A series of measurements and calculations has been carried out for angle-differential elastic e-Cs scattering in the intermediate-energy region from 4 eV to 25 eV. The experiment used spin-polarized beams to obtain several spin-asymmetry functions and the relative cross section in the angular range from 40° to 140°. Two theoretical methods were used for the calculations: A nonrelativistic convergent close-coupling treatment, which can predict the differential cross section and the (spin) exchange asymmetry, and a semirelativistic R matrix with pseudostates approach, which also predicts nonvanishing results for two other asymmetries that require the presence of relativistic effects. Given the difficulty of the problem, the overall agreement between the experimental data and the theoretical predictions is very satisfactory.

We study the time-dependent dynamics of ${\mathrm{N}}^{4+}$ ions colliding with atomic hydrogen for projectile energies ranging from a fraction of an eV/amu up to 25 keV/amu using the electron-nuclear dynamics (END) formalism. The END theory obtains the electron-nuclear coupled equations of motion from the time-dependent variational principle employing a coherent state parametrization of the wave function. This approach leads to a simultaneous nonadiabatic dynamics of all the electrons and nuclei. We calculate and discuss dynamical trajectories, deflection functions, final charge states, differential cross sections, and energy loss. Quantum effects of the forward peak scattering are emphasized. Due to the strong interaction between the heavy ion and the hydrogen atom, a “diffuse ion” (vide infra) is formed, leading to acceleration or energy gain of the projectile. For the case of the electron transfer cross section, we found that it does not follow the Langevin-type cross section at low projectile energies as reported by other methods. Present results show good agreement with available experimental data.

In this paper, we solve for the exact wave functions of a two-dimensional harmonic oscillator under the influence of a static magnetic field. This is done through the use of the so-called Ermakov invariants, similarity transformed so as to obtain a time-independent Schrödinger equation. In the same manner, time-dependent eigenvalues are also computed. It is shown that previous results for the invariants are particular cases for the ones found in this work.

Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum mechanics. Recent interest in quantum communications and cryptography, however, has provided retrodiction with a potential practical application. For this purpose quantum retrodiction in open systems should be more relevant than in closed systems isolated from the environment. In this paper we study retrodiction in open systems and develop a general master equation for the backward time evolution of the measured state, which can be used for calculating preparation probabilities. We solve the master equation, by way of example, for the driven two-level atom coupled to the electromagnetic field.

Fisher information (FI) is normally developed and applied within the context of classical mathematical statistics. Here we show that it alternatively arises as physical properties of a generally decoherent system. Two kinds of Fisher information are treated: the classical FI $I\left[p\right]$ and the FI channel capacity 〈I〉. These are shown to be linearly related to the partition function Z, the coherence function $\rho {(x,x}^{\prime }),$ the two-point coherence function $\tau \left(\Delta x\right),$ the entropy of fluctuation $H\left(\Delta x\right),$ and the cross entropy $H_{\mathrm{KL}}\left(\rho {/r}_{\Delta }\right)$ between the system probability density function $\rho \mathrm{}(x,x)\mathrm{}$ and its shifted version $\rho (x+\Delta x,x+\Delta x).\mathrm{}$

Parity nonconservation due to the nuclear weak charge is considered. We demonstrate that the radiative corrections to this effect due to the vacuum fluctuations of the characteristic size larger than the nuclear radius $r_0$ and smaller than the electron Compton wavelength ${\lambda }_C$ are enhanced because of the strong electric field of the nucleus. The parameter that allows one to classify the corrections is the large logarithm $\ln \left({\lambda }_C{/r}_0\right).\mathrm{}$ The vacuum polarization contribution is enhanced by the second power of the logarithm. Although the self-energy and the vertex corrections do not vanish, they contain only the first power of the logarithm. The value of the radiative correction is 0.4% for Cs and 0.9% for Tl, Pb, and Bi. We discuss also how the correction affects the interpretation of the experimental data on parity nonconservation in atoms.

We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the extreme points of a convex set of states with constant fidelity, and use this to prove tight lower and upper bounds on the fidelity for a given amount of entanglement.

For a system of N indistinguishable fermions or bosons, we give a parametrization of the surface of a convex set of N-representable second-order density matrices, a polynomial equation for the exact energy levels, and an explanation of quantum phase transitions. We display the crucial role played by the Kummer variety as a graph of the 2-matrices for pure discrete states of an N-body system in quantum mechanics.

An approach based on parametric equations of motion for the transition operator and the Green’s operator is presented. The formulation applies generally to discrete and continuous states of quantum-mechanical many-body systems. The method provides an alternative to solving the Schrödinger equation as a boundary value problem by replacing it with an equivalent initial value problem.

The dynamics of an atom waveguide X-junction beam splitter becomes truly one dimensional in a regime of low temperatures and densities and large positive scattering lengths where the transverse mode becomes frozen and the many-body Schrödinger dynamics becomes exactly soluble via a generalized Fermi-Bose mapping theorem. We analyze the interferometric response of a double-X-junction interferometer of this type due to potential differences between the interferometer arms.

