We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of the trapping geometry on the stability of the condensate as well as the effects of the dipole-dipole interaction on the excitation spectrum. We discuss also the ground state and excitations of a gas composed of two antiparallel dipolar components.

Quasi-instantaneous transverse patterns have been measured in a broad-aperture class A laser, using an ultrafast camera. The evolution from order to fully developed turbulence is observed as the Fresnel number increases up to 110. In the turbulent regime, two very different spatial scales coexist, one order of magnitude apart. The linear analysis allows us to interpret most of the features of the experiment.

Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum-trajectory method. A method is developed for calculating the resonance fluorescence spectra from numerical simulations. It is shown that in the case of dominant incoherent perturbation, the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.

We study two sets of rate equations for sympathetic cooling of harmonically trapped Bose gases. Calculations for mixtures of Na-Rb and Li-Cs show that both sets yield similar results for the cooling times. The equilibration rates are in fair agreement with each other and differ considerably from classical rates. The onset of Bose-Einstein condensation is rather sudden and nonexponential in time, and the growth of the condensate differs for the two different mixtures we studied.

We investigate the propagation of light with ultralow group velocity in a Bose-Einstein condensate where the phase is not uniform. The light is shown to couple strongly to the phase gradient of the condensate. The interaction between the light and the condensate enables us to perform a phase imprinting where the phase of the condensate is imprinted on the light. We illustrate the effect by showing how one can measure the fluctuating phase in an elongated quasicondensate.

We suggest a quantum-measurement model in an ion trap that specifies the probability distribution of two distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter that, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables us to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question as to what extent the Bell inequality can be considered as a measure of entanglement.

Self-energy corrections involving logarithms of the parameter $Z\alpha$ can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic nonlogarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by $\alpha$ the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy “potentials” that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient $B_{62}$ for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of $B_{62}$ based on nonrelativistic quantum electrodynamics. In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.

We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary parts of the coherent state parameter $\alpha ;$ (ii) these states contain only one charge component. Three cases are considered: free particle, relativistic rotator, and particle in a constant homogeneous magnetic field. For the rotational motion of the two latter cases, such a description leads to the appearance of the so-called nonlinear coherent states.

The classical Hamiltonian for which the dynamics is represented by trajectories in a multidimensional phase (coset) space is quantized via Lyapunov analysis. A system of one electron in four sites and the vibration of ${\mathrm{H}}_2\mathrm{O}$ with Fermi resonance is studied. The quantization condition is that the average Lyapunov exponents show local minima as a function of the classical energy. This means that it requests the least global chaoticity. This quantization algorithm leads to results consistent with those obtained by the quantal models.

We investigate the dynamics of two interacting electrons in coupled quantum dots driven by an ac field. We find that the two electrons can be trapped in one of the dots by the ac field, in spite of the strong Coulomb repulsion. In particular, we find that the interaction may enhance the localization effect. We also demonstrate the field excitation procedure to generate the maximally entangled Bell states. The generation time is determined by both analytic and numerical solutions of the time-dependent Schrödinger equation.

For the understanding of irreversibility at the quantum level, the formation and decay of transient (unstable) states play a fundamental role. If the system is treated within Hermitian quantum mechanics, the resulting energy distribution of the resonance state, whose Fourier transform yields the time-dependent probability of decay, $P\left(t\right),$ is real. The physical constraint of the lower bound in the energy spectrum introduces “memory,” and causes nonexponential decay (NED) to set in after $t\gg \tau ,$ where τ is the lifetime defined by exponential decay. The closer to threshold the decaying state is, the earlier NED appears. Apart from the constraint of $E>~0,$ the constraint of $t>~0$ must be accounted for at the same time. It results from the discontinuity at $t=0\mathrm{}$ of the solution of the time-dependent Schrödinger equation, which breaks the unitarity associated with the S matrix and gives rise to a complex energy distribution, as a manifestation of the non-Hermitian property of the decaying states. For a narrow isolated resonance state, for which the self-energy is essentially energy-independent, analytic results for $P_{\mathrm{NED}}\mathrm{}\left(t\right)\mathrm{}$ obtained from semiclassical path-integral calculations agree with the quantum-mechanical ones when both physical constraints $E>\mathrm{}0\mathrm{}$ and $t>\mathrm{}0\mathrm{}$ are taken into account. As an example of the difference in the magnitude of the $P_{\mathrm{NED}}\mathrm{}\left(t\right)\mathrm{}$ when using a real and a complex energy distribution, application is made to the decay of the unstable ${\mathrm{He}}_2^{2+}{}^1{\Sigma }_g^{+}$ ground molecular state.

