We study the quantum dynamics of a model of molecular matter-wave amplifier proposed by Search and Meystre [Phys. Rev. Lett. 93, 140405 (2004)], which employs a strongly damped optical cavity to convert an atomic Bose-Einstein condensate into vibrational ground-state molecules. By using the Monte Carlo wave-function method, we calculate the quantum evolution of the atomic and molecular matter waves. We find that the system always evolves into a pure ground-state molecular matter wave even if initially there was no ground-state molecules. Statistical properties of these atomic and molecular matter waves are also investigated. The final state of the molecular field is sub-Poissonian. Two-mode correlation functions exhibit anticorrelated properties.

We consider the adiabatic evolution of an atom-molecule dark state in a collisional two-color Raman photoassociation condensate system. By linking nonadiabaticity with the population growth in the collective excitations of the dark state, we develop an adiabatic theorem where we have consistently addressed the issues related to the Goldstone mode and the biorthonormality of the collective modes. We apply this theorem to specific examples to demonstrate its use in designing pulses that can optimize the yield of ground molecule production in the stimulated Raman adiabatic passage process.

We show that the phase of a condensate in a finite temperature gas spreads linearly in time at long times rather than in a diffusive way. This result is supported by classical field simulations, and analytical calculations which are generalized to the quantum case under the assumption of quantum ergodicity in the system. This superdiffusive behavior is intimately related to conservation of energy during the free evolution of the system and to fluctuations of energy in the prepared initial state.

We discuss the issue of measuring the mean position (center of mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultralow temperatures, and discuss this limit in the context of both photons and ultracold atoms. In the case of non-interacting harmonically trapped fermions, we present evidence that the Pauli exclusion principle has a strongly beneficial effect, giving rise to a $1∕N$ scaling in the position standard deviation—as opposed to a $1∕\sqrt{N}$ scaling for bosons. The difference between the actual mean-position fluctuation and this limit is evidence for quantum wave-packet spreading in the center of mass. This macroscopic quantum effect cannot be readily observed for noninteracting particles, due to classical pulse broadening. For this reason, we also study the evolution of photonic and matter-wave solitons, where classical dispersion is suppressed. In the photonic case, we show that the intrinsic quantum diffusion of the mean position can contribute significantly to uncertainties in soliton pulse arrival times. We also discuss ways in which the relatively long lifetimes of attractive bosons in matter-wave solitons may be used to demonstrate quantum interference between massive objects composed of thousands of particles.

By using a three-dimensional finite-difference time-domain parallel code, the linear and nonlinear propagation of light pulses in a disordered assembly of scatterers, generated by a molecular dynamics code, is simulated. We calculate the static and dynamical light diffusion constant and the transmission in the presence of localized states. We numerically demonstrate the “modulational instability random laser”: at high input peak power, energy is transferred to localized states from the input pulse, resulting in a power-dependent nonexponential time decay of the transmitted pulse.

We examine the mode structures of photons emitted by collective spontaneous decay of $N_A>1$ excited atoms confined in a small volume. By introducing the notion of dynamical modes, we show how the emission process selects a set of time-dependent mode functions in which photons are optimally occupied. In particular we show that the effective number of such dynamical modes is governed by the separability of the two-time correlation function of atomic dipoles. Due to the nonlinearity of atomic dipoles and quantum fluctuations, more than one mode can be involved even in the large-atom-number limit.

We describe the theory of paired photon generation in a double-$\Lambda$ atomic system. Using the Heisenberg-Langevin formalism we evaluate and analyze the spectral generation rates and intensity correlation function for the output fields. Different regimes of parametric down conversion are analyzed. We discuss the influence of the optical depth and Langevin noise fluctuations on the paired photon generation and predict that at the optical depth of 100 or more the contribution of Langevin noise fluctuations is small and therefore Stokes and anti-Stokes photons are generated mostly in pairs. Comparison between the theory and experiments shows good agreement.

We have demonstrated purification of a single qubit by two collinear photons, one of which was time-delayed. Our method can be applied to a single qubit many times, and the qubit can be purified to an arbitrarily high degree of purity. Thus, by repeating this method we can make the statistical error that single qubits incur along a transmission channel much smaller.

In this paper we address the question: where in configuration space is the entanglement between two particles located? We present a thought experiment, equally applicable to discrete or continuous-variable systems, in which one or both parties makes a preliminary measurement of the state with only enough resolution to determine whether or not the particle resides in a chosen region, before attempting to make use of the entanglement. We argue that this provides an operational answer to the question of how much entanglement was originally located within the chosen region. We illustrate the approach in a spin system, and also in a pair of coupled harmonic oscillators. Our approach is particularly simple to implement for pure states, since in this case the subensemble in which the system is definitely located in the restricted region after the measurement is also pure, and hence its entanglement can be simply characterized by the entropy of the reduced density operators. For our spin example we present results showing how the entanglement varies as a function of the parameters of the initial state; for the continuous case, we also find how it depends on the location and size of the chosen regions. Hence we show that the distribution of entanglement is very different from the distribution of the classical correlations.

