Nonlocal dispersion cancellation is generalized to frequency-entangled states with large photon number N. We show that the same entangled states can simultaneously exhibit a factor of $1/\sqrt{N}$ reduction in noise below the classical shot noise limit in precise timing applications, as was previously suggested by Giovannetti, Lloyd, and Maccone [Nature (London) 412, 417 (2001)]. The quantum-mechanical noise reduction can be destroyed by a relatively small amount of uncompensated dispersion and entangled states of this kind have larger timing uncertainties than the corresponding classical states in that case. Similar results were obtained for correlated states, anticorrelated states, and frequency-entangled coherent states, which shows that these effects are a fundamental result of entanglement.

With a three-bit nuclear magnetic resonance quantum computer, we have experimentally realized a quantum search algorithm that can take a desired function value (or target) t as its input and give the corresponding function argument $x_0$ such that ${f(x}_0)=t$ as a result. The function value is not retrieved from an existing table, but evaluated by the search algorithm in the manner of a typical algorithmic search. A single-query version of the quantum search algorithm is used to search for one of two function arguments.

Numerical integration of the Schrödinger equation for the resonant single-photon excitation from the $1s$ to $10p$ state in atomic hydrogen has been used to produce solutions converged to a precision of a few parts per million. At all intensities investigated (in the range $10–100{\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^2),$ the population in the states having angular momentum higher than $\mathcal{l}=1\mathrm{}$ after a narrowband (500 fs) laser pulse are found to be neglible. This shows that off-resonant states can effectively suppress Raman-like transitions to degenerate states of higher angular momentum. Instead of such mixing, strong Rabi-like oscillations between $1s$ and the $\mathrm{np}$ Rydberg series are observed.

We investigate the effect of phase randomness in Ising-type quantum networks. These networks model a large class of physical systems. They describe micro- and nanostructures or arrays of optical elements such as beam splitters (interferometers) or parameteric amplifiers. Most of these stuctures are promising candidates for quantum information processing networks. We demonstrate that such systems exhibit two very distinct types of behavior. For certain network configurations (parameters), they show quantum localization similar to Anderson localization whereas classical stochastic behavior is observed in other cases. We relate these findings to the standard theory of quantum localization.

There are two density-functional approaches to obtaining the transition energies of many-electron systems. One involves taking the difference of the excited-state and the ground-state energies, both obtained by static density-functional calculation, and the other involves applying the time-dependent density-functional method. In this paper, we apply both methods to get transition energies of low-lying excited states of some open-shell atomic systems and compare their accuracy. We find that while both methods give accurate energies for most of the systems, they lead, inexplicably, to substantial errors in some cases.

We calculate the elementary excitations and pairing of a trapped atomic Fermi gas in the superfluid phase. The level spectra and pairing gaps undergo several transitions as the strength of the interactions between atoms and the number of atoms are varied. For weak interactions, the Cooper pairs are formed between particles residing in the same harmonic oscillator shell. In this regime, the nature of the paired state is shown to depend critically on the position of the chemical potential relative to the harmonic oscillator shells and on the size of the mean field. For stronger interactions, we find a region where pairing occur between time-reversed harmonic oscillator states in different shells also.

We develop a systematic analytical approach to consider the dynamics of linear and nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with repulsive atom-atom interactions. We show that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigenmodes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. The linear excitations of the system have a Bogoliubov-type spectrum with the excitation frequency varying slowly along the axial direction. We find that, in a weak nonlinear approximation, the amplitude of a nonlinear excitation is governed by a variable coefficient Korteweg–de Vries equation with additional terms contributed from the transverse structure and the inhomogeneity in the axial direction of the condensate, which results in varying amplitude, width, and velocity for dark solitons. Because of the inhomogeneity the dark solitons undergo deformation and emit radiations when traveling along the axial direction. We finally demonstrate that a dark soliton will disintegrate into several ones plus a residual wave train when passing over a steplike potential.

The behavior of an ideal D-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrary to a long-standing belief, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at $T\ne 0$ for $D=1,2,3\mathrm{}$ if there is a pointlike impurity at the bottom of the vessel containing the gas.

A mechanism for the stabilization of the output of filamentary broad-area edge-emitting semiconductor lasers is analyzed experimentally and theoretically. This mechanism occurs when the carrier density is profiled in the transverse direction. The laser structure consisted of a wide-aperture edge-emitting laser diode operating in pulsed mode to avoid thermal guiding effects. The injection current profile was modified from the usual step-function case to a Lorentzian-like profile through the inclusion of a 10 μm p-type epitaxial spreading layer. The resulting nonlinear transverse mode is described and the possibility of its observation in two transverse dimensions is discussed.