The notions of three-particle entanglement and three-particle nonlocality are discussed in the light of Svetlichny’s inequality [Phys. Rev. D 35, 3066 (1987)]. It is shown that there exist sets of measurements, which can be used to prove three-particle entanglement, but which are nevertheless useless at proving three-particle nonlocality. In particular, it is shown that the quantum predictions giving a maximal violation of Mermin’s three-particle Bell inequality [Phys. Rev. Lett. 65, 1838 (1990)] can be reproduced by a hybrid hidden variables model in which nonlocal correlations are present only between two of the particles. It should be possible, however, to test the existence of both three-particle entanglement and three-particle nonlocality for any given quantum state via Svetlichny’s inequality.

The helium ground-state nonrelativistic energy with 24 significant digits is presented. The calculations are based on variational expansion with randomly chosen exponents. This data can be used as a benchmark for other approaches for many-electron and/or three-body systems.

We present an analytical solution of the coupled Maxwell-Bloch equations for the case of a laser-driven and coherently prepared medium with one upper state and N lower states. We show that under specific conditions the medium can become either completely opaque or completely transparent to the laser pulses. We also study the potential for efficient parametric generation of $N-m$ laser pulses and show that this is possible by injecting the system with m input pulses.

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover’s algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor’s algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.

General conditions are derived for preventing the decoherence of a single two-state quantum system (qubit) in a thermal bath. The employed auxiliary systems required for this purpose are merely assumed to be weak for the general condition while various examples such as extra qubits and extra classical fields are studied for applications in quantum information processing. The general condition is confirmed by well known approaches toward inhibiting decoherence. An approach to decoherence-free quantum memories and quantum operations is presented by placing the qubit into the center of a sphere with extra qubits on its surface.

We report an experimental determination of the state-to-state rate constants of ${\mathrm{N}}_2$ in the vibrational ground state as a function of temperature, in the range $3<T<\mathrm{}16\mathrm{}\mathrm{K}.$ These rate constants were obtained by inversion of the master equation in a procedure not resorting to any particular fitting law. The coefficients of the master equation were obtained experimentally on the basis of Raman spectroscopic data from supersonic expansions of ${\mathrm{N}}_2.$

Energy distributions of ${\mathrm{He}}^{+}$ and ${\mathrm{He}}_2^{+}$ ions produced in ultracold $\mathrm{He}\left(2\mathrm{}{}^3{S}_1\right)+\mathrm{He}\left(2\mathrm{}{}^3{P}_2\right)$ collisions are presented. These helium metastable atoms are trapped and cooled in a magneto-optical trap, and have a temperature of $1.1\pm 0.2\hspace{0.5em}\mathrm{mK}.$ Initial kinetic energies of the product ${\mathrm{He}}^{+}$ and ${\mathrm{He}}_2^{+}$ ions are analyzed in energy, using a weak electrostatic extraction field in combination with a time-of-flight technique. A pronounced structure is observed in the ${\mathrm{He}}^{+}$ ion distribution, which can be well explained by a theoretical model that considers the avoided crossings between only three metastable ${}^3{\Sigma }_{\mathrm{g}}^{+}$ states of the transient ${\mathrm{He}}_2$ molecule. The measured ${\mathrm{He}}_2^{+}$ distribution has a width that is consistent with the maximum recoil energy of 1.1 meV.

We consider theoretically the novel technique in magnetic-resonance-force microscopy that is called “oscillating-cantilever-driven adiabatic reversals.” We present an analytical and numerical analysis for the stationary cantilever vibrations in this technique. For reasonable values of parameters, we estimate the resonant frequency shift as 6 Hz per the Bohr magneton. We analyze also the regime of small oscillations of the paramagnetic moment near the transversal plane and the frequency shift of the damped cantilever vibrations.

We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the diffusion Monte Carlo method, we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.

This paper presents a detailed analysis, based on the first-principles finite-difference time-domain method, of the resonant frequency, quality factor $\mathrm{}\left(Q\right),$ mode volume $\mathrm{}\left(V\right),$ and radiation pattern of the fundamental ${(HE}_{11})$ mode in a three-dimensional distributed-Bragg-reflector (DBR) micropost microcavity. By treating this structure as a one-dimensional cylindrical photonic crystal containing a single defect, we are able to push the limits of $Q/V$ beyond those achievable by standard micropost designs, based on the simple rules established for planar DBR microcavities. We show that some of the rules that work well for designing large-diameter microposts (e.g., high-refractive-index contrast) fail to provide high-quality cavities with small diameters. By tuning the thicknesses of mirror layers and the spacer, the number of mirror pairs, the refractive indices of high- and low-refractive index regions, and the cavity diameter, we are able to achieve Q as high as ${10}^4,$ together with a mode volume of $1.6$ cubic wavelengths of light in the high-refractive-index material. The combination of high Q and small V makes these structures promising candidates for the observation of such cavity-quantum-electrodynamics phenomena as strong coupling between a quantum dot and the cavity field, and single-quantum-dot lasing.