The interaction of nonrelativistic matter with the quantized electromagnetic field is investigated in the classical limit of large photon numbers. Quantization of both matter, say an atom, and the field results in a time-independent Schrödinger equation (TISE). However, for very strong fields (quantum mechanically, large photon numbers) this is impractical to solve. The standard approach then is simply to replace the quantized field by a classical field to give a time-dependent Schrödinger equation (TDSE) for the atom alone. Here we show how this TDSE can be derived from the TISE for atom plus field, illustrating at each stage the approximations that are necessary to treat the field classically. An important difficulty at the semiclassical stage is a breakdown of the approximation at classical turning points. We show how the use of coherent field states can circumvent this problem. In the limit that the field can be treated classically, time emerges from the Maxwell equations and a TDSE for the atom alone results.

We have observed self-modulation and self-compression of a femtosecond laser pulse after passing the beam through a Raman-active medium of hydrogen. Femtosecond pulses produce Stokes emissions of ortho-hydrogen and para-hydrogen, depending on the input beam conditions. The shape of the output pulses drastically changed as a function of the intensity of the Stokes emissions and the total width of the spectrum. This is attributed to nonlinear modulation of the wave form induced by coherent rotational motions of hydrogen molecules in the time domain.

We show that inconclusive photon subtraction (IPS) on a twin beam produces non-Gaussian states that violate Bell’s inequality in the phase space. The violation is larger than for the twin beam itself irrespective of the IPS quantum efficiency. The explicit expression for the IPS map is given both for the density matrix and the Wigner function representations.

The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic potential, is studied focusing on its non-Markovian regime. Both an analytic approach and a stochastic wave-function approach are used to describe the exact time evolution of the system. The border between two very different dynamical regimes, the Lindblad and non-Lindblad regimes, is identified and the relevant physical variables governing the passage from one regime to the other are singled out. The non-Markovian short-time dynamics is studied in detail by looking at the mean energy, the squeezing, the Mandel parameter, and the Wigner function of the system.

We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single-qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron transistor arrays based on quantum dots or insulating interfaces typically allow for electrostatic controls where the interisland tunneling is considered constant, e.g., determined by the thickness of an insulating layer. A representative array of $3\times 3$ quantum dots with two mobile electrons is analyzed using a Hubbard Hamiltonian and a capacitance matrix formalism. Our study shows that it is easy to realize the first quantum gate for single-qubit operations, but that a second quantum gate comes only at the cost of compromising the low-energy two-level system that encodes the qubit. We use perturbative arguments and the Feshbach formalism to show that this compromising of the two-level system is a rather general feature for electrostatically interacting qubits and is not just related to the specific details of the system chosen. We show further that full implementation requires tunable tunneling or external magnetic fields.

Typical circuit implementations of Shor’s algorithm involve controlled rotation gates of magnitude $\pi ∕2^{2L}$ where $L$ is the binary length of the integer $N$ to be factored. Such gates cannot be implemented exactly using existing fault-tolerant techniques. Approximating a given controlled $\pi ∕2^d$ rotation gate to within $\delta =O(1∕2^d)$ currently requires both a number of qubits and a number of fault-tolerant gates that grows polynomially with $d$. In this paper we show that this additional growth in space and time complexity would severely limit the applicability of Shor’s algorithm to large integers. Consequently, we study in detail the effect of using only controlled rotation gates with $d$ less than or equal to some $d_{\max }$. It is found that integers up to length $L_{\max }=O\left(4^{d_{\max }}\right)$ can be factored without significant performance penalty implying that the cumbersome techniques of fault-tolerant computation only need to be used to create controlled rotation gates of magnitude $\pi ∕64$ if integers thousands of bits long are desired factored. Explicit fault-tolerant constructions of such gates are also discussed.

We study a quantum information storage scheme based on an atomic ensemble with near (also exact) three-photon resonance electromagnetically induced transparency (EIT). Each 4-level-atom is coupled to two classical control fields and a quantum probe field. Quantum information is adiabatically stored in the associated dark polariton manifold. An intrinsic nontrivial topological structure is discovered in our quantum memory implemented through the symmetric collective atomic excitations with a hidden $\mathrm{SU}\left(3\right)$ dynamical symmetry. By adiabatically changing the Rabi frequencies of two classical control fields, the quantum state can be retrieved up to a non-Abelian holonomy and thus decoded from the final state in a purely geometric way.

