytical model, selection rules for the harmonic orders in this field configuration, a generalized cutoff for the harmonic spectra, and an integral expression for the harmonic dipole strength are provided. The numerical results are employed to test the predictions of the analytical model. The scaling of the cutoff as a function of both one of the laser intensities and frequency ratio $\eta$ as well as entire spectra for different $\eta$ and laser intensities are presented and analyzed. The theoretical cutoff is found to be an upper limit for the numerical results. Other discrepancies between analytical model and numerical results are clarified by taking into account the probabilities of the absorption processes involved.

We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero-order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover the truncated Wigner approximation, where the evolution is still classical but the initial conditions are distributed according to the Wigner transform of the initial density matrix. Further corrections can be characterized as quantum scattering events, which appear in the form of a nonlinear response of the observable to an infinitesimal displacement of the field along its classical evolution. At the end of the paper we give a few numerical examples to test the formalism.

By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture.

We report a theoretical study of the simultaneous high-efficiency, equal-level outputs of second and third harmonics in a quasiperiodic optical superlattice at any given fundamental intensity. The principle is that nonlinear coupling is effectively controlled by introducing proper quasiphase mismatches, by use of the tunability of linear refractive index gratings induced by applying a dc electric field based on the electro-optic effect. The theoretical results verify that this approach is feasible and very efficient. In addition, we also make a comparison with temperature tuning control, demonstrating that the performance of electro-optic control is much better than that of temperature tuning control.

We use a traveling-wave numerical model of the temporal dynamics in semiconductor lasers to investigate the dynamics and coherence properties of a multimode semiconductor laser subject to optical feedback. Considering an external cavity of intermediate length, we have observed features characteristic of the so-called short-cavity regime in a region where the relaxation oscillations frequency is larger than the external-cavity frequency. The time scales of the dynamics are controlled in this case by the strength of the optical feedback. We have examined the coherence properties of the multimode emission and have studied how the coherence time is reduced as the laser becomes more multimode.

When a measurement is made on a quantum system in which classical information is encoded, the measurement reduces the observers’ average Shannon entropy for the encoding ensemble. This reduction, being the mutual information, is always non-negative. For efficient measurements the state is also purified; that is, on average, the observers’ von Neumann entropy for the state of the system is also reduced by a non-negative amount. Here we point out that by rewriting a bound derived by Hall [Phys. Rev. A 55, 100 (1997)], which is dual to the Holevo bound, one finds that for efficient measurements, the mutual information is bounded by the reduction in the von Neumann entropy. We also show that this result, which provides a physical interpretation for Hall’s bound, may be derived directly from the Schumacher-Westmoreland-Wootters theorem [Phys. Rev. Lett. 76, 3452 (1996)]. We discuss these bounds, and their relationship to another bound, valid for efficient measurements on pure state ensembles, which involves the subentropy.

Significant difference in charge transfer cross sections between collisions of ${\mathrm{H}}^{+}$ ions with ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules has been observed in the energy range from 0.18 to 1.5 keV/u. The cross section ratio $\sigma {(}_{{\mathrm{D}}_2})/\sigma {(}_{{\mathrm{H}}_2})$ of charge transfer from ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ has been found to be $0.59\pm 0.08$ at 0.18 keV/u and gradually increases at higher energies and, then, eventually approaches unity at the highest energies around 2 keV/u. Nevertheless, the difference due to the isotope effect is pronounced even at high eV/u to 1 keV/u regions. This marked feature originates from a combination of small offset in binding and vibrational energies and different space occupied by nuclear wave functions of the target ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules.

Limits of state transformations in quantum mechanics are studied. Impossibility of physical implementation of the transformation ${\varrho }^{\otimes n}\to {\varrho }^n$ in quantum mechanics is proved. The most natural notions of structural completely positive approximation and structural physical approximations of nonphysical map are introduced. It is shown that these always exist for linear Hermitian maps and can be optimized under natural conditions. It is pointed out that it is physically possible to measure in a simple way the traces of $n\mathrm{th}$ power of quantum state $\mathrm{Tr}\left({\varrho }^n\right)$ if only joint measurements on n copies of the system are allowed. This gives the interpretation of Tsallis entropies as values of “multicopy” observables. Following this observations, the notion of multicopy entanglement witnesses is defined and examples are provided. Finally, using notion of multicopy observable, a simple method of spectrum state estimation is discussed.

We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which attempts to provide a “scalable” implementation on an expectation-value NMR quantum computer. We show that this ensemble implementation of the DJ algorithm is at best as efficient as the classical random algorithm. As soon as any attempt is made to classify all possible functions with certainty, the implementation requires an exponentially large number of molecules. The discrepancies arise out of the interpretation of mixed state density matrices.

We present a strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir. We discuss the applicability of this strategy by studying the dependence of the decoherence suppression on the shape of the coupling spectral density. We find that the effectiveness of this strategy arises from the non-Markovian nature of dynamical motion of the reservoir.

