We analyze the possibility and efficiency of nonholonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary units of arbitrary physical nature, and can be employed efficiently for universal quantum computations and simulation of quantum-field dynamics. As an example we describe a toy device that can perform Toffoli-gate transformations and discrete Fourier transform on 9 qubits.

We propose an optimal strategy for continuous-variable teleportation in a realistic situation. We show that the typical imperfect quantum operation can be described as a combination of an asymmetrically decohered quantum channel and perfect apparatuses for other operations. For the asymmetrically decohered quantum channel, we find some counterintuitive results: teleportation does not necessarily get better as the channel is initially squeezed more. We show that decoherence-assisted measurement and transformation may enhance fidelity for an asymmetrically mixed quantum channel.

Experimental cross sections in the extreme ultraviolet (EUV) wavelength range for the excitation of helium following electron and ${\mathrm{H}}^{+},$ ${\mathrm{H}}_2^{+},$ and ${\mathrm{H}}_3^{+}$ ion impact are presented for $\mathrm{He}\mathrm{}I$ $\mathrm{}\left(1snp\right)\mathrm{}$ ${}^1{P}^o$ states with $n=2\mathrm{}–5.$ These measurements extend over large velocity ranges 3.8–8.5 a.u. for electrons, 1.4–7.5 a.u. for protons, and 1.4–4.0 a.u. for ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$ ions, respectively, and represent the most complete data set obtained so far in the EUV. Furthermore, the methods of convergent close coupling and R matrix with pseudostates have been used here to predict excitation cross sections for the $\mathrm{He}\mathrm{}I$ $\mathrm{}\left(1snp\right)\mathrm{}$ ${}^1{P}^o$ states following electron impact and the atomic-orbital close-coupling expansion for proton impact. In particular, our theoretical results are presented and compared with our EUV experimental cross sections for equal projectile velocities together with previous experimental results, including cross sections derived from scaling procedures. The electron cross sections are found to deviate from the proton data at intermediate and lower energies $(v<\mathrm{}3.8\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}).\mathrm{}$

A retardation correction to the high-energy limit of the dipole photoionization cross section and to the ratio of the double-to-single electron photoionization cross sections is calculated. This correction comes from the quasifree mechanism of the two-electron photoionization and is determined by the probability to find both ionizing electrons at the same point in the initial state. The calculations are performed for ${\mathrm{H}}^{-},$ the helium atom and the heliumlike ions in the ground and some excited states using high-precision wave functions. The nuclear charge dependence of this correction for heliumlike ions in the ground and four lowest ${}^{1}S$ exited states is calculated. The possibility to detect this correction experimentally is discussed.

The photodetachment cross section of the $1s2s2p{}^4{P}^o$ metastable state of ${\mathrm{He}}^{-}$ in the region of the $1s$ threshold has been calculated using our enhanced R-matrix code with the asymptotic part upgraded to handle a negative-ion system. The results show a $1s$ photodetachment cross section with numerous structures, completely different from similar situations in atoms or positive ions. This is found to be due to the dominance of correlation of both initial and final states of the negative ion. Specifically, interchannel coupling and a newly identified multiconfiguration overlap effect are primarily responsible for the dramatic $1s$ photodetachment cross-section phenomenology. Comparison with a previous calculation has been made and, while there are some areas of excellent agreement, overall there are very serious discrepancies, as much as an order of magnitude.

We report an experimental observation of doubly dressed states in ${}^{87}\mathrm{Rb}$ atoms cooled and confined in a magneto-optical trap. The doubly dressed states are produced by a strong-coupling laser and a moderate pump laser in a three-level atomic configuration. The absorption spectrum of a weak probe laser reveals a three-peaked spectral profile that can be interpreted by a dressed-state picture and agrees well with calculations based on the density-matrix equations.

The population dynamics of a two-level system coherently driven by oscillating transverse and longitudinal fields is investigated under the condition that the frequency of longitudinal component is much faster than the characteristic time of a population change due to the transverse component. The approximation of coherent averaging over rapid oscillation is successfully applied to the analysis of transition dynamics, and it is shown that a new type of dynamical localization occurs for a wide range of frequency ratio of the transverse and longitudinal fields.

The evolution and collision of dark solitary waves (solitons) appearing in cigar-shaped Bose-Einstein condensates with repulsive atom-atom interaction are here considered using a Boussinesq-Korteweg–de Vries description. We provide theoretical predictions and computer experiment evidence about their phase shifts or change of trajectories, in the space-time plot, corresponding upon collisions. Details are also given about a suggested experiment that could assess their genuine solitonic nature.

We consider the effect of interactions on the line shape of the two-photon $1s-2s$ transition in a (doubly) spin-polarized atomic hydrogen gas in terms of the interatomic interaction potentials. We show that the frequency-weighted sum rule for the intensity of the line is not given simply in terms of the pseudopotentials that describe the interactions between low-energy atoms. The origin of the departures from the simple pseudopotential result for the frequency-weighted sum rule is traced to what we refer to as incoherent contributions to the spectral weight. These arise from more complicated final states of the many-body systems than the ones usually considered. In particular, we show how the relevant response function may be treated in a manner similar to the density-density response function for Fermi liquids, and express it as a coherent part coming from single particle-hole pairs, and an incoherent part coming from other excitations. We argue that in experiments only the coherent part of the response of the system is observed, and its contribution to the frequency-weighted sum rule is shown to be given correctly by the pseudopotential approximation. Finally we calculate the width of the coherent part of the line due to collisional damping.