We analyze a quantum search protocol to retrieve phase information from a Rydberg-atom data register using a subpicosecond half-cycle electric field pulse. Calculations show that the half-cycle pulse can perform the phase retrieval only within a range of peak field values. By varying the phases of the constituent orbitals of the Rydberg wave packet register, we demonstrate coherent control of the phase retrieval process. By specially programming the phases of the orbitals comprising the initial wave packet, we show that it is possible to use the search method as a way to synthesize single energy eigenstates.

The advantages of using quantum systems for performing many computational tasks have already been established. Several quantum algorithms have been developed which exploit the inherent property of quantum systems such as superposition of states and entanglement for efficiently performing certain tasks. The experimental implementation has been achieved on many quantum systems, of which nuclear magnetic resonance has shown the largest progress in terms of number of qubits. This paper describes the use of a spin-7/2 as a three-qubit system and experimentally implements the half-adder and subtractor operations. The required qubits are realized by partially orienting ${}^{133}\mathrm{Cs}$ nuclei in a liquid-crystalline medium, yielding a quadrupolar split well-resolved septet. Another feature of this paper is the proposal that labeling of quantum states of system can be suitably chosen to increase the efficiency of a computational task.

We propose a method to produce entangled spin squeezed states of a large number of atoms inside an optical cavity. By illuminating the atoms with bichromatic light, the coupling to the cavity induces pairwise exchange of excitations which entangles the atoms. Unlike most proposals for entangling atoms by cavity QED, our proposal does not require the strong coupling regime $g^2/\kappa \Gamma \gg 1,$ where g is the atom cavity coupling strength, $\kappa$ is the cavity decay rate, and $\Gamma$ is the decay rate of the atoms. In this work the important parameter is ${\mathrm{Ng}}^2/\kappa \Gamma ,$ where N is the number of atoms, and our proposal permits the production of entanglement in bad cavities as long as they contain a large number of atoms.

Consider a set of N systems and an arbitrary interaction Hamiltonian H that couples them. We investigate the use of local operations and classical communication (LOCC), together with the Hamiltonian H, to simulate a unitary evolution of the N systems according to some other Hamiltonian $H^{\prime }.$ First, we show that the most general simulation using H and LOCC can also be achieved, with the same time efficiency, by just interspersing the evolution of H with local unitary manipulations (LU) of each system and a corresponding local ancilla (in a so-called LU+anc. protocol). Thus, the ability to make local measurements and to communicate classical information does not help in nonlocal Hamiltonian simulation. Second, we show that both for the case of two d-level systems $\mathrm{}(d>\mathrm{}2\mathrm{}),$ or for that of a setting with more than two systems $\mathrm{}(N>\mathrm{}2\mathrm{}),$ LU+anc. protocols are more powerful than LU protocols. Therefore local ancillas are a useful resource for nonlocal Hamiltonian simulation. Third, we use results of majorization theory to explicitly solve the problem of optimal simulation of two-qubit Hamiltonians using LU (equivalently, LU+anc., LO, or LOCC).

We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noises acting on quantum channels. If the quantum channels are subject to isotropic noise, the average fidelity decays to $1/2,$ which is smaller than the best possible value of $2/3$ obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than $2/3.$

An auxiliary system is defined by adiabatic connection. In the ground state the diagonal of the spin-independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term of completely kinetic origin.

Using Lie-algebraic techniques and the simpler expressions of the matrix elements of Majorana operators given by us, we obtain an effective Hamiltonian operator which conveniently describes vibrational spectra of linear tetratomic molecules, including both stretching and bending modes. For a linear symmetrical four-atom molecule ${\mathrm{C}}_2{\mathrm{H}}_2,$ the highly excited vibrational levels are obtained by applying the $\mathrm{u}\mathrm{}\left(4\right)\mathrm{}$ algebraic approach. We have found that the spectra are made up of a clustering structure. The number of levels in one cluster depends on the total quantum number of stretching and bending vibrations. In addition, some other properties, such as the level assignment and the labeling of calculated theoretical results, are also discussed.

Excitation energies, oscillator strengths, and transition rates are calculated for ${(5d}^2{+5d6s+6s}^2\left)-\mathrm{}\right(5d6p+5d5f+6s6p)\mathrm{}$ electric dipole transitions in Yb-like ions with nuclear charges Z ranging from 72 to 100. Relativistic many-body perturbation theory (RMBPT), including the retarded Breit interaction, is used to evaluate retarded $E1\mathrm{}$ matrix elements in length and velocity forms. The calculations start from a $\left[\mathrm{Xe}\right]{4f}^{14}$ core Dirac-Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients, and second-order RMBPT is used to determine matrix elements. A detailed discussion of the various contributions to energy levels and dipole matrix elements is given for ytterbiumlike rhenium, $Z=75.\mathrm{}$ The resulting transition energies are compared with experimental values and with results from other recent calculations. Trends of excitation energies, line strengths, oscillator strengths, and transition rates as functions of nuclear charge Z are shown graphically for selected states and transitions. These calculations are presented as a theoretical benchmark for comparison with experiment and theory.