A theory of dissociative electron attachment to molecules condensed at surfaces and embedded within bulk media is developed. The theory of low-energy electron diffraction is used to obtain the width for electron-molecule resonance scattering in the condensed phase from the width for the gas phase. It is then employed for the calculation of dissociative attachment in the framework of the nonlocal complex potential theory. Specific calculations using the effective mass approximation are carried out for electron attachment to $\mathrm{C}{\mathrm{H}}_3\mathrm{Cl}$ and $\mathrm{C}{\mathrm{F}}_3\mathrm{Cl}$ molecules physisorbed on the surface of a Kr film. The role of image states and image-potential resonances is analyzed. The results show an increase by several orders of magnitude in the cross section for physisorbed molecules as compared with gas-phase molecules. This is in general agreement with the measured cross sections. However, the position of the peak in the cross section for $\mathrm{C}{\mathrm{H}}_3\mathrm{Cl}$ is significantly shifted towards higher energies as compared to experiment [K. Nagesha et al., J. Chem. Phys. 114, 4934 (2001)], and the magnitude of the calculated cross section for $\mathrm{C}{\mathrm{F}}_3\mathrm{Cl}$ at the surface is significantly higher than the measured value. Possible reasons for disagreements are analyzed.

Electron emission coming from the valence band of metal surfaces due to grazing incidence of high-frequency ultrashort laser pulses is studied. We introduce a distorted-wave method, named impulsive jellium-Volkov (IJV) approximation, in which the surface is represented by the jellium model while the interaction with the laser field is described by means of the Volkov phase. With the purpose of examining the proposed approach, we compare IJV results with values derived from the numerical solution of the corresponding time-dependent Schrödinger equation (TDSE). For Al(111) surfaces, double and single differential probability spectra are calculated considering different durations of the laser pulse. Very good agreement between IJV and TDSE results was found. The total probability dependence on the intensity and carrier-envelope phase of the pulse is also investigated.

We have studied theoretically and numerically the cooling of CN molecules in a high-finesse optical cavity and show that these molecules can be cooled from $100\mathrm{mK}$ temperatures to submillikelvin temperatures in less than $1\mathrm{ms}$. We establish that the cooling time does not change significantly with molecular numbers and initial temperatures over a wide range. We have further studied the scaling of the system for extending the current results for hundreds of molecules to a very large molecular ensemble. The results indicate that a gas of ${10}^9\text{molecules}$ can be cooled in the cavity by use of a far-off-resonant and high-intensity pump source.

A semiclassical molecular nonsequential double ionization theory is developed based on the rescattering model. We show that, in the nonsequential double ionization of ${\mathrm{D}}_2$, the kinetic energy of the returning electron changes from below to above the ionization threshold of the parent ion as the laser varies from short to long wavelength, resulting in the dominance of collisional ionization at shorter laser wavelength and field ionization at longer laser wavelength. We also calculate the double ionization time distribution of ${\mathrm{D}}_2$ and the kinetic energy distribution of ${\mathrm{D}}^{+}$. The theoretical results are qualitatively consistent with experimental measurements. The nonsequential double to single ionization ratio of $\mathrm{N}_2{}^{2+}∕\mathrm{N}_2{}^{+}$ is also calculated and compared with available experimental results.

The influence of a weak random potential on the collective modes of a trapped interacting Bose-Einstein condensate at zero temperature is calculated in the limit when the correlation length of the disorder is smaller than the healing length of the superfluid. The problem is solved in the Thomas-Fermi limit by generalizing the superfluid hydrodynamic equations to allow for the presence of weak disorder. We find that the disorder-induced frequency shifts of the low-energy excitations can be of the same order of magnitude as the beyond mean-field corrections in the normal interaction recently observed experimentally.

We study the signatures of rotational and phase symmetry breaking in small rotating clouds of trapped ultracold Bose atoms by looking at rigorously defined condensate wave function. Rotational symmetry breaking occurs in narrow frequency windows, where energy degeneracy between the lowest energy states of different total angular momentum takes place. This leads to a complex condensate wave function that exhibits vortices clearly seen as holes in the density, as well as characteristic local phase patterns, reflecting the appearance of vorticities. Phase symmetry (or gauge symmetry) breaking, on the other hand, is clearly manifested in the interference of two independent rotating clouds.