Femtosecond stimulated emission pumping has been employed as a technique to prepare small clusters with well-known amounts of internal excitation. In this way ${\mathrm{I}}_2^{-}({\mathrm{CO}}_2{)}_{4,5}$ clusters are prepared with 0.58 to 0.99 eV of internal energy. Subsequent evaporation of between two and four ${\mathrm{CO}}_2$ monomers from the primary cluster is observed as a function of excitation energy using tandem time-of-flight mass spectrometry. Analysis of the appearance energies of the open channels using phase-space theory and photoelectron spectroscopy data yields binding energies of the first eight ${\mathrm{CO}}_2$ molecules to ${\mathrm{I}}_2^{-}({\mathrm{CO}}_2{)}_n$ clusters.

This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, tilted, time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework leading to fully analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics.

We perform and compare different analyses of triply degenerate four-wave mixing in the regime where three fields of the same frequency interact via a nonlinear medium with a field at three times the frequency. As the generalized Fokker-Planck equation (GFPE) for the positive-$P$ function of this system contains third-order derivatives, there is no mapping onto genuine stochastic differential equations. Using techniques of quantum field theory, we are able to write stochastic difference equations that we may integrate numerically. We compare the results of this method with those obtained by the use of approximations based on semiclassical equations, and on truncation of the GFPE leading to stochastic differential equations. In the region where the difference equations converge, the stochastic methods agree for the field intensities, but give different predictions for the quantum statistics.

We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry, we understand that the transformation $\{|+\overrightarrow{〉}|+〉,|-\overrightarrow{〉}-|-〉\}$ leaves the set of states invariant. The obtained measurement strategy minimizes the error probability. An experimental realization for polarized photons, realizable with current technology, is suggested.

The predissociation decay behavior of molecule carbonyl sulfide (OCS) has been investigated by resonance-enhanced multiphoton ionization spectroscopy using the pump-probe technique of dichroic femtosecond lasers in real time. The lifetime of excited OCS around $74720\hspace{0.5em}{\mathrm{cm}}^{-1}$ by two-photon absorption of 268 nm, corresponding to ${\upsilon }_1=1\mathrm{}$ of the Rydberg state ${[}^2{\Pi }_{1/2}\left]4p\pi {(}^1{\Sigma }^{+}\right),$ is directly determined to be ${\tau }_D=1071\mathrm{}\pm 11\hspace{0.5em}\mathrm{fs}.$ This picosecond decay process indicates that the excited state is predissociative. The temporal information of dissociation enriches the knowledge of the potential-energy surface of the associative excited state.

The kinetic-energy distributions of fragment ions formed in slow ${\mathrm{Xe}}^{25+}-{\mathrm{C}}_{60}$ collisions have been determined with high-resolution time-of-flight mass spectrometry. The energy releases as well as the fragment size distributions are analyzed as functions of the number of electrons stabilized at the projectile, i.e., as a function of the average charge state of the intermediately formed ${\mathrm{C}}_{60}$ molecular ion. The evaluated energy releases are much higher than those reported for multiply charged ion collisions performed at high energies. The obtained results are consistent with the Coulomb explosion model, a fact which can be understood in terms of the high charge states involved.

We have measured the probability of inner-electron ionization (IEI) of Sr $5s16l$ atoms when exposed to intense 230-fs laser pulses. We find that the probability of IEI rises sharply at $l=5\mathrm{}$ and is approximately equal to one for $l>\mathrm{}5\mathrm{}$. For $l=5\mathrm{}$ the classical inner-turning point is at ${15a}_0$, far greater than the size of the Sr${}^{+}$ ionic core, ruling out core penetration as the factor governing inner-electron ionization. For the Sr ${5p}_{1/2}16l$ states of $l>\mathrm{}5\mathrm{}$ the autoionization lifetime, which is due to the electrostatic interaction between two-valence electrons, is greater than the Kepler orbit time. These comparisons suggest that both inner-electron ionization and autoionization are governed by long-range electrostatic interactions.

We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent-state description assumed within the Gross-Pitaevskii mean-field approach. Continuous weak measurements allow us instead to replace, for time scales short enough, the exact problem with its mean-field approximation through a stochastic analog of the Gross-Pitaevskii equation. The latter is used to show the unwinding of a dark soliton undergoing a continuous imaging.

We demonstrate high-order harmonic generation in high-density vapors of laser-aligned molecules. Ensembles of aligned ${\mathrm{CS}}_2$ and ${\mathrm{N}}_2$ are formed in the focus of a 300 ps duration laser pulse with sufficient density $(\sim {10}^{17}$ molecules ${\mathrm{cm}}^{\mathrm{-}3}$) to enable efficient high-order harmonic generation by a second, 70-fs, high-intensity laser pulse. We are able to modulate and significantly enhance the harmonic intensity in aligned molecules compared to the randomly oriented case. Our results are explained by considering the influence of an anisotropic dipole phase. Strong support for this interpretation is provided by theoretical results for high-order harmonic generation in the aligned ${\mathrm{H}}_2^{+}$ model system.

Simple thermodynamics considers kinetic energy to be an extensive variable which is proportional to the number N of particles. We present a quantum state of N noninteracting particles for which the kinetic energy increases quadratically with N. This enhancement effect is tied to the quantum centrifugal potential whose strength is quadratic in the number of dimensions of configuration space.