Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is required between arbitrarily distant pairs of lattice qubits. An alternative model of quantum computation based on quantum cellular automata (QCA) requires only homogeneous local interactions that can be implemented in parallel. This would be a huge simplification in an actual experiment. We find some minimal physical requirements for the construction of unitary QCA in a one-dimensional Ising spin chain and demonstrate optimal pulse sequences for information transport and entanglement distribution. We also introduce the theory of nonunitary QCA and show by example that nonunitary rules can generate environment assisted entanglement.

We measured the ${\mathrm{Ne}}^{q+}$ charge-state yield distribution for Ne atoms multiply ionized by 1-MeV/amu ${\mathrm{H}}_2^{+},$ in coincidence with the final state of the projectile, for both breakup and nonbreakup channels. Measurements with 1-MeV ${\mathrm{H}}^{+}$ projectiles were also performed. While the ${\mathrm{H}}_2^{+}$ nonbreakup channel produces results similar to equal-velocity proton or electron projectiles, the breakup channels lead to a charge-state yield distribution very close to the known Ne ${2s}^{-1}$ postcollisional decay distribution, measured through photoionization [T. A. Carlson, W. E. Hunt, and M. O. Krause, Phys. Rev. 151, 41 (1966)]. This behavior suggests that, in the breakup channels, contributions to multiple ionization from mechanisms that are usually considered to be dominant in ion-atom collisions are less important than the postcollisional decay.

A practical scaling law that predicts photoelectron angular distributions (PADs) is derived using angular distribution formulas which explicitly contain spontaneous emission. The scaling law is used to analyze recent PAD measurements in above-threshold ionization, and to predict results of future experiments. Our theoretical and numerical studies show that, in the non-relativistic regime and long-wavelength approximation, the shapes of PADs are determined by only three dimensionless numbers: (1) $u_p\equiv U_p/ħ\omega ,$ the ponderomotive number (ponderomotive energy in units of laser photon energy); (2) ${\epsilon }_b\equiv E_b/ħ\omega ,$ the binding number (atomic binding energy in units of the laser photon energy); (3) j, the absorbed-photon number. The scaling law is shown to be useful in predictions of results from strong-field Kapitza-Dirac effect measurements; specifically, the application of this scaling law to recently reported Kapitza-Dirac diffraction is discussed. Possible experimental tests to verify the scaling law are suggested.

Evolution of a dark soliton in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a deep soliton, main characteristics of its motion such as frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well.

The generation of dark solitons from large initial excitations and their evolution in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. We consider three different techniques of controllable creation of multisoliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multisoliton effects are discussed.

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature $T_c$ for a system of a weakly interacting homogeneous dilute Bose gas. We carry out explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-$N$ limit, when the relevant effective static action describing the system is extended to $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ symmetry. Then, using an efficient resummation method, we show how the LDE can already exactly reproduce the known large-$N$ result for $T_c$ at the first nontrivial order. Next, we consider the finite $N=2\mathrm{}$ case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature, allowing comparison with recent Monte Carlo estimates of them. To illustrate the method, we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.

We describe the mechanism of squeezing and entanglement in the ground-state spin subsystems of macroscopic atomic ensembles via the process of stimulated cooperative Raman-type scattering of correlated photon pairs. This mechanism is analogous to common optical pumping techniques normally used for depopulation of Zeeman sublevels in macroscopic atomic ensembles. We show that, by the excitation of atoms, oriented in their angular momenta, with nonclassical light consisting of a rare flux of strongly correlated photon pairs, essential correlations in the macroscopic spin fluctuations can be transferred and accumulated. In turn this leads to squeezing or entanglement in the quasispin (alignment) subsystems of macroscopic ensembles. We discuss in particular a scheme for an interferometer that would be available for the control or teleportation of quantum states created in quasispin subsystems. Such squeezed and entangled states can be stored in long-lived spin subsystems and can be further used in quantum information protocols based on the continuous variable technique.

We present a quantization scheme for the electromagnetic field interacting with atomic systems in the presence of dispersing and absorbing magnetodielectric media, including left-handed material having negative real part of the refractive index. The theory is applied to the spontaneous decay of a two-level atom at the center of a spherical free-space cavity surrounded by magnetodielectric matter of overlapping band-gap zones. Results for both big and small cavities are presented, and the problem of local-field corrections within the real-cavity model is addressed.

We consider pulse propagation in a $\Lambda$-type medium with spatially dependent coherence. It has been shown in previous works that it is impossible to get complete nonlinear energy conversion between an injected pulse and a generated pulse for homogenous coherence distribution. The aim of our work is to achieve unity conversion efficiency. We show by analytic considerations and numerical simulations that this can be achieved only if the propagation satisfies the conditions of adiabaticity in the local frame on the position domain. We also derive an exact analytic model for pulse propagation in our $\Lambda$-type medium, which is valid even if adiabaticity is not satisfied.

Analysis of the generation of spin entanglement from nonrelativistic QED is presented. The results of entanglement are obtained with relativistic correction to the leading order of ${\mathrm{}(v/c)\mathrm{}}^2.$ It is shown that to this order, the degree of entanglement of a singlet state does not change under time evolution, whereas the triplet state can change.

Model wave functions are developed for the excited $\mathrm{}\left(1s\right)\mathrm{}\left(\mathrm{ns}\right)\mathrm{}{}^{1,3}S$ and $\mathrm{}\left(1s\right)\mathrm{}\left(\mathrm{np}\right)\mathrm{}{}^{1,3}P$ states of He and isoelectronic ions, incorporating the asymptotic behavior when one of the electrons is far away, coalescence property when it is close to the nucleus, and cusp property when the two electrons are close to each other. They lead to accurate values for the energies and other properties, and provide an insight into their physical structure.

