We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.

We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schrödinger equation using only annihilation and creation operators of four harmonic oscillators, coupled by various terms of degree up to 12. We analyze in detail the discrete symmetry properties of the eigenstates. The energy levels and eigenstates of the two-dimensional helium atom are obtained numerically, by expanding the Schrödinger equation on a convenient basis set that gives sparse banded matrices, and thus opens up the way to accurate and efficient calculations. We give some very accurate values of the energy levels of the first bound Rydberg series. Using the complex coordinate method, we are also able to calculate energies and widths of doubly excited states, i.e., resonances above the first ionization threshold. For the two-dimensional ${\mathrm{H}}^{-}$ ion, only one bound state is found.

We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfine states of the BEC. We find that the presence of intrinsic interatomic collisions creates degeneracy in energy that allows implementation of the non-Abelian geometric phases as well. The evolutions produced can be used to produce interference between different atomic species with high numbers of atoms or to fine control the difference in atoms between the two species. Finally, we show that errors in the standard Berry phase due to elastic collisions may be corrected by controlling inelastic collisions between atoms.

We consider the Casimir interaction of a pair of systems at a large separation r and at a temperature T. For atoms a and b, $V_{a,b}\mathrm{}(r,0\mathrm{})\mathrm{}$ has long been known and $V_{a,b}\mathrm{}(r,T)\mathrm{}$ has recently been calculated. $V_{I,El}\mathrm{}(r,0\mathrm{})\mathrm{}$ for an ion and a bound electron—specifically, for ${\mathrm{He}}^{+}$ and a Rydberg electron—has also long been known. The analyses were quantum theoretical, as is our study of $V_{I,El}(r,T\sim \infty );$ it, and $V_{a,b}(r,T\sim \infty ),$ are classical (that is, $ħ$ independent), the real photons dominating the virtual photons. We show that both classical results can also be obtained within a completely classical context; they represent classical Casimir effects. (The physical picture of the origin of $V_{a,b}(r,T\sim \infty )$ and $V_{I,El}(r,T\sim \infty )$ is the same classically and quantum mechanically. The Casimir energy arises from the interference between a wave scattered directly by system A and a wave first scattered by system B and then scattered by system A. Scattering by A alone or B alone does not contribute to the interaction of A and B.) We also consider $V_{El,El}(r,T\sim \infty ),$ $V_{W,El}(r,T\sim \infty ),$ and $V_{W,At}(r,T\sim \infty ),$ the interactions of two electrons, of a wall and an electron, and of a wall and an atom.

Photoelectron angular distributions and total photoionization cross sections of near-threshold $1s$ photoionization of Li from the oriented-in-space endohedral $\mathrm{Li}@{\mathrm{C}}_{60}$ fullerene are investigated within the framework of our recently developed photoionization theory of multicenter formations. Both at-the-center and off-the-center endohedral Li are considered, and off-the-center effects are shown to be of extreme importance, in contrast to the conventional wisdom. Multiple-scattering effects on the outgoing photoelectron are included and found to influence the photoionization spectra strongly, e.g., decreasing the cross section by more than an order of magnitude in certain cases, as compared to the situation when such effects are neglected. Diffraction resonances in the photoionization cross section of the endohedral Li atom are found as a result of the multicenter nature of the ${\mathrm{C}}_{60}$ surrounding cage, and these are compared with the results of other empirical and ab initio theories. Since there is nothing particularly special about Li $1s$ with respect to photoionization, the trends uncovered in this paper should qualitatively apply to near-threshold inner-shell $\mathrm{ns}$ photoionization spectra of virtually any endohedral atom A from any $A@{\mathrm{C}}_{60}$ endohedral fullerene formation.

Collision-induced absorption spectra for mixed neon-argon clusters are investigated in the temperature range from 1 K to 250 K using classical molecular dynamics simulations. With increasing cluster size the spectra reproduce the results known from experiment. For smaller clusters $(n+m\approx 10),$ the simulated spectra depend strongly on the composition of the clusters. Pairwise, Ne-Ne, Ne-Ar, and Ar-Ar interactions designed to accurately describe macroscopic and microscopic properties are used. The influence of two different parametrizations of the dipole moment function is investigated and discussed. For the largest clusters $\left({\mathrm{Ne}}_{10}{\mathrm{Ar}}_{90}\right),$ the maximum intensity of the collision-induced infrared spectrum as a function of the temperature closely follows the experimental observations.

The theoretical foundations of a general approach to the measurement problem of vibrational observables in trapped ion systems is reported. The method rests upon the introduction of a simple vibronic coupling structure appropriately conceived to link the internal ionic state measurement outcomes to the mean value of a motional variable of interest. Some applications are provided and discussed in detail, bringing to light the feasibility and the wide potentiality of the proposal.

