For a fast rotating condensate in a harmonic trap, we investigate the structure of the vortex lattice using wave functions minimizing the Gross-Pitaevskii energy in the lowest Landau level. We find that the minimizer of the energy in the rotating frame has a distorted vortex lattice for which we plot the typical distribution. We compute analytically the energy of an infinite regular lattice and of a class of distorted lattices. We find the optimal distortion and relate it to the decay of the wave function. Finally, we generalize our method to other trapping potentials.

We present a numerical study of dispersion manipulation and formation of matter-wave gap solitons in a Bose-Einstein condensate trapped in an optical superlattice. We demonstrate a method for controlled generation of matter-wave gap solitons in a stationary lattice by using an interference pattern of two condensate wave packets, which mimics the structure of the gap soliton near the edge of a spectral band. The efficiency of this method is compared to that of gap soliton generation in a moving lattice recently demonstrated experimentally by Eiermann et al. [Phys. Rev. Lett., 92, 230401 (2004)]. We show that, by changing the relative depths of the superlattice wells, one can fine-tune the effective dispersion of the matter waves at the edges of the minigaps of the superlattice Bloch-wave spectrum and, therefore, effectively control both the peak density and the spatial width of the emerging gap solitons.

The rotational properties of an attractively interacting Bose gas are studied using analytical and numerical methods. We study perturbatively the ground-state phase space for weak interactions, and find that in an anharmonic trap the rotational ground states are vortex or center-of-mass rotational states; the crossover line separating these two phases is calculated. We further show that the Gross-Pitaevskii equation is a valid description of such a gas in the rotating frame and calculate numerically the phase-space structure using this equation. It is found that the transition between vortex and center-of-mass rotation is gradual; furthermore, the perturbative approach is valid only in an exceedingly small portion of phase space. We also present an intuitive picture of the physics involved in terms of correlated successive measurements for the center-of-mass state.

We propose a protocol implementing optimal partial deterministic quantum teleportation for qubits. This is a teleportation scheme realizing deterministically an optimal $1\to 2$ asymmetric universal cloning where one imperfect copy of the input state emerges at the sender’s station while the other copy emerges at receiver’s possibly distant station. The optimality means that the fidelities of the copies saturate the asymmetric cloning inequality. The performance of the protocol relies on the partial deterministic nondemolition Bell measurement that allows us to continuously control the flow of information among the outgoing qubits. We also demonstrate that the measurement is optimal two-qubit operation in the sense of the trade-off between the state disturbance and the information gain.

The angular correlations in the two-photon decay of hydrogenlike ions are studied within the framework of second-order perturbation theory, based on Dirac’s equation. Particular attention has been paid to the effects which arise from the higher (nondipole) terms in the expansion of the electron-photon interaction. It is shown that the photon-photon angular correlation function, which is found symmetric with respect to the angle $\theta =90°$ in the electric dipole approximation, becomes asymmetric because of the nondipole contributions, and that this effect is enhanced as the nuclear charge $Z$ increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2s_{1∕2}\to 1s_{1∕2}$ and $3d_{5∕2}\to 1s_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon $\left({\mathrm{Xe}}^{53+}\right)$ and uranium $\left({\mathrm{U}}^{91+}\right)$ ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).

We present results from $R$-matrix (close-coupling) calculations for elastic scattering and electron impact excitation of Zn. The overall agreement between the predictions from two independent models, using either a semiempirical core potential or a recently developed $B$-spline approach with nonorthogonal orbitals, is very satisfactory. The latter method, however, yields particularly good agreement with the few existing experimental benchmark data for resonances at low incident energies.

In view of the possibilities of laser spectroscopy with very short pulses and relatively high frequencies, we examine aspects of the theory of atom-field interactions that are related to violation of the condition of the long-wavelength approximation (LWA) according to which $kr⪡1$, where $r$ is “of the order of atomic dimensions” and $k$ is the magnitude of the wave vector. On- and off-resonance transitions are considered, with $kr$ being larger than unity due to the large extent of the two wave functions involved in the coupling matrix element. The implementation of the analysis uses bound-free transition matrix elements with the $n=50$ and 80 hydrogenic functions as initial states and values of $k$ up to $27\mathrm{eV}$, which is sufficient to produce $kr>1$, thereby rendering the LWA inoperative. In spite of this, it is shown that, for on-resonance transitions, the results from the use of the well-known multipole operators resulting from the LWA [e.g., the electric dipole approximation (EDA)] agree with those from the exact expressions derived here from the application of the multipolar Hamiltonian. This numerical agreement is proven analytically. As a test of the kind of convergence of the multipole series expansion for small values of $k$ and large $r$, it is shown that the lowest-order ratio of electric dipole to quadrupole matrix elements decreases rapidly within 1.0 atomic unit above threshold. Finally, it is shown that off-resonance couplings lead to differences between the full-interaction operator and the EDA which cannot be neglected. In the extreme case of intrashell couplings for the $n=50$ shell, calculation shows that the $50p$ state is coupled to angular momentum states up to $\ell =21$, compared to the electric dipole coupling of $\Delta \ell =\pm 1$.

We present a detailed comparison of strong-field ionization of diatomic molecules and their companion atoms with nearly equal ionization potentials. We perform calculations in the length and velocity gauge formulations of the molecular strong-field approximation and with the molecular tunneling theory, and in both cases we consider effects of nuclear motion. A comparison of our results with experimental data shows that the length gauge strong-field approximation gives the most reliable predictions.

