We consider quantum systems that interact strongly with a rapidly varying environment and derive a Schrödinger-like equation that describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be taken to be Hermitian provided all states are rotated using an appropriate-unitary transformation. The formalism is applied to a variety of systems and is compared and contrasted with related results describing stochastic resonances.

We present a unified treatment of three cases of quasi-exactly-solvable problems, namely, a charged particle moving in Coulomb and magnetic fields for both the Schrödinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasiexactly solvable owing to the existence of a hidden ${\mathrm{sl}}_2$ algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytical expressions of the energies and the allowed frequencies for the three cases are given in terms of roots of one and the same set of Bethe ansatz equations.

We study how correlations in a state of an open quantum system affect the intrinsic uncertainties of the expectation values of an arbitrary pair of noncommuting observables. We show that for such observables, there exist Heisenberg-type uncertainty relations that take fully into account correlations in the state of the system. If the quantum system is in a pure state, such uncertainty relations reduce to the conventional one. We obtain an equation for the density operator of a general state that minimizes the new uncertainty relations, and demonstrate that in the important case of coordinate and momentum operators, the minimum-uncertainty states are displaced squeezed thermal states.

We describe an algorithm for converting one bipartite quantum state into another using only local operations and classical communication, which is much simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436 (1999)]. Our algorithm uses only a single measurement by one of the parties, followed by local unitary operations which are permutations in the local Schmidt bases.

We present a study of the influence of a constant uniform electric field on the doubly excited resonances of the negative positronium ion associated with the $N=2\mathrm{}$ positronium threshold. The calculation is performed in the framework of the complex coordinate rotation method, allowing us to obtain positions and widths of the resonance states. Results are given for the $M=0\mathrm{}$ Stark components of the following Feshbach resonances associated with the $N=2\mathrm{}$ positronium threshold: ${}^1{S}^e\mathrm{}\left(1\right),$ ${}^1{S}^e\mathrm{}\left(2\right),$ ${}^1{S}^e\mathrm{}\left(3\right),$ ${}^1{P}^o\mathrm{}\left(1\right),$ ${}^1{P}^o\mathrm{}\left(2\right),$ ${}^1{D}^e\mathrm{}\left(1\right),$ and ${}^1{D}^e\mathrm{}\left(2\right).$

Low-energy electron collisions with the HBr and DBr molecules are addressed from the experimental and theoretical points of view. Relative differential cross sections for the excitation of vibrational levels of HBr and DBr up to $v=6\mathrm{}$ have been measured as a function of the incident electron energy in the range 0–4 eV. In addition to the shape resonance near 2 eV collision energy, intense and narrow threshold peaks are found for the excitation of the $v=1\mathrm{}$ level of HBr and the $v=1\mathrm{}$ and $v=2\mathrm{}$ levels of DBr. Measurements with high resolution for rotationally cooled molecules have revealed the existence of sharp oscillatory structures in the elastic and $v=\overrightarrow{0}1$ cross sections in a narrow range below the dissociative-attachment threshold. The dissociative-attachment cross section has been measured with high resolution of the incident electrons in the range 0.2–1.4 eV. The theoretical analysis is based on an improved nonlocal resonance model, which has been constructed on the basis of existing fixed-nuclei electron-HBr scattering phase shifts and accurate ab initio calculations of the bound part of the ${\mathrm{HBr}}^{-}$ potential-energy function. This purely ab initio-based model is used to calculate integral electron-scattering and dissociative-attachment cross sections for HBr and DBr. The theoretical cross sections agree very well with the experimental data. The observed threshold peaks and Wigner cusp structures in the vibrational excitation functions are correctly reproduced. The sharp structures in the $v=\overrightarrow{0}0$ and $v=\overrightarrow{0}1$ cross sections below the dissociative-attachment threshold, consisting of a superposition of boomerang-type oscillations and quasibound levels of the outer well of the ${\mathrm{HBr}}^{-}$ potential-energy function, are quantitatively described by the theory. The high degree of agreement between experiment and theory indicates that the essentials of low-energy electron-HBr collision dynamics are completely understood.