The quantum and classical dynamics in a two-dimensional (2D) periodic potential influenced by a constant force is discussed and compared. Classically, the dynamics is chaotic. A branched flow of the particles similar but more structured than the coherent branched flow in a 2D electron gas is observed. In the classical case, the formation of separate decay channels is explained by dynamical trapping. The quantum dynamics closely follows the classical one.

We present a comprehensive analysis of the nonlinear Landau-Zener tunneling. We find characteristic scaling or power laws for the critical behavior that occurs as the nonlinear parameter equals to the gap of avoided crossing energy levels. For the nonlinear parameter larger than the energy gap, a closed-form solution is derived for the nonlinear tunneling probability, which is shown to be a good approximation to the exact solution for a wide range of the parameters. Finally, we discuss the experimental realization of the nonlinear model and possible observation of the scaling or power laws using a Bose-Einstein condensate in an accelerating optical lattice.

We have demonstrated a method of generation and real-time detection of nanostructures in a cold Rb cloud. These structures, which are periodic gratings of atomic density, appear as a result of interference of atoms diffracted by pulses of an optical standing wave of wavelength $\lambda .$ We have detected structures of period $\lambda /2\mathrm{}$ and $\lambda /4.\mathrm{}$ Calculations indicate that these density gratings have period $\lambda /2N$ for integer N. While the structures with the period $\lambda /2\mathrm{}$ are easily detected by Bragg scattering of an optical probe beam, the shorter-period structures are not. For their detection we have developed a three-pulse echo method, in which the shorter-period gratings get converted into the structures with period $\lambda /2,$ readily detected in real time. Applications related to lithography are discussed.

The relative stability of various axisymmetric vortices in a spinor Bose-Einstein condensate with $F=1\mathrm{}$ is examined within extended Bogoliubov theory. This yields the phase diagram in the plane of external rotation frequency vs magnetization. We compare antiferromagnetic, nonmagnetic, and ferromagnetic cases. The excitation spectrum is evaluated under rotation to investigate the local stability of the possible vortices and the vortex nucleation frequency.

A general theory for solving the Hamilton-Jacobi partial differential equations for constrained Hamiltonian systems is proposed. The quantization of constrained systems is then applied using the WKB approximation. The constraints become conditions on the wave function to be satisfied in the semiclassical limit.

We investigate teleportation of bipartite pure entanglement through two equally noisy quantum channel states, namely, a mixture of Bell states. There is a particular mixed-state channel for which all pure entangled states in a known biorthogonal product basis remain entangled after this inexact teleportation, which occurs for the duration of the entanglement. The Werner state channel lacks both these features. The relation of these noisy channels to the violation of Bell’s inequality and quantum two-entropy inequality is studied.

When sending a quantum state which originally has nonclassical properties such as various kinds of squeezing and photon antibunching effects according to the protocol for teleportation of continuous variables [S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998)], we investigate to what extent those nonclassical properties can be preserved in the teleported field. Explicit conditions of the squeezing parameter for the second- and fourth-order quadrature-phase squeezings, the squared amplitude squeezing, and the photon antibunching effect to survive in the teleported field are obtained.

It has been conjectured that the entangled output state from a beam splitter requires nonclassicality in the input state [M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002)]. Here we give a proof for this conjecture.

We consider the dense coding of entangled qubits shared between two parties, Alice and Bob. The efficiency of classical information gain through quantum entangled qubits is also considered for the case of pairwise entangled qubits and maximally entangled qubits. We conclude that using the pairwise entangled qubits can be more efficient when two parties communicate whereas using the maximally entangled qubits can be more efficient when the N parties communicate.

The behavior of the dipole moments of molecular transitions is analyzed as a function of the internuclear distance R and it is shown that for allowed transitions the departure of the dipole moment from the value for the unperturbed atom varies as $R^{-3}$ with a coefficient that can be obtained from the dynamic polarizability of one atom evaluated at the unperturbed transition frequency of the other.

We investigate the stabilization of hydrogen atoms in a circularly polarized laser field. We use a three-dimensional, time-dependent approach to study the quantum dynamics of hydrogen atoms subject to high-intensity, short-wavelength, laser pulses. We find an enhanced survival probability as the field is increased under fixed envelope conditions. We also confirm wave packet behaviors previously seen in two-dimensional time-dependent computations.

We present a method for creating a monopole in an antiferromagnetic spin-1 Bose-Einstein condensate. The required phase engineering of the multicomponent condensate is achieved using light shifts, which depend on both the magnetic substate $m_F$ and polarization of the incident laser beam.

We show that the nonlinear quadrature-dependent Bogoliubov transformations proposed by Siena et al. [Phys. Rev. A 64, 063803 (2001)] can in fact be constructed by the combination of two unitary transformations, a quadrature-dependent displacement followed by the standard squeezed transformation. Such a decomposition turns a nonlinear problem into an essentially linear one so that we are able to express explicitly the mean values and deviations of the quadrature operators and the photon variables under the multiphoton states in terms of those quantities averaged over the standard squeezed states involving only the quadrature-independent Bogoliubov transformation.