Siegert pseudostates (SPS) are a finite basis representation of Siegert states (SS) for finite-range potentials. This paper presents a generalization of the SPS formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura [Phys. Rev. A 58, 2077 (1998)] for s-wave scattering in the one-channel case, to s-wave scattering in the two-channel case. This includes the investigation of the properties of orthogonality and completeness of two-channel SPS and the derivation of the SPS expansions for the two-channel Green function, wave function, and scattering matrix. Similar to the one-channel case, two types of expansions for the scattering matrix are obtained: one has a form of a sum and requires the knowledge of both the SPS eigenvalues and eigenfunctions, while the other has a form of a product and involves the eigenvalues only. As the size of the basis tends to infinity, the product formulas obtained here in terms of SPS coincide with those given by Le Couteur [Proc. R. Soc. London, Ser. A 256, 115 (1960)] in terms of SS; all the other relations, as far as we know, have no counterparts in the literature. Partial widths of resonances in the case when both channels are open for decay are identified in terms of SPS—a feature that is absent in the one-channel case. The results are illustrated by numerical calculations for two model potentials.

The moment of inertia $\Theta$ is one of the possible observables for the experimental determination whether a trapped Fermi system has reached the BCS transition or not. In this article we investigate in detail the temperature dependence of $\Theta$ below the critical temperature $T_c.$ Special care is taken to account for the small size of the system, i.e., for the fact that the trapping frequency $ħ\omega$ is of the same order of magnitude as the gap $\Delta .$ It is shown that the usual transport approach, corresponding to the leading order of an expansion in powers of $ħ,$ is not accurate in this case. It turns out that $\Theta$ does not change rapidly if T becomes smaller than $T_c,$ but it rather decreases slowly. Qualitatively this behavior can be explained within the two-fluid model, which again corresponds to the leading order in $ħ.$ Quantitatively we find deviations from the two-fluid model due to the small system size.

When a quasiresonant laser beam illuminates an optically thick cloud of laser-cooled rubidium atoms, the average diffuse intensity reflected off the sample is enhanced in a narrow angular range around the direction of exact backscattering. This phenomenon is known as coherent backscattering (CBS). By detuning the laser from resonance, we are able to modify the light scattering mean-free path inside the sample and we record accordingly the variations of the CBS cone shape. We then compare the experimental data with theoretical calculations and Monte Carlo simulations including the effect of the light polarization and of the internal structure of the atoms. We confirm that the internal structure strongly affects the enhancement factor of the cone and we show that the unusual shape of the atomic medium—approximately a spherically-symmetric, Gaussian density profile—strongly affects the width and shape of the cone.

In this paper, we present a simple approach for understanding some general aspects of the irreversible dynamics of the generalized Jaynes-Cummings model. By working in the dressed-state representation, it is possible to split the dynamics of populations and coherences. Then it can be shown that the coherence dynamics may present localization and dispersivelike decay behavior, whereas the population dynamics are characterized in terms of a classical diffusive process. These phenomena are studied by developing a perturbation theory that provides simple analytical results that could be applicable to any general source of irreversibility in the Jaynes-Cummings model. As an application, we extend and analytically characterize our previous reported results on heating and decoherence in trapped ions [Phys. Rev. A 65, 041402 (2002)].

Steady state and dynamics of the self-phase-locked $(3\mathrm{}\overrightarrow{\omega }2\omega ,\omega )$ subharmonic optical parametric oscillator are analyzed in the pump-and-signal resonant configurations, using an approximate analytical model and a full propagation model. The upper branch solutions are found always to be stable, regardless of the degree of pump enhancement. The domain of existence of stationary states is found to critically depend on the phase mismatch of the competing second-harmonic process.

A simple experimental setup consisting of a spontaneous parametric down-conversion source and passive linear optics is proposed for conditional preparation of a maximally entangled polarization state of two photons. Successful preparation is unambiguously heralded by coincident detection of four auxiliary photons. The proposed scheme utilizes the down-conversion term corresponding to the generation of three pairs of photons. We analyze imperfect detection of the auxiliary photons and demonstrate that its deleterious effect on the fidelity of the prepared state can be suppressed at the cost of decreasing the efficiency of the scheme.

The dynamics of a Bose-Einstein condensate nonadiabatically loaded into a one-dimensional optical lattice is studied by analyzing the phase coherence between sites along the lattice as well as the radial profile of the condensate after a time-of flight. A simple model is proposed that predicts the short-time dephasing as a function of the condensate parameters. In the radial direction, heavily damped oscillations are observed, as well as an increase in the condensate temperature. These findings are interpreted as a rethermalization due to dissipation of the initial condensate excitations into high-lying modes.

Uhlmann’s mixed state geometric phase [Rep. Math. Phys. $24,$ 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly with increasing decoherence rate and that it is most fragile to weak decoherence for pure or nearly pure initial states. In the unitary case, we compare Uhlmann’s geometric phase for mixed states with that occurring in standard Mach-Zehnder interferometry [Phys. Rev. Lett. $85,$ 2845 (2000)] and show that the latter is more robust to reduction in the length of the Bloch vector. We also describe how Uhlmann’s geometric phase in the present case could in principle be realized experimentally.

