The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions.

It is shown that spin-flipping transitions in low energy collisions of ${}^2\Sigma$ diatomic molecules in the lowest rotational $N=0\mathrm{}$ level with structureless atoms proceed through coupling to the rotationally excited $N>\mathrm{}0\mathrm{}$ levels, and are determined by the spin-rotation interaction in the rotationally excited molecule. We carry out calculations for collisions of CaH and ${}^3\mathrm{He}.$ For the spin-flip rate coefficient corresponding to an interaction potential that does not generate a shape resonance, we obtain $1.20\times {10}^{-17}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at a temperature of 0.4 K consistent with the measured value of ${10}^{-17\pm 1}{\mathrm{cm}}^3{\mathrm{s}}^{-1}.$ We make predictions as to which molecules should have the least probability of spin-flipping in collisions with atoms.

We present an implementation of the convergent close-coupling (CCC) method, in which the Laguerre-based target states are replaced with box-based eigenstates. Discrete energies are obtained by taking the states that vanish at the box radius $R_0,$ with convergence being established by simply varying $R_0.$ Excellent agreement between box- and Laguerre-based CCC, exterior complex scaling, and renormalized experiment is obtained for one of the most difficult three-body Coulomb breakup problems, near-threshold electron-impact ionization of atomic hydrogen. The simplicity of the box-based CCC method is expected to lead to a greater understanding of the close-coupling formalism generally.

We show first reconstructions of the photon-number distribution obtained with a multichannel fiber-loop detector. Apart from analyzing the statistics of light pulses this device can serve as a sophisticated postselection device for experiments in quantum optics and quantum information. We quantify its efficiency by means of the Fisher information and compare it to the efficiency of the ideal photodetector.

The behavior of an atomic double $\Lambda$ system in the presence of a strong off-resonant classical field and a few-photon resonant quantum field is examined. It is shown that the system possesses properties that allow a single-photon state to be distilled from a multiphoton input wave packet. In addition, the system is also capable of functioning as an efficient photodetector discriminating between one- and two-photon wave packets with high efficiency.

An exact density matrix of a phase-damped Jaynes-Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single-mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local $2\times 2$ projections of the full $2\times \infty$ JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of the atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both the magnitude and phase of the Bell-like initial state contribution increase. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibit negative regions called “supercorrelated” states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times. It may be feasible to experimentally investigate the results presented here using the Rabi oscillation methods of microwave and optical cavity quantum electrodynamics since pure photon number states have recently been produced and observed.

We consider corrections to the Lamb shift of the p-wave atomic states due to the finite nuclear size (FNS). In other words, these are radiative corrections to the atomic isotope shift related to the FNS. It is shown that the structure of the corrections is qualitatively different to that for the s-wave states. The perturbation theory expansion for the relative correction for a $p_{1/2}$ state starts with a $\alpha \ln (1/Z\alpha )$ term, while for the $s_{1/2}$ states it starts with a $Z{\alpha }^2$ term. Here, $\alpha$ is the fine-structure constant and Z is the nuclear charge. In the present work, we calculate the $\alpha$ terms for that $2p$ states, the result for the ${2p}_{1/2}$ state reads $(8\mathrm{}\alpha /9\mathrm{}\pi )\mathbf{\{}\ln [1/(Z\alpha {)}^2]+0.710\mathrm{}\mathbf{\}}.$ Even more interesting are the $p_{3/2}$ states. In this case the “correction” is several orders of magnitude larger than the “leading” FNS shift. However, absolute values of energy shifts related to these corrections are very small.

We extend the analytical transfer matrix method to solve the energy splitting in an arbitrary symmetric double-well potential. Dispersion equations corresponding to the split energy levels are presented in a very explicit form. Numerical calculation shows that the proposed method can give extremely accurate results for symmetric double-well potentials.

We examine the appearance of Zeno and anti-Zeno effects when the unitary evolution of a two-level system is observed. We demonstrate that, contrary to previous claims, the anti-Zeno effect can occur in two-level systems so that the observation can enhance the transition probability. Moreover, for nonresonant couplings we show that the Zeno and anti-Zeno effects always appear sequentially in the evolution of the same system: there is Zeno effect in the short-time regime and anti-Zeno effect in the long-time regime.

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. Śliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schrödinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schrödinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of the Maxwell equations with embedded vortex lines are given. Vortex lines in the Laguerre-Gaussian beams are treated in some detail.

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum-information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular ${\sigma }_z{\sigma }_z$ system-environment couplings which induce coherence (phase) damping, although the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase damping, and we use this solution to describe the model’s behavior in some limiting cases. In the limit of small stochastic phase kicks the system’s coherence decays exponentially at a rate that increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on a nuclear magnetic resonance quantum-information processor.

We present the normal form of the covariance matrix for three-mode tripartite Gaussian states. By means of this result, the general form of a necessary and sufficient criterion for the possibility of a state transformation from one tripartite entangled Gaussian state to another with three modes is found. Moreover, we show that the conditions presented include not only inequalities but equalities as well.

