We use a Wannier-function formalism to describe the optical Wannier-Stark ladder in superstructure Bragg gratings with a linear chirp. The coupled mode equations are solved in a two-band approximation and an ansatz in which the solutions are given by a superposition of Wannier functions. We find that the expansion coefficients are Bessel functions of integer order, as in the case of the one-dimensional Schrödinger equation with periodic potential in a uniform electric field. The analytical results are in good agreement with a numerical solution of the coupled-mode equations, particularly at low chirp values.

A scheme for infrared generation without population inversion between subbands in quantum-well and quantum-dot lasers is presented. The scheme is based on the resonant nonlinear mixing of the optical laser fields on the two interband transitions that are generated in the same active region and that serve as the coherent drive for the infrared field. This mechanism for frequency down-conversion does not rely upon any ad hoc assumptions of long-lived coherences in the semiconductor active medium, and it should work efficiently at room temperature with injection current pumping. For optimized waveguide and cavity parameters, the intrinsic efficiency of the down-conversion process can reach the limiting quantum value corresponding to one infrared photon per one optical photon. Due to the parametric nature of infrared generation, the proposed inversionless scheme is especially promising for long-wavelength (far-infrared) operation.

The author calls attention to previous work with related results, which to his knowledge has escaped scrutiny before the publication of the paper “Nonlinear quantum evolution with maximal entropy production” [Phys. Rev. A 63, 022105 (2001)].

In this paper we investigate the dense coding with a three-particle entangled state. In this case one party (Alice) can send information to the second party (Bob), whereas the local measurement of the third party (Cliff) serves as quantum erasure. The quantum channel between Alice and Bob is controlled by Cliff via the measurement.

It has been argued that there exists only one inverse of the linear-response function $\chi ,$ i.e., ${\chi }^{-1},$ which depends symmetrically on its spatial-times variables [M. K. Harbola and A. Banerjee, Phys. Rev. A 60, 5101 (1999)]. Some brief comments on this consideration are presented here. We show in contrast to Harbola and Banerjee, that it is possible to construct the causal inverse also. At the same time, we confirm the main statement of [Harbola and Banerjee] that in fact there is no contradiction between the symmetry and causality.

By employing the equation derived by Amusia and Shaginyan in their comment on our work, we show that the potential corresponding to a time-dependent density is a noncausal functional of the density. We further strengthen this conclusion on the basis of the exact equation satisfied by the density.

We propose an experiment to test Bell’s inequality violation in condensed-matter physics. We show how to generate, manipulate, and detect entangled states using ballistic electrons in Coulomb-coupled semiconductor quantum wires. Due to its simplicity (only five gates are required to prepare entangled states and to test Bell’s inequality), the proposed semiconductor-based scheme can be implemented with currently available technology. Moreover, its basic ingredients may play a role towards large-scale quantum-information processing in solid-state devices.

It is a generally held belief that inelastic transition probabilities and cross sections in slow, nearly adiabatic atomic collisions decrease exponentially with the inverse of the collision velocity $v$ [i.e., $\sigma \propto \exp (-\mathrm{const}/v)].$ This notion is supported by the Landau-Zener approximation and the hidden crossings approximation. We revisit the adiabatic limit of ion-atom collisions and show that for very slow collisions radial transitions are dominated by the topology of the branch points of the radial velocity rather than the branch points of the energy eigensurface. This can lead to a dominant power-law dependence of inelastic cross sections, $\sigma \propto v^n.$ We illustrate the interplay between different contributions to the transition probabilities in a one-dimensional collision system for which the exact probabilities can be obtained from a direct numerical solution of the time-dependent Schödinger equation.

Working with ytterbium (Yb), we demonstrate dual-isotope magneto-optic traps of extreme experimental simplicity yet containing either fermion-boson or boson-boson isotope pairs. Pairs studied include ${}^{171}{\mathrm{Y}\mathrm{b}+}^{172}\mathrm{Yb}$ (a fermion-boson mixture) and ${}^{176}{\mathrm{Y}\mathrm{b}+}^{174}\mathrm{Yb}$ and ${}^{174}{\mathrm{Y}\mathrm{b}+}^{172}\mathrm{Yb}$ (boson-boson mixtures). Trapping is performed using the Yb ${(6s}^2{)}^1{S}_0{-\left(6s6p\right)\mathrm{}}^1{P}_1$ transition, an uncooled thermal source, and bichromatic trapping beams. Static and dynamic properties of the composite cloud are conveniently probed on the spin-forbidden ${(6s}^2{)}^1{S}_0{-\left(6s6p\right)\mathrm{}}^3{P}_1$ transition. A unique strategy for continuously loading these samples into magnetic traps is described.

We numerically investigate the dynamics of multiply charged hydrogenic ions in near-optical linearly polarized laser fields with intensities of order ${10}^{16}–{10}^{17}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The weakly relativistic interaction is appropriately described by the Hamiltonian arising from the expansion of the Dirac equation up to the second order in the ratio of the electron velocity $v$ and the speed of light c. Depending on the charge state Z of the ion, the relation of strength between laser field and ionic core changes. We find around $Z=12,$ typical multiphoton dynamics and for $Z=3\mathrm{}$ tunneling behavior, however, with clear relativistic signatures. In first order in $v/c$ the magnetic field component of the laser field induces a Z dependent drift in the laser propagation direction and a substantial Z dependent angular momentum with repect to the ionic core. While spin oscillations occur already in first order in $v/c$ as described by the Pauli equation, spin induced forces via spin-orbit coupling only appear in the parameter regime where ${\mathrm{}(v/c)\mathrm{}}^2$ corrections are significant. In this regime for $Z=12\mathrm{}$ ions, we show strong splittings of resonant spectral lines due to spin-orbit coupling and substantial corrections to the conventional Stark shift due to the relativistic mass shift while those to the Darwin term are shown to be small. For smaller charges or higher laser intensities, parts of the electronic wave packet may tunnel through the potential barrier of the ionic core and when recombining, are shown to give rise to keV harmonics in the radiation spectrum. Some parts of the wave packet do not recombine after ionization and we find very energetic electrons in the weakly relativistic regime of above threshold ionization.