The multifold differential cross section of the ionization of hydrogen molecular ion by fast-electron impact is calculated by a direct approach, which involves the reduction of the initial six-dimensional (6D) Schrödinger equation to a 3D evolution problem followed by the numerical modeling of the wave-packet dynamics. This approach avoids the use of stationary Coulomb two-center functions of the continuous spectrum of the ejected electron that demands cumbersome calculations. The results obtained, after verification of the procedure in the case of atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.

As demonstrated by Boto et al. [Phys. Rev. Lett. 85, 2733 (2000)], quantum lithography offers an increase in resolution below the diffraction limit. Here, we generalize this procedure in order to create patterns in one and two dimensions. This renders quantum lithography a potentially useful tool in nanotechnology.

We present a simple scheme for generating topological phase states such as dark soliton and vortex states of a spinor Bose-Einstein condensate using applied magnetic fields. The realization of complex composite spinor vortices is described and we examine the subsequent dynamical evolution of these states.

We present a Green’s-function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in mesoscopic systems containing a large number N of Fermi particles moving independently on a line under an external potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux density, entering the equations of generalized hydrodynamics, and the kinetic energy density, which is relevant to the density-functional theory. As a further application of the method we explicitly display the quantum mean square fluctuations of these quantities. We also study some properties of the kinetic energy functional $E_{\mathrm{kin}}\left[n\right(x\left)\mathrm{}\right]$ in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relationship between the density derivative of $E_{\mathrm{kin}}\left[n\right(x\left)\mathrm{}\right]$ and the particle density $n\left(x\right)\mathrm{}$ is demonstrated and evaluated for various values of the number of particles in the system.

The problem of field quantization in a half space is discussed based on the detector modes, which provide a useful basis for the study of atomic or molecular interaction with radiation modes involving evanescent electromagnetic waves. The detector modes, each of which involves a single outgoing wave, are introduced in terms of the time-reversal and spatial-rotation transforms of the widely used triplet modes given by Carniglia and Mandel. The derivation of the orthogonal relation for the detector modes is therefore straightforward. We represent the creation and annihilation operators for the detector modes in terms of those for the triplet modes, and obtain the field operator, Hamiltonian, number operator, and pseudomomentum operator. Based on this formalism, we evaluate the differential radiation probability for atomic dipole radiation near a dielectric surface. The evaluation of the final-state mode density is straightforward for the detector modes involving single outgoing waves. With respect to the image dipole picture, the quantum-to-classical correspondence is clear in the detector-mode formalism.

Generation and propagation of high-order harmonics by intense, ultrashort laser pulses in static gas cells and gas-filled hollow waveguides are numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schrödinger and wave equations. It is shown that, when the 30-fs laser pulse is focused into a gas cell the emission spectrum consists of discrete and well-resolved harmonics. These high-order harmonics can be used for generation of a train of subfemtosecond pulses. When the 5-fs laser pulse propagates along a gas-filled hollow waveguide the emission spectrum exhibits a quasicontinous structure that permits the generation of a single subfemtosecond pulse. The effects of laser intensity and position of the interacting medium relative to the laser focus on the emission spectrum and pulse profile are investigated. The differences between results obtained by our model and by the model that uses the strong-field approximation for single-atom calculations are discussed.

We employ the maximum entropy ansatz to obtain reasonably accurate densities for a few quantum oscillators and discrete dynamical systems. An optimization scheme is suggested that does not require any a priori knowledge of values for moments. Instead, moment recursion relations are used as constraints. Pilot calculations, with trial densities conforming to correct asymptotic behavior as and when necessary, reveal the advantages readily.

With a beam of unenriched lanthanum, the hyperfine structure (hfs) of ${}^{138,139}\mathrm{La}$ has been measured for the transition from the ${5d6s}^2{}^2{D}_{3/2}$ ground state to the $5d6s6p{}^4{F}_{5/2}$ level at 675.304 nm by means of atomic-beam diode-laser spectroscopy. Magnetic-dipole (A) and electric-quadrupole $\mathrm{}\left(B\right)\mathrm{}\mathrm{hfs}$ constants of the 0.090% abundant ${}^{138}\mathrm{La},$ as well as those of ${}^{139}\mathrm{La},$ have been determined for the ${5d6s}^2{}^2{D}_{3/2}$ and $5d6s6p{}^4{F}_{5/2}$ levels; this serves as a measurement of hyperfine structure constants A and B for ${}^{138}\mathrm{La}.$ The isotope shift between ${}^{139}\mathrm{La}$ and ${}^{138}\mathrm{La}$ has been obtained for the 675.304-nm transition and change in mean-square nuclear charge radii $\delta 〈r^2〉$ derived.