To discuss one-photon polarization states we find the explicit form of the Wigner’s little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the physical states, only the value of the phase factor is relevant. We show that this phase factor depends only on the direction of the momentum $\mathbf{k}/|\mathbf{k}|$ and does not depend on the frequency $k^0.$ Finally, we use this observation to discuss the transformation properties of the linearly polarized photons and the corresponding reduced density matrix. We find that they transform properly under Lorentz group.

We represent generalized density matrices of a d-complex dimensional quantum system as a subcone of a real pointed cone of revolution in $R^{d^2},$ or indeed a Minkowskian cone in $E^{{1,d}^2-1}.$ Generalized pure states correspond to certain future-directed lightlike vectors of $E^{{1,d}^2-1}.$ This extension of the generalized Bloch sphere enables us to cater for non-trace-preserving quantum operations, and in particular to view the per-outcome effects of generalized measurements. We show that these consist of the product of an orthogonal transform about the axis of the cone of revolution and a positive real linear transform. We give detailed formulas for the one-qubit case and express the post-measurement states in terms of the initial-state vectors and measurement vectors. We apply these results in order to find the information gain versus disturbance trade-off in the case of two equiprobable pure states. Thus we recover Fuchs and Peres’s formula in an elegant manner.

A classical method of effective rotational energy describing the molecular rotation is analyzed from the viewpoint of relative equilibria approach. Explicit formulas for the effective rotational energy up to sixth order in angular-momentum components are derived and compared with the results of quantum approach. The method is applied to get the analytical description of bifurcation in rotational dynamics of ${\mathrm{H}}_{2}X$ molecules without the suggestion of constant bond length.

The spin virial theorem is derived in the time-dependent density-functional theory. It establishes a relationship between the differences of kinetic and potential energies and the currents. It provides a way of checking accuracy of approximations.

We have measured the vector and tensor polarization of an atomic deuterium target as a function of the target density. The polarized deuterium was produced in an atomic beam source and injected into a storage cell. For this experiment, the atomic beam source was operated without rf transitions, in order to avoid complications from the unknown efficiency of these transitions. In this mode, the atomic beam is vector and tensor polarized and both polarizations can be measured simultaneously. We used a 1.2-cm-diam and 27-cm-long storage cell, which yielded an average target density between 3 and $9\times {10}^{11}{\mathrm{a}\mathrm{t}/\mathrm{c}\mathrm{m}}^3.$ We find that the tensor polarization decreases with increasing target density while the vector polarization remains constant. The data are in quantitative agreement with the calculated effect of spin exchange between deuterium atoms at low field.

A split diabatic representation is proposed as a technique for generating diabatic potential curves with the maximal physical content and favorable computational characteristics. This method is a mixed adiabatic-diabatic representation, in which smoothly varying couplings appear in both the kinetic- and potential-energy matrices. It requires the solution of the first-order differential equation for the transformation matrix of the standard strict diabatic representation for which an efficient numerical scheme is also presented. A transformation propagator, akin to the Cayley-Hamiltonian time evolution operator, is employed to obtain the diabatic states while preserving unitarity. Several examples illustrate the advantages of the proposed split diabatic representation.

Radiation emitted by unpolarized high-energy electrons penetrating crystals may be linearly polarized. This occurs when the particle velocity makes an angle with respect to some major crystal axis that is appreciably larger than the axial-channeling angle. For such an orientation, a complete description of spectral and polarization characteristics of the radiation is derived. At planar channeling, a nonperturbative contribution to the probability of the process appears to be caused by the plane field, and we must solve exactly a one-dimensional mechanical problem. For that, the approximate form of the actual plane potential is suggested which provides a precise fit for any crystal plane and an analytical solution to the motion problem. In a practical case, we must consider electron-photon showers developing in sufficiently thick crystals. For the first time, to our knowledge, this development is described taking into account the polarization of photons. We discuss qualitative features of the phenomenon, present results of numerical calculations for thin and thick crystals, and evaluate the possibility of the use of differently oriented crystals in a polarized hard-photon source.

We study the insulator-superfluid transition of spin-1 bosons in an optical lattice in a uniform magnetic field. Based on a mean-field approximation we obtained a zero-temperature phase diagram. We found that depending on the particle number the transition for bosons with antiferromagnetic interaction may occur into different polar superfluid phases with spins aligned along or opposite to the field direction. This is qualitatively different from the field-free transition for which the mean-field theory predicts a unique polar superfluid state for any particle number.

Experimental and numerical investigation of single-beam and pump-probe interaction with a resonantly absorbing dense extended medium under strong and weak field-matter coupling is presented. Significant probe beam amplification and conical emission were observed. Under relatively weak pumping and high medium density, when the condition of strong coupling between field and resonant matter is fulfilled, the probe amplification spectrum has a form of spectral doublet. Stronger pumping leads to the appearance of a single peak of the probe beam amplification at the transition frequency. The greater probe intensity results in an asymmetrical transmission spectrum with amplification at the blue wing of the absorption line and attenuation at the red one. Under high medium density, a broadband of amplification appears. The theoretical model is based on the solution of the Maxwell-Bloch equations for a two-level system. Different types of probe transmission spectra obtained are attributed to complex dynamics of a coherent medium response to broadband polychromatic radiation of a multimode dye laser.