The “pushing gate” proposed by Cirac and Zoller for quantum logic in ion traps is discussed, in which a force is used to give a controlled push to a pair of trapped ions and thus realize a phase gate. The original proposal had a weakness in that it involved a hidden extreme sensitivity to the size of the force. Also, the physical origin of this force was not fully addressed. Here, we discuss the sensitivity and present a way to avoid it by choosing the spatial form of the pushing force in an optimal way. We also analyze the effect of imperfections in a pair of $\pi$ pulses which are used to implement a “spin echo” to cancel correlated errors. We present a physical model for the force, namely, the dipole force, and discuss the impact of unwanted photon scattering, and of finite temperature of the ions. The main effect of the temperature is to blur the phase of the gate owing to the ions exploring a range of values of the force. When the distance scale of the force profile is smaller than the ion separation, this effect is more important than the high-order terms in the Coulomb repulsion which were originally discussed. Overall, we find that whereas the pushing gate is not as resistant to imperfection as was supposed, it remains a significant candidate for ion trap quantum computing since it does not require ground-state cooling, and in some cases it does not require the Lamb-Dicke limit, while the gate rate is fast, close to (rather than small compared to) the trap vibrational frequency.

A quantum key distribution scheme is described, in which a time (or phase) entangled-photon pair posteriorly generated by a single-photon source and a simple beam splitter. This scheme offers an efficient entanglement-based quantum key distribution system superior to the system using a standard parametric down-converter.

We introduce a protocol that maps finite-dimensional pure input states onto approximately Gaussian states in an iterative procedure. This protocol can be used to distill highly entangled bipartite Gaussian states from a supply of weakly entangled pure Gaussian states. The entire procedure requires only the use of passive optical elements and photon detectors, which solely distinguish between the presence and absence of photons.

We study a set of localized spins coupled through exchange interaction and subject to an external magnetic field. We demonstrate, for such a class of one-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the anisotropy parameter in the Hamiltonian and by introducing impurities into the systems. In particular, for certain parameters, the entanglement is zero up to a critical point ${\lambda }_c,$ where a quantum phase transition occurs, and is different from zero above ${\lambda }_c.$

We have studied collisions between ${\mathrm{D}}_2^{+}$ molecular ions and doubly charged projectiles at collision velocities ranging from 0.19 a.u. to 0.51 a.u. Using a molecular ion gives us the unique opportunity to investigate electron capture from a true one-electron, two-center target. The experimental results indicate that electron capture is preferred if the molecular axis is perpendicular to the collision velocity, independent of projectile and magnitude of collision velocity. We also present results from a theoretical model calculation. The calculation qualitatively supports the experimental findings, although some features in the calculation are not reproduced by the experiment. We discuss whether those features are natural.

We have measured kinetic energy releases in asymmetric fission, ${\mathrm{C}}_{60}^{r+}\to {\mathrm{C}}_{58}^{\left(r-1\right)+}+{\mathrm{C}}_2^{+}$ $(r=6\mathrm{}–9)$ and evaporation ${\mathrm{C}}_{60}^{r+}\to {\mathrm{C}}_{58}^{r+}+{\mathrm{C}}_2$ $\mathrm{}(r=2,3\mathrm{}),$ following multiple-electron removal from ${\mathrm{C}}_{60}$ in ${\mathrm{He}}^{2+}$ and ${\mathrm{Xe}}^{17+}$ collisions at $3q\mathrm{keV}\mathrm{}(q=2,17\mathrm{}).$ We used the recoil-ion momentum technique and limited the initial momentum distribution of the target molecules by collimation of the effusive ${\mathrm{C}}_{60}$ jet. This yielded a resolution of 3 meV for the final kinetic energies of the charged ${\mathrm{C}}_{58}$ fragments, mapped out as two-dimensional position distributions at the end of a linear time-of-flight mass spectrometer. The present results for asymmetric fission are in agreement with earlier ones deduced from time-of-flight ${\mathrm{C}}_2^{+}$ peak-shape and sector-field ${\mathrm{C}}_{58}^{\left(r-1\right)+}$-energy analysis. Model calculations treating ${\mathrm{C}}_{58}^{\left(r-1\right)+}$ and ${\mathrm{C}}_2^{+}$ as conducting spheres indicate that the autocharge-transfer process, which has been proposed to link asymmetric fission to neutral ${\mathrm{C}}_2$ emission, most likely is inactive for all r. Using a charge-independent activation energy for ${\mathrm{C}}_2$ emission from ${\mathrm{C}}_{60}^{r+}$ of $E_a=10\mathrm{}\mathrm{eV},$ we deduce fission barriers indicating lower (semiempirical) and upper (model) ${\mathrm{C}}_{60}^{r+}$-stability limits of $r=11\mathrm{}$ and $r=18,$ respectively.

Using high precision wave functions describing the triplet ground and excited ${}^{3}S$ states of the He atom and heliumlike ions, the cross sections of single- and double-electron photoionization are calculated. The dependence of the ratio R of the double and single ionization cross sections on the nuclear charge Z and the principal quantum number of excitation n is studied. The results obtained are compared to those for previously studied singlet states.

We have observed a frequency-domain photodetachment spectrum from trapped ${\mathrm{O}}^{-}$ in a magnetic field. The structure observed near threshold shows clear modulation of the relative detachment cross section due to the departing electron’s discrete cyclotron levels. The current results are shown to corroborate the experimental results from a previous time-domain investigation, and a value for the ${}^{16}\mathrm{O}$ electron affinity is reported.