The hydrodynamic equations of an ideal fluid formed by a dilute quantum gas in a parabolic trapping potential are studied analytically and numerically. Due to the appearance of internal modes in the fluid stratified by the trapping potential, the spectrum of low-lying modes is found to be dense in the high-temperature limit, with an infinitely degenerate set of zero-frequency modes. The spectrum for Bose fluids and Fermi fluids is obtained and discussed.

Light propagation in a photonic crystal with incomplete band gap, infiltrated with polarizable molecules is considered. We demonstrate that the interplay between the spatial dispersion caused by Bragg diffraction and polaritonic frequency dispersion gives rise to alternative propagating excitations, or photonic-crystal-polaritons (PCP), with intragap frequencies. We derive the PCP dispersion relation and show that it is governed by two parameters, namely, the strength of light-matter interaction and detuning between the Bragg frequency and that of the infiltrated molecules. We also study defect-induced states when the photonic band gap is divided into two subgaps by the PCP branches and find that each defect creates two intragap localized states inside each subgap.

We study the propagation of a drive and probe bichromatic field in a compound electronuclear system [Opt. Commun. 179, 525 (2000)] from the viewpoint of inversionless amplification. In the regimes of adiabatic pulse and steady-state propagation, part of the ground-state population is trapped in a dark state thereby reducing the absorption of a probe field. This is reinforced by spontaneous emission for the steady-state case, for which the optimal amplification length is calculated. Beyond this length, the medium becomes absorbent for the probe field. In the complementary limit of ultrashort pulses, the medium reduces to a V scheme in which the drive field can self-induce transparency.

We demonstrate a systematic approach to subwavelength resolution lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of $\lambda /\left[2\right(N+1\mathrm{}\left)\mathrm{}\right]$ by using a particular 2M-photon, multimode entangled state, where $N<~M,$ and banks of birefringent plates. By preparing such a statistically mixed state, one can form any pixel pattern on a $2^{M-N}\mathrm{}(N+1\mathrm{})\mathrm{}\times 2^{M-N}\mathrm{}(N+1\mathrm{})\mathrm{}$ pixel grid occupying a square with side ${L=2\mathrm{}}^{M-N-1}\lambda .$ Hence, there is a trade off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under nonideal conditions, albeit with somewhat poorer performance.

Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as $|i_1{i}_2\cdots i_n〉$ with $i_j$ being either 0 or 1, but it is a nontrivial task to construct an arbitrary superposed quantum state. We present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires ${O(Nn}^2)$ standard 1- and 2-bit gate operations, without introducing additional quantum bits. Application of the scheme in some special cases is discussed.

The dynamics of two-component Bose-Einstein condensates with coupling drive is studied using a pair of bosonic operators. We demonstrate that the effect of the coupling drive on the evolution of the relative phase of the two-component Bose-Einstein condensates depends on the initial relative phase difference between the two condensates. In some special initial phase differences $(\phi =0\mathrm{}$ and $\pi )$ the condensate density are not sinusoidal functions of time, and the interference pattern is not steady either. The coupling drive also reduces the amplitude and the period of the oscillation. Our theoretical result confirms the experimental observations reported in Phys. Rev. Lett. 81, 1543 (1998).

Recently, Olavo has proposed several derivations of the Schrödinger equation from different sets of hypothesis [Phys. Rev. A 61, 052109 (2000)]. One of them is based on the infinitesimal inverse Weyl transform of a classically evolved phase-space density. We show, however, that the Schrödinger equation can only be obtained in that manner for linear or quadratic potential functions.

Double-pair emission from type-II parametric down-conversion results in a highly entangled four-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and construct a Bell-type inequality, which gives a necessary and sufficient condition for a four-photon test of local realistic hidden variable theories.

We construct a Heisenberg-like algebra for the one-dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic-oscillator algebra. These physical operators are obtained with the help of variables used in a recently developed noncommutative differential calculus. This “square-well algebra” is an example of an algebra in a large class of generalized Heisenberg algebras recently constructed. This class of algebras also contains q oscillators as a particular case. We also discuss the physical content of this large class of algebras.

The energy and Auger width for the singly core-excited Be-like ${1s2s}^{2}2p{}^3{P}^o,$ ${\mathrm{}\left(1s2s\right)\mathrm{}}^3{S,2p}^2{}^{3}P,$ ${\mathrm{}\left(1s2s\right)\mathrm{}}^1{S,2p}^2{}^{3}P,$ and ${1s2s2p}^2{}^3{S}^{3}D$ states are calculated using a saddle-point complex-rotation method. The decay branching ratios of these states are calculated to check the spin-alignment-dependent Auger decay theory recently proposed by Chung. These branching ratios also enable us to make many positive identifications in the observed Auger spectra. In addition, the photoionization cross section (PICS) from the Be ${1s}^{2}2s2p{}^3{P}^o$ state is calculated for photon energies from 30 eV to 125 eV, including the resonance region. Accurate initial and final state wave functions are used. We find that although the Auger width of the ${\mathrm{}\left(1s2s\right)\mathrm{}}^3{S,2p}^2{}^{3}P$ transition is smaller than that of ${\mathrm{}\left(1s2s\right)\mathrm{}}^1{S,2p}^2{}^{3}P$ by a factor of 2.5, its peak PICS is larger by a factor of more than 300.

Due to a transient quantum interference during a wave packet collision with a potential barrier, a particular momentum, that depends on the potential parameters, but is close to the initial average momentum, becomes suppressed. The hole left pushes the momentum distribution outwards leading to a significant constructive enhancement of lower and higher momenta. This is explained in the momentum complex-plane language in terms of a saddle point and two contiguous “structural” poles, which are not associated with resonances but with incident and transmitted components of the wave function.