In this article, localized linear defect modes due to band gap guidance in two-dimensional photonic lattices with localized or nonlocalized defects are investigated theoretically. First, when the defect is localized and weak, eigenvalues of defect modes bifurcated from edges of Bloch bands are derived analytically. It is shown that in an attractive (repulsive) defect, defect modes bifurcate out from Bloch-band edges with normal (anomalous) diffraction coefficients. Furthermore, distances between defect-mode eigenvalues and Bloch-band edges decrease exponentially with the defect strength, which is very different from the one-dimensional case where such distances decrease quadratically with the defect strength. It is also found that some defect-mode branches bifurcate not from Bloch-band edges, but from quasiedge points within Bloch bands, which is very unusual. Second, when the defect is localized but strong, defect modes are determined numerically. It is shown that both the repulsive and attractive defects can support various types of defect modes such as fundamental, dipole, quadrupole, and vortex modes. These modes reside in various band gaps of the photonic lattice. As the defect strength increases, defect modes move from lower band gaps to higher ones when the defect is repulsive, but remain within each band gap when the defect is attractive, similar to the one-dimensional case. The same phenomena are observed when the defect is held fixed while the applied dc field (which controls the lattice potential) increases. Lastly, if the defect is nonlocalized (i.e., it persists at large distances in the lattice), it is shown that defect modes can be embedded inside the continuous spectrum, and they can bifurcate out from edges of the continuous spectrum algebraically rather than exponentially.

Non-photon-number-resolving single-photon-counting modules (SPCM’s), also called on-off photon detectors, have been used in quantum optics for investigating the properties of various light fields based on the Hanbury-Brown-Twiss (HBT) experiment. However, for different incident light fields the experimental conditions can affect the measured photon statistics. In this paper, the second-order degree of coherence $g^{\left(2\right)}$, known as the important factor for quantitying a single-photon source, is experimentally investigated by means of the HBT scheme consisting of two SPCM’s. By comparing the results of coherent field with that of the thermal field, we show that the measured $g^{\left(2\right)}$ is affected by the photon-counting rate and the resolution time from pulsed to continuous wave fields. The proper counting rate and resolution time for characterizing the exact photon statistical properties of input fields are determined.

We introduce the $N$-photon quantum superposition of two orthogonal generalized binomial states of an electromagnetic field. We then propose, using resonant atom-cavity interactions, nonconditional schemes to generate and reveal such a quantum superposition for the two-photon case in a single-mode high-$Q$ cavity. We finally discuss the implementation of the proposed schemes.

The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for the particle motion on a torus are obtained, and the relation of the suggested map to the Radon transform on the plane is elucidated. The generalization to the case of a multidimensional torus is elaborated, and the geometrical meaning of the tomographic probability densities as marginal distributions on the helix discussed.

Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive, but we present several counterexamples, notably a simple type of quantum graph in which the sign of the force depends upon the number of edges. We also show that Casimir forces in quantum graphs can be reliably computed by summing over the classical orbits, and study the rate of convergence of the periodic orbit expansion. In generic situations where no analytic expression is available, the sign and approximate magnitude of Casimir forces can often be obtained using only the shortest classical orbits.

We discuss three applications of efficient quantum algorithms to determining properties of permutations and group automorphisms. The first uses the Bernstein-Vazirani algorithm to determine an unknown homomorphism from $Z_{p-1}^m$ to $\mathit{Aut}\left(Z_p\right)$ where $p$ is prime. The remaining two make use of modifications of the Grover search algorithm. The first finds the fixed point of a permutation or an automorphism (assuming it has only one besides the identity). It can be generalized to find cycles of a specified size for permutations or orbits of a specified size for automorphisms. The second finds which of a set of permutations or automorphisms maps one particular element of a set or group onto another. This has relevance to the conjugacy problem for groups. We show how two of these algorithms can be implemented via programmable quantum processors. This approach opens new perspectives in quantum information processing when both the data and the programs are represented by states of quantum registers. In particular, quantum programs that specify control over data can be treated using methods of quantum information theory.