We consider the Lindblad-type master equation of an open system. We address the question how to construct a functional of the quantum state which displays a monotonic behavior in time. This thus defines uniquely the direction of time in the system. As the generator of time evolution is not a Hermitian operator, the theory requires the considerations of right and left eigenstates. In this paper we assume them to form two complete bases, which allows us to construct the desired quantity. This can be interpreted as a generalized entropy functional. We show how the construction is carried out in the general case, and we illustrate the theory by solving the case of an externally driven and damped two-level system. The treatment is related to earlier work in the field, and its possible relation to time inversion is discussed.

In this paper, we derived a Lorentz-covariant quantum Liouville equation for the density operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced density operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.

The security of two-state quantum-key distribution against individual attack is estimated when the channel has losses and noises. We assume that Alice and Bob use two nonorthogonal single-photon polarization states. To make our analysis simple, we propose a modified $B92\mathrm{}$ protocol in which Alice and Bob make use of inconclusive results, and Bob performs a kind of symmetrization of received states. Using this protocol, Alice and Bob can estimate Eve’s information gain as a function of a few parameters that reflect the imperfections of devices, or Eve’s disturbance. In some parameter regions, Eve’s maximum information gain shows counterintuitive behavior, namely, it decreases as the amount of disturbances increases. For a small noise rate, Eve can extract perfect information in the case where the angle between Alice’s two states is small or large, while she cannot extract perfect information for intermediate angles. We also estimate the secret key gain, which is the net growth of the secret key per pulse. We show the region where the modified $B92\mathrm{}$ protocol over a realistic channel is secure against individual attack.

We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target—they give a phase shift only. In other words, the T matrix of the system is of rank N, and the eigenmodes are eigenvectors corresponding to nonzero eigenvalues of the T matrix. The eigenmode expansion approach can give insight to the total scattering cross section; the position, width, and superradiant or subradiant nature of resonance peaks; the unsymmetric Fano line shape of sharp proximity resonance peaks based on the high-energy tail of a broadband; and other properties. Off-resonant eigenmodes for identical proximate scatterers are approximately angular-momentum eigenstates.

Recently, a new optimization procedure that combines the power of artificial neural-networks with the versatility of the genetic algorithm (GA) was introduced. This method, called neural-network-assisted genetic algorithm (NAGA), uses a neural network to restrict the search space and it is expected to speed up the solution of global optimization problems if some previous information is available. In this paper, we have tested NAGA to determine the ground-state geometry of ${\mathrm{Si}}_n$ $(10\mathrm{}<~n<~15)$ according to a tight-binding total-energy method. Our results indicate that NAGA was able to find the desired global minimum of the potential energy for all the test cases and it was at least ten times faster than pure genetic algorithm.

A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper.

The quasienergy spectrum of hydrogenlike Rydberg atoms in a precessing electric field of constant amplitude is found in simple form. Resonant intrashell transitions occur for specific field values when a (small) additional static electric field perpendicular to the precession axis is present. Sequences of such transitions may enhance the microwave ionization of a Rydberg atom. C. H. Cheng and T. F. Gallagher [Phys. Rev. A 61, 063411 (2000)] recently observed a one-photon resonance of this type. We evaluate the widths of one-photon intrashell resonances, and develop a general approach to the N-photon case within the framework of a quasienergy representation.

The photoabsorption spectrum of the ${\mathrm{HeH}}^{+}$ molecular ion is investigated. The theoretical study includes transitions to electronically excited states and to the ionization continuum. The influence of autoionizing resonances is discussed. In the absorption spectrum, vibrational motion is considered within the Born-Oppenheimer approximation, whereas the reflection approximation is applied for the photoionization spectrum. The importance of the photoabsorption spectrum for the ongoing tritium neutrino-mass experiments is discussed. In order to assess the accuracy of the numerical approach, the doubly excited states of ${\mathrm{HeH}}^{+}$ (position and width) and the photoionization spectrum of ${\mathrm{H}}_2$ are compared to literature data.

In the number-conserving Bogoliubov theory of the Bose-Einstein condensate, the Bogoliubov transformation between quasiparticles and particles is nonlinear. We invert this nonlinear transformation and give a general expression for eigenstates of the Bogoliubov Hamiltonian in particle representation. The particle representation unveils the structure of a condensate multiparticle wave function. We give several examples to illustrate a general formalism.

A cold-neutron interferometer using four independent multilayer mirrors is demonstrated. We have observed interference fringes with a contrast of 60%. The interferometer is based on a pair of devices using etalons with an air gap of $9.75\mu \mathrm{m}$ in spacing. The optical system is equivalent to the Jamin-type interferometer, which allows much larger spatial separation between the two coherent beams than the previous type of multilayer interferometer to broaden the applicability of neutron interferometry.

We study the response of a trapped Bose-Einstein condensate to a sudden turn on of a rotating drive by numerically solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by a quasiparticle projection method. In a quadrupolar resonant regime, which depends on the trap anisotropy, simple periodic oscillations in surface-mode populations disappear and the system exhibits stochastic dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.

We show that an image of an object is obtained when at least one of the photons of a parametric down-converted pair illuminates the object and the two photons are detected in coincidence after they have been transmitted by two lenses. The image is mathematically described by a quantum fourth-order correlation function that differs from the classical image description in two aspects. The quantum image is produced by a nonlocal effective lens whose aperture is described by a compressed convolution of the magnitude of lens transmission functions. The image is generated by the entangled state two-photon light source in which the effective wavelength is equal to the de Broglie wavelength $\lambda /2,$ where $\lambda$ is the wavelength associated to the individual photons. Images can be obtained with a resolution better than the obtained with coherent classical light sources. Better resolution and strong apodization effects are observed.