Control of the transfer of quantum information encoded in quantum wave packets moving along a spin chain is demonstrated. Specifically, based on a relationship with control in a paradigm of quantum chaos, it is shown that wave packets with slow dispersion can automatically emerge from a class of initial superposition states involving only a few spins, and that arbitrary unspecified traveling wave packets can be nondestructively stopped and later relaunched with perfection. The results establish an interesting application of quantum chaos studies in quantum information science.

We derive the nonretarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate numerically. For an atom close to a semi-infinite half plane we determine the exact Green’s function of the Laplace equation and use it to derive the exact energy shift for an arbitrary position of the atom. These results can be used to estimate the energy shift of an atom close to etched microstructures that protrude from substrates.

The scattering process influenced by the intersection of potential energy surfaces is studied. Exact quantum-mechanical solutions to the two-dimensional two- and three-state models have been found for the collision energy equal to the potential energy at the intersection point. The models considered are the Jahn-Teller and Renner-Teller intersections and the triple intersection of the double cone with a plane. Closed analytical expressions for the scattering amplitudes have been obtained. The results reveal the geometric phase effect and the nonadiabatic phase impact on the differential cross section.

We report the total integrated cross section (TICS) of two-photon double ionization of helium in the photon energy range from $42\text{to}50\mathrm{eV}$. Our computational procedure relies on a numerical solution of the time-dependent Schrödinger equation on a square-integrable basis and subsequent projection of this solution on a set of final field-free states describing correlation in the two-electron continuum. Our results suggest that the TICS grows monotonically as a function of photon energy in the region of $42–50\mathrm{eV}$, possibly reaching a maximum in the vicinity of $50\mathrm{eV}$. We also present fully resolved triple-differential cross sections for selected photon energies.

An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser ($800\mathrm{nm}$, ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$). The laser dresses the core-excited atomic states, which introduces a dependence of the cross section on the angle between the polarization vectors of the two linearly polarized radiation sources. We use the Hartree-Fock-Slater approximation to describe the atomic many-particle problem in conjunction with a nonrelativistic quantum-electrodynamic approach to treat the photon-electron interaction. The continuum wave functions of ejected electrons are treated with a complex absorbing potential that is derived from smooth exterior complex scaling. The solution to the two-color (x-ray plus laser) problem is discussed in terms of a direct diagonalization of the complex symmetric matrix representation of the Hamiltonian. Alternative treatments with time-independent and time-dependent non-Hermitian perturbation theories are presented that exploit the weak interaction strength between x rays and atoms. We apply the theory to study the photoabsorption cross section of krypton atoms near the $K$ edge. A pronounced modification of the cross section is found in the presence of the optical laser.

Almost isotropic angular distributions are observed for fragment ions from ${\mathrm{Xe}}_2$ produced with intense femtosecond laser pulses ($800\mathrm{nm}$, $4\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$). The results observed for ${\mathrm{Xe}}_2$ present a great contrast to those for ${\mathrm{I}}_2$ molecules used as reference molecules, which show typical anisotropic angular distributions resulting from enhanced ionization. The kinetic energy spectra of the fragment ions from ${\mathrm{Xe}}_2$ reveal that the internuclear distance remains near the equilibrium distance for various pulse widths from 45 to $710\mathrm{fs}$, indicating that in the rising edge of the pulses, the internuclear distance of ${\mathrm{Xe}}_2^{n+}$ ($n=0$, 1, 2) does not reach the favorable region for enhanced ionization even though enhancement can potentially work for ${\mathrm{Xe}}_2^{n+}$. The dynamic alignment of neutral ${\mathrm{Xe}}_2$ during the pulses is also discussed on the basis of numerical simulations.

We report results of a systematic analysis of the stability of dissipative optical solitons, with intrinsic vorticity $S=0$ and 1, in the three-dimensional complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, which is a model of a dispersive optical medium with saturable self-focusing nonlinearity and bandwidth-limited nonlinear gain. The stability is investigated by means of computation of the instability growth rate for eigenmodes of small perturbations, and the results are verified against direct numerical simulations. We conclude that the presence of diffusivity in the transverse plane is necessary for the stability of vortex solitons (with $S=1$) against azimuthal perturbations, while zero-vorticity solitons may be stable in the absence of the diffusivity. On the other hand, the solitons with $S=0$ and $S=1$ have their stability regions at both anomalous and normal group-velocity dispersion, which is important to the experimental implementation. At values of the nonlinear gain above their existence region, the solitons either develop persistent intrinsic pulsations, or start expansion in the longitudinal direction, keeping their structure in the transverse plane.

Bipartite quantum entanglement for qutrits and higher-dimensional objects is considered. We analyze the possibility of violation of monogamy inequality, introduced by Coffman, Kundu, and Wootters, for some systems composed of such objects. An explicit counterexample with a three-qutrit totally antisymmetric state is presented. Since three-tangle has been confirmed to be a natural measure of entanglement for qubit systems, our result shows that the three-tangle is no longer a legitimate measure of entanglement for states with three qutrits or higher-dimensional objects.

We consider calculations for maximum visibility of the atomic fringe pattern generated by optical phase gratings presented by Strekalov et al. It is shown that the phase grating technique offers higher maximum visibilities for the atomic fringe patterns than those calculated by the authors.