We elaborate our theoretical framework to treat low-energy electron scattering from helical macromolecules. A model of simple scatterers organized into a helical structure is proposed with application to base-pair arrangements in DNA. We extend our analysis to $A$-type DNA as well as nonperiodic arrangements in $B$-type DNA. Diffraction patterns due to base-pair spacing are observed under all conditions. We discuss the role of electron diffraction in electron attachment to the bases leading to the formation of shape and core-excited resonances. The decay of such transient anions into dissociative-state channels producing DNA strand breaks is also described. We find $\mathrm{A}$-type DNA to be much more sensitive to low-energy electrons than $\mathrm{B}$ type.

A many-body theory approach is developed for the problem of positron-atom scattering and annihilation. Strong electron-positron correlations are included nonperturbatively through the calculation of the electron-positron vertex function. It corresponds to the sum of an infinite series of ladder diagrams, and describes the physical effect of virtual positronium formation. The vertex function is used to calculate the positron-atom correlation potential and nonlocal corrections to the electron-positron annihilation vertex. Numerically, we make use of $B$-spline basis sets, which ensures rapid convergence of the sums over intermediate states. We have also devised an extrapolation procedure that allows one to achieve convergence with respect to the number of intermediate-state orbital angular momenta included in the calculations. As a test, the present formalism is applied to positron scattering and annihilation on hydrogen, where it is exact. Our results agree with those of accurate variational calculations. We also examine in detail the properties of the large correlation corrections to the annihilation vertex.

Single ionization cross sections for heavy-ion impact on ${\mathrm{H}}_2$ are calculated by applying the continuum-distorted-wave–eikonal-initial-state model. We have used a representation of the bound-state initial wave function which takes into account the molecular character of the target. To describe the final continuum state we have used the two-effective-center approximation, previously employed with success to study electron capture from ${\mathrm{H}}_2$ by ion impact. Interference effects are also analyzed and the dependence of the oscillation frequency with the projectile velocity and ejection angle is presented. The importance of adequately describing the target as a molecule is emphasized.

It is pointed out that two separated quantum channels and three classical authenticated channels are sufficient resources to achieve detectable broadcast.

The dynamical behavior of entanglement for excitons in two quantum dots placed in two separately single-mode optical cavities driven by an external broadband two-mode squeezed vacuum is studied in the low exciton density regime. It is found that if the field in the two separate cavities is initially prepared in a pure two-mode squeezed vacuum state, the excitons in the two quantum dots can evolve into a pure entangled state only when the dissipation of the cavities and exciton modes is negligible. When the effect of the dissipation is included, the excitons will be in a two-mode Gaussian entangled mixed state whose properties are decided by the externally driven field and the initial field. The dependence of the entanglement property of the excitons in the two quantum dots on the squeezing properties of the fields in the two cavities is also discussed.

The dynamics of quantum and classical probability distributions are computed for a model of two coupled rotors (or pendulums), with emphasis on the $\hslash$ scaling of the quantum-classical (QC) differences. This scaling is not the same for coarse-grained and fine-grained quantities. The QC differences in the averages of observables scale as ${\hslash }^{2∕3}$ for chaotic states, but as ${\hslash }^2$ for regular states. The QC differences in probability distributions scale as ${\hslash }^{1∕3}$ for chaotic states. No simple scaling is found for those differences in regular states, although their overall magnitudes are similar to those in chaotic states. QC differences arise first in the short-wavelength regime, and subsequently spread to all wavelengths. A satisfactory classical limit is obtained without invoking environmental decoherence, which in any case would be effective in suppressing only short-wavelength QC differences.

We study the ordering of two-qubit states with respect to the degree of bipartite entanglement using the Wootters concurrence—a measure of the entanglement of formation—and the negativity—a measure of the entanglement cost under the positive-partial-transpose-preserving operations. For two-qubit pure states, the negativity is the same as the concurrence. However, we demonstrate analytically on simple examples of various mixtures of Bell and separable states that the entanglement measures can impose different orderings on the states. We show which states, in general, give the maximally different predictions (i) when one of the states has the concurrence greater but the negativity smaller than those for the other state and (ii) when the states are entangled to the same degree according to one of the measures, but differently according to the other.