It is shown that by an appropriate modification of the trapping potential, one may create collective excitation in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally—it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.

We have performed ab initio mixed-states and sum-over-states calculations of parity-nonconserving (PNC) electric dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transition amplitudes between $s-d$ electron states of Cs, Fr, ${\mathrm{Ba}}^{+},$ and ${\mathrm{Ra}}^{+}.$ For the lower states of these atoms we have also calculated energies, $E1\mathrm{}$ transition amplitudes, and lifetimes. We have shown that PNC $E1\mathrm{}$ amplitudes between $s-d$ states can be calculated to high accuracy. Contrary to the Cs $6s-7s$ transition, in these transitions there are no strong cancellations between different terms in the sum-over-states approach. In fact, there is one dominating term which deviates from the sum by less than $20\%.$ This term corresponds to an ${s-p}_{1/2}$ weak matrix element, which can be calculated with an accuracy of better than $1\%,$ and a $p_{1/2}{-d}_{3/2}$ $E1\mathrm{}$ transition amplitude, which can be measured. Also, the $s-d$ amplitudes are about four times larger than the corresponding $s-s$ amplitudes. We have shown that by using a hybrid mixed-states–sum-over-states approach the accuracy of the calculations of PNC $s-d$ amplitudes could compete with that of Cs $6s-7s$ if $p_{1/2}{-d}_{3/2}$ $E1\mathrm{}$ amplitudes are measured to high accuracy.

We present a scheme for demonstrating the violation of Bell’s inequalities using a spin-$\frac{1}{2}$ system entangled with a pair of classically distinguishable wave packets in a harmonic potential. For electromagnetic fields, such wave packets can be represented by coherent states of a single radiation mode. The proposed scheme involves standard spin-$\frac{1}{2}$ projections and continuous measurements of the position and the momentum of the harmonic-oscillator system, which for a radiation mode can be realized by means of homodyne detection. We discuss effects of imperfections, including nonunit efficiency of the detectors, and analyze a direct link between the visibility of interference and the violation of Bell’s inequalities in the described scheme. We also point out the role of Bell’s inequalities as a sensitive probe for decoherence effects.

In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.

An analogous model system for quantum information processing is discussed, based on classical wave optics. The model system is applied to three examples that involve three qubits: (i) three-particle Greenberger-Horne-Zeilinger entanglement, (ii) quantum teleportation, and (iii) a simple quantum error correction network. It is found that the model system can successfully simulate most features of entanglement, but fails to simulate quantum nonlocality. Investigations of how far the classical simulation can be pushed show that quantum nonlocality is the essential ingredient of a quantum computer, even more so than entanglement. The well-known problem of exponential resources required for a classical simulation of a quantum computer, is also linked to the nonlocal nature of entanglement, rather than to the nonfactorizability of the state vector.

The nuclear polarization (NP) correction is calculated for the ground states of the hydrogenlike ${}_{\hspace{0.5em}82}^{208}\mathrm{Pb}$ and ${}_{\hspace{0.5em}92}^{238}\mathrm{U}\mathrm{}$ ions. We take into account the transverse interaction, ignored in the previous studies, as well as the Coulomb interaction. The NP correction is formulated in the bound-state QED formalism with the ladder and cross diagrams of two-photon exchange between an electron and a nucleus. We take into account nuclear excitations of low-lying states and giant resonances with multipolarities of ${\lambda }^{\pi }{=0\mathrm{}}^{+},$ $1^{-},$ $2^{+},$ and $3^{-},$ and describe them in a collective model. The NP corrections are obtained to be $-0.2$ and $-180.7$ meV, respectively, for ${}_{\hspace{0.5em}82}^{208}\mathrm{Pb}$ and ${}_{\hspace{0.5em}92}^{238}\mathrm{U}.$ The effect of the transverse interaction is found to be essential to the NP correction for electric dipole giant resonances, strongly canceling a contribution of the Coulomb interaction. Dependence of the NP correction on different nuclear excitations is investigated.