We analyze the proposal that gravity may originate from a van der Waals type of residual force between particles due to the vacuum electromagnetic zero-point field. Starting from the Casimir-Polder integral, we show that the proposed approach can be analyzed directly, without recourse to approximations previously made. We conclude that this approach to Newtonian gravity does not work, at least not with this particular starting point. Only by imposing different or additional physical constraints, or by treating the underlying dynamics differently than what are embodied in the inherently subrelativistic Casimir-Polder integral, can one expect to escape this conclusion.

The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. Finally, we present strong evidence that all bound entangled states with positive partial transpose in ${\mathcal{C}}^3\otimes {\mathcal{C}}^3$ have Schmidt number 2.

We have calculated, independently, the ${}^{1}S$ singly differential cross section for the electron-impact ionization of hydrogen at an incident energy of 4.0 eV above threshold using two different methods: time-dependent close coupling and exterior complex scaling. The absolute value of the ${}^{1}S$ cross section for equal energy sharing is critical in assessing recent theoretical and experimental results for coplanar triply differential cross sections at low energies. Convergence of the cross section is studied as a function of the number of coupled channels. We find that at this energy the singly differential cross section is relatively flat over the entire ejected-energy range as predicted by semiclassical calculations.

The $2p$ photoelectron spectrum of free Mn atoms is presented. The experimental results are interpreted with the aid of Hartree-Fock calculations. Multiplet splitting and valence-shell recoupling in the core excited state give rise to the numerous main and satellite lines observed. The strong influence of these intra-atomic interactions on the Mn $2p$ photoelectron spectra of Mn compounds is verified by comparison of the corresponding spectra.

Fission of multiply charged sodium clusters ${\mathrm{Na}}_n^{q+}$ produced in collisions of neutral clusters with protons at 20 keV is investigated with an event-by-event acquisition technique. The analysis of fragment correlations shows that clusters undergo a strongly asymmetrical binary fission with ${\mathrm{Na}}^{+},\hspace{0.5em}{\mathrm{Na}}_2^{+},\hspace{0.5em}{\mathrm{Na}}_3^{+},\hspace{0.5em}{\mathrm{Na}}_4^{+},$ and ${\mathrm{Na}}_5^{+}$ as the small fragments, ${\mathrm{Na}}_3^{+}$ dominating with approximately 70%. For a given charge q, the branching ratio of ${\mathrm{Na}}_3^{+}$ over ${\mathrm{Na}}^{+}$ emission increases with n, which is interpreted in terms of a decreasing temperature of the parent cluster following proton impact.

We launch Cs atoms using a moving three-dimensional (3D) optical lattice. Atoms are initially spin polarized and cooled to the ground state of the optical potential using 3D Raman sideband cooling and then accelerated in the lattice to velocities of up to $3\hspace{0.5em}\mathrm{m}/\mathrm{s}.$ Subsequent adiabatic lowering of the potential releases the atoms from the lattice. Three-dimensional kinetic temperatures as low as $200\hspace{0.5em}\mathrm{nK}$ were achieved. The observed temperature of the launch is independent of the acceleration and final velocity of the atoms. In an alternative approach, we first accelerate the atoms to velocities of up to 5 m/s using moving molasses and then cool them with the lattice in the comoving frame of the atoms to temperatures as low as 150 nK.

We have measured the emission spectra of two-level-like atoms driven by a spatially inhomogeneous bichromatic field comprised of one resonant and one off-resonant component. Under these excitation conditions, observed spectra consist of several narrow peaks appearing on top of a broad continuumlike structure. This experimental approach provides for selective observation of those spectral features having a Rabi-frequency-independent emission frequency. Such emission processes involve multiphoton transitions, with one leg being spontaneous, between dressed-state levels differing only in their photonic quantum numbers; i.e., between equivalent dressed-state-doublet sublevels. Related vacuum-mediated transitions have recently been invoked as an underlying mechanism of inversionless gain.

It is demonstrated that stable, standing dark solitons can be created in current dilute-gas Bose-Einstein condensate experiments by the proper combination of phase and density engineering. Other combinations result in a widely controllable range of gray solitons. The phonon contribution is small and is calculated precisely. The ensuing dynamics should be observable in situ, i.e., without ballistic expansion of the condensate.

We show, both experimentally and theoretically, that sympathetic cooling of ${}^{87}\mathrm{Rb}$ atoms in the $|{F=2,m}_F=2\mathrm{}〉$ state by evaporatively cooled atoms in the $|{F=1,m}_F=-1〉$ state can be precisely controlled so as to produce a condensate in either or both states. We also study the thermalization rate between two species. Our model renders a quantitative account of the observed role of the overlap between the two clouds and verifies that sympathetic cooling becomes inefficient when the masses are very different. Our calculation also yields an analytical expression of the thermalization rate for a single species.

A method of fundamental solutions has been used to investigate transitions in two-energy-level-systems with no level crossing in a real time. Compact formulas for transition probabilities have been found in their exact form as well as in their adiabatic limit. No interference effects resulting from many-level complex crossings as announced by Joye, Mileti, and Pfister [Phys. Rev. A 44, 4280 (1991)] have been detected in either case. It is argued that these results of this work are incorrect. However, some effects of Berry’s phases are confirmed.