The four Bell-type entangled coherent states, $\mid \alpha ⟩\mid -\alpha ⟩\pm \mid -\alpha ⟩\mid \alpha ⟩$ and $\mid \alpha ⟩\mid \alpha ⟩\pm \mid -\alpha ⟩\mid -\alpha ⟩$, can be discriminated with a high probability using only linear optical means, as long as $\mid \alpha \mid$ is not too small. Based on this observation, we propose a simple scheme to almost completely teleport a superposed coherent state. The nonunitary transformation that is required to complete the teleportation can be achieved by embedding the receiver’s field state in a larger Hilbert space consisting of the field and a single atom and performing a unitary transformation on this Hilbert space.

The stability and structure of the $(m^{Z+},e^{-},e^{-},e^{+})$ system is studied as a function of the mass of the $m^{Z+}$ particle and for $Z=1$, 2, 3, and 10. The $Z=1$ system can be regarded as an analog of the $A\mathrm{Ps}$ system (where $A$ is a group I or IB atom of the periodic table) and was found to be stable for all values of $m^{+}$. This is supportive of the idea that all the group I and IB atoms can bind Ps. The $(m^{2+},e^{-},e^{-},e^{+})$ system is stable for all $m^{2+}∕m_e⩽0.68$ and evolves into a configuration best described as $(m^{2+},{\mathrm{Ps}}^{-})$ when $m^{2+}∕m_e\to 0$. The $(m^{3+},e^{-},e^{-},e^{+})$ system was stable for a mass range given by $m^{3+}∕m_e⩽0.06632$, which suggests that positrons could form Feshbach resonances in collisions with positive ions which are isolectronic with the group II and IIB columns of the periodic table. The $(m^{3+},e^{-},e^{-},e^{+})$ system has the unusual property that it has a mass range where it becomes more compact while its binding energy simultaneously decreases. The $(m^{10+},e^{-},e^{-},e^{+})$ system is also stable at $m^{10+}∕m_e=0.00254$, which implies stability for all mass ratios less than 0.002 54. In total, the calculations suggest that the $(m^{Z+},e^{-},e^{-},e^{+})$ system is stable whenever the $m^{Z+}+{\mathrm{Ps}}^{-}$ or $(m^{Z+},e^{-})+\mathrm{Ps}$ breakups represent the lowest energy dissociation channel. As part of the analysis some improved estimates of the properties of the KPs ground state are reported.

In this work, we present results for high-angular-momentum resonances in positron-hydrogen scattering obtained by using the method of complex-coordinate rotations. Resonance states with angular momenta of $L=3$ to 6 are calculated using highly correlated Hylleraas-type wave functions. Furthermore, for the $L=0$ and 1 states, we present our updated results. Comparisons with other calculations are made.

In this work, we report a theoretical study on electron collisions with $\mathrm{OH}$ radicals in the low and intermediate energy ranges. Calculated elastic differential, integral, and momentum-transfer cross sections as well as grand-total (elastic $+$ inelastic) and total absorption cross sections for electron-$\mathrm{OH}$ collisions are reported in the $1–500\text{−}\mathrm{eV}$ range. A complex optical potential composed by static, exchange, correlation-polarization plus absorption contributions, derived from a fully molecular wave function, is used to describe the interaction dynamics. The Schwinger variational iterative method combined with the distorted-wave approximation is applied to calculate scattering amplitudes. Present calculated results are compared with the existing data for electron-$\mathrm{OH}$ scattering in the literature. Also, comparison made between our calculated cross sections for elastic scattering with the theoretical and experimental results for electron-${\mathrm{H}}_2\mathrm{O}$ collisions has revealed remarkable similarity even at incident energies as low as $2\mathrm{eV}$.

We present a different method of extracting the angular distribution of ejected electrons in an ion-atom collision from a two-centered finite Hilbert basis-set calculation. We obtain good agreement with experiment for a $p+\mathrm{H}$ collision at $20\mathrm{keV}$ if we include an interference between the target centered and projectile centered amplitudes.

The transition probability for the emission of a Bessel photon by an atomic system is calculated within first order perturbation theory. We derive a closed expression for the electromagnetic potentials beyond the paraxial approximátion that permits a systematic multipole approximation. The matrix elements for the center of mass and internal motion are explicitly evaluated for some particularly relevant cases. This permits to clarify the feasibility of observing the rotational effects of twisted light on atoms predicted by the calculations. It is shown that the probability that the internal state of an atom acquires orbital angular momentum from light is, in general, maximum for an atom located at the axis of a Bessel mode. For a Gaussian packet, the relevant parameter is the ratio of the spread of the atomic center of mass wave packet to the transversal wavelength of the photon.