We study how the spontaneous relaxation of a qubit affects a continuous quantum nondemolition measurement of the initial state of the qubit. Given some noisy measurement record $\Psi$, we seek an estimate of whether the qubit was initially in the ground or excited state. We investigate four different measurement protocols, three of which use a linear filter (with different weighting factors) and a fourth which uses a full nonlinear filter that gives the theoretically optimal estimate of the initial state of the qubit. We find that relaxation of the qubit at rate $1∕T_1$ strongly influences the fidelity of any measurement protocol. To avoid errors due to this decay, the measurement must be completed in a time that decrease linearly with the desired fidelity while maintaining an adequate signal to noise ratio. We find that for the nonlinear filter the predicted fidelity, as expected, is always better than the linear filters and that the fidelity is a monotone increasing function of the measurement time. For example, to achieve a fidelity of 90%, the box car linear filter requires a signal to noise ratio of $\sim 30$ in a time $T_1$, whereas the nonlinear filter only requires a signal to noise ratio of $\sim 18$.

We propose to quantify three-qubit entanglement using global negativity along with $K$-way negativities, where $K=2$ and 3. The principle underlying the definition of $K$-way negativity for pure and mixed states of $N$ subsystems is a positive partial transpose sufficient condition. However, $K$-way partial transpose with respect to a subsystem is defined so as to shift the focus to $K$-way coherences instead of $K$ subsystems of the composite system. A quantum state of a three-qubit system is characterized by the coherences measured by global, two-way, and three-way negativities. For a canonical state of three-qubit system, entanglement measures for genuine tripartite entanglement, W-like entanglement, and bipartite entanglement can be related to two-way and three-way negativities.

Valence double photoionization of Ne atom has been investigated by multielectron spectroscopy. Complete information on energy correlation between ejected electrons allows the identification of ${\mathrm{Ne}}^{2+}$ final states and their formation mechanism. In addition to simultaneous two-electron emission from the valence shells, indirect processes mediated by singly charged excited states have been observed. We have first obtained direct double-photoionization cross sections state-selectively in a wide photon energy region, by evaluating the contributions of the indirect processes. We have also applied the coincidence spectroscopy to three-electron emission from the valence shells. Even in the three-electron emission, the coincidence analysis enables to observe individual ${\mathrm{Ne}}^{3+}$ final states related to the triple-photoionization process and to obtain the state-selective cross sections.

Atom interferometers require atom mirrors and beam splitters that can maintain high fidelity even when experimental parameters vary from the ideal. We address the use of chirped laser pulses to provide such elements via rapid adiabatic passage, and present a prescription for practical pulses that offer controlled adiabaticity throughout. Full- and half-adiabatic pulses, providing mirrors and beam splitters, respectively, are derived, and the latter examined for robustness and suitability for experimental implementations.

The photorefractive surface waves with photorefractive nonlinearity of diffusion, drift, and photovoltaic effect is studied numerically for the first time. We find out that the essential cause of photorefractive surface waves is diffusion mechanism, but not drift and photovoltaic effects. The photovoltaic effect only has strong influence on the profile of photorefractive surface waves; the applied external electric field can also change the profile of the surface waves, and even destroy the mode upon a threshold, which provides a possible method to transform the modes of surface waves between high-frequency modes and low-frequency modes.

A method to coherently control electron dynamics is proposed using a few-cycle laser pulse in combination with a controlling field. It is shown that this method not only broadens the attosecond pulse bandwidth, but also reduces the chirp; thus an isolated $80\text{‐}\mathrm{as}$ pulse is straightforwardly obtained, and even shorter pulses are achievable by increasing the intensity of the controlling field. Such ultrashort pulses allow one to investigate ultrafast electronic processes. In addition, the few-cycle synthesized pulse is expected to be useful for manipulating a wide range of laser-atom interactions.

The geometric manipulation of the quantum states of two-level atoms with two laser-controlled resonant $\pi$ pulses with a relative phase difference was evaluated using a time-domain atom interferometer comprising a cold sodium atom ensemble and two copropagating two-photon Raman pulses. It was verified that the relative phase shift between two states is double the control phase difference and that the rotation around the axis 3 of the Bloch sphere can be controlled by geometric manipulation.

We present a full experimental characterization of continuous-variable quantum-communication channels established by shared entanglement together with local operations and classical communication. The resulting teleportation channel was fully characterized by measuring all elements of the covariance matrix of the shared two-mode squeezed Gaussian state. From the experimental data we determined the lower bound to the quantum channel capacity, the teleportation fidelity of coherent states, and the logarithmic negativity and purity of the shared state. Additionally, a positive secret key rate was obtained for two of the established channels.