We consider the problem of designing a measurement to minimize the probability of a detection error when distinguishing between a collection of possibly nonorthogonal mixed quantum states. We show that if the quantum state ensemble consists of linearly independent density operators, then the optimal measurement is an orthogonal von Neumann measurement consisting of mutually orthogonal projection operators, and not a more general positive operator-valued measure.

We discuss the generation of entangled states of two two-level atoms inside an optical cavity. The cavity mode is supposed to be coupled to a white noise with adjustable intensity. We describe how the entanglement between the atoms arise in such a situation. The entanglement is maximized for intermediate values of the noise intensity, while it is a monotonic function of the atomic decay rate. This resembles the phenomenon of stochastic resonance and sheds more light on the idea to exploit the white noise in quantum-information processing.

We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and classical walks different. We also study the behavior of the system when the quantum coin carried by the walker interacts with an environment. We show that for this system quantum coherence is robust for initially delocalized states of the walker. The use of phase-space representation enables us to develop an intuitive description of the nature of the decoherence process in this system.

The hyperspherical time-dependent method with semiclassical outgoing waves for study of double photoionization of helium is presented. It is closely related to the hyperspherical R-matrix method with semiclassical outgoing waves [Phys. Rev. A 65, 032711 (2002)]: both split configuration space into two regions to solve the stationary inhomogeneous Schrödinger equation associated with the one-photon ionization problem, and both apply the same treatment to the outer region. However, the two methods differ radically in their treatments of the problem in the inner region: the most recent one applies a time-dependent approach for calculating the stationary wave function, while the previous one uses a R-matrix treatment. The excellent agreement observed between the triple differential cross sections obtained from these two basically different methods provides very strong support for both of them. Importantly, the very different numerical structures of both methods might make the most recent one a better candidate for investigating the near-threshold region.

We have measured electron kinetic energy spectra from the interaction of a low-density beam of noble-gas clusters with a high-intensity femtosecond laser pulse. Electron energies were measured both through their time of flight and through measurements of electron signals as a function of retarding voltages up to 7 kV. We have observed electrons with energies up to 6 keV and a sharp peak at an arrival time consistent with the detection of photons. The electrons had a broad angular distribution peaked along the polarization axis, while the sharp peak had an isotropic angular distribution. We attribute this sharp peak to uv, xuv, or x-ray photons formed as a result of the laser-cluster interaction and were unable to observe the two-lobed electron kinetic energy distribution reported by Shao et al. [Phys. Rev. Lett. 77, 3343 (1996)] with any combination of the laser and cluster parameters used.

A detailed theory-versus-experiment comparison is worked out for ${\mathrm{H}}_2^{+}$ intense laser dissociation, based on angularly resolved photodissociation spectra recently recorded in Figger’s group. As opposite to other experimental setups, it is an electric discharge (and not an optical excitation) that prepares the molecular ion, with the advantage for the theoretical approach, to neglect without loss of accuracy, the otherwise important ionization-dissociation competition. Abel transformation relates the dissociation probability starting from a single rovibrational state to the probability of observing a hydrogen atom at a given pixel of the detector plate. Some statistics on initial rovibrational distributions, together with a spatial averaging over laser focus area, lead to photofragments kinetic spectra, with well separated peaks attributed to single vibrational levels. An excellent theory-versus-experiment agreement is reached not only for the kinetic spectra, but also for the angular distributions of fragments originating from two different vibrational levels resulting into more or less alignment. Some characteristic features can be interpreted in terms of basic mechanisms such as bond softening or vibrational trapping.

Using the concept of diffused vorticity and the formalism of rotational hydrodynamics we calculate the eigenmodes of a harmonically trapped Bose-Einstein condensate containing an array of quantized vortices. We predict the occurrence of a new branch of anomalous excitations, analogous to the Kelvin modes of the single vortex dynamics. Special attention is devoted to the excitation of the anomalous scissors mode.

The Bose-Hubbard model of a twofold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose gas.

Strongly confining an ultracold atomic gas in one direction to create a quasi-two-dimensional system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong confinement results in a shift in the position of the Feshbach resonance as a function of the magnetic field. This shift, as well as the change of the width of the resonance, is computed. We find that the resonance is strongly damped in the thermal gas, but in the condensate the resonance remains sharp due to many-body effects. We introduce a two-dimensional model system, suited for the study of resonant superfluidity and having the same scattering properties as the tightly confined real system near a Feshbach resonance. Exact relations are derived between measurable quantities and the model parameters.

Propagation of optical pulses in a resonantly absorbing medium is studied. Propagation time of nanosecond pulses was measured for the Rb $D_1$ transition. At the center of two absorption lines, delay of the pulse peak which is about ten times as large as the pulse width was observed, where zero delay is defined for the propagation with the light velocity in vacuum. On the other hand, at the peak of an absorption line, negative delay was observed for large absorption, where the advance time is as large as 25% of the pulse width. Simulation including the effect of absorption and phase shift reproduced well the experimental results.