Recent experiments have observed condensation behavior in a strongly interacting system of fermionic atoms. We interpret these observations in terms of a mean-field version of resonance superfluidity theory. We find that the objects condensed are not bosonic molecules composed of bound fermion pairs, but are rather spatially correlated Cooper pairs whose coherence length is comparable to the mean spacing between atoms. We propose experiments that will help to further probe these novel pairs.

We consider the Bose-Hubbard model of atoms in an optical lattice potential when the atom-atom interactions are attractive. If the lowest-energy lattice sites are degenerate (such as in the homogeneous case), then, at a critical value of the interaction strength, a phase-coherent condensate becomes unstable to a quantum superposition such that the number distribution of each of the degenerate sites becomes double peaked. In the limit when the interaction dominates, the superposition becomes macroscopic and has the form $\mid \psi ⟩\propto {\sum }_j{e}^{i{\varphi }_j}{\widehat{b}}_j^{\mathrm{†}N}\mid \mathrm{vac}⟩$, where $N$ is the total number of atoms and the sum ranges over the energy-degenerate sites.

We show that, if one combines the Jaynes-Cummings and anti-Jaynes-Cummings dynamics in a trapped-ion system driven by a laser, additional series of collapses and revivals of the vibrational state of the ion can be generated.

It is our aim to study the dynamics of a two-level atom immersed in the modified radiation field of a photonic band-gap material using non-Markovian stochastic Schrödinger equations. Up to now, such methodology has only been applied to toy models and not to physically realistic systems as the one presented here. In order to check its validity, we shall study several of the physical phenomena already described in the literature within non-Markovian master equations, such as the long-time-limit residual population in the excited level of the atom and the population inversion which occurs in the atomic system when applying an external laser field. In addition to the stochastic equation, we propose a non-Markovian master equation derived from the stochastic formalism, which in contrast to the current models of master equation preserves positivity. We propose a correlation function for the radiation field (environment) that captures many of the physically relevant aspects of the problem and describes the short-time behavior in a more accurate way than previously proposed ones. This characteristic permits a correct description of the fluctuations of the electromagnetic field, which in the stochastic formalism are represented by the noise, and a better description of the non-Markovian effects in the atomic dynamics. The methodology presented in this paper to apply stochastic Schrödinger equations can be followed to study more complex systems, like many-level atoms embedded in more complicated photonic band-gap structures.

The diatomic gas-phase dications ${\mathrm{BeH}}^{2+}$ and ${\mathrm{BeD}}^{2+}$ with only three electrons have been produced by ${\mathrm{Ar}}^{+}$ sputtering of a Be metal foil with exposure of the surface to toluene $\left({\mathrm{C}}_7{\mathrm{H}}_8\right)$ or water (a mixture of ${\mathrm{D}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{O}$) vapor. ${\mathrm{BeH}}^{2+}$ and ${\mathrm{BeD}}^{2+}$ were observed and unambiguously identified by (mass)/(charge) determination in a magnetic sector mass spectrometer. They survived flight times of $\sim 4\mu \mathrm{s}$. These observations confirm the discovery of ${\mathrm{BeD}}^{2+}$ in an atom-probe experiment by Barofsky and Müller [Surf. Sci. 10, 177 (1968)] and support theoretical predictions of long-lived metastable ${\mathrm{BeH}}^{2+}$.

Within the mean field theory we extend the effective quasi-one-dimensional nonpolynomial Schrödinger equation (NPSE) approach to the description of a spin-1 atomic condensate in a tight radial confinement geometry for both weak and strong atom-atom interactions. Detailed comparisons with full time-dependent 3D numerical simulations show excellent agreement as in the case of a single component scalar condensate, demonstrating our result as an efficient and effective tool for the understanding of spin-1 condensate dynamics observed in several recent experiments.

Intense laser pulse duration effects in the Coulomb explosion of the ${\mathrm{N}}_2$ molecule are studied using 10- and 40-fs laser pulses in the ${10}^{14}–{10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ intensity range. At 10 fs, no significant molecular stretching is observed during multi-ionization events up to the ${\mathrm{N}}^{2+}+{\mathrm{N}}^{2+}$ fragmentation channel. Kinetic energy releases are larger and fragmentation yields are lower at 10 fs than at 40 fs due to the $1∕R$ scaling of the molecular multi-ionization thresholds. These results open the way to Coulomb explosion imaging of neutral molecules using intense sub-10-fs laser pulses.

We investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons. In particular, we systematically derive the so-called Dolinar scheme that achieves the minimum-error discrimination of binary coherent states. Moreover, we show that the Dolinar-type approach can also be applied to projection measurements in the regime of photonic-qubit signals. Our results demonstrate that for implementing a projection measurement with linear optics, in principle, unit success probability may be approached even without the use of expensive entangled auxiliary states, as they are needed in all known (near-)deterministic linear-optics proposals.

Time-ordered superoperators are used to develop a unified description of nonlinear density response and spontaneous fluctuations of many-electron systems. The $p\mathrm{th}$-order density response functions are decomposed into $2^{p+1}$ non-causal Liouville space pathways. Individual pathways are symmetric to the interchange of their space, time, and superoperator indices and can thus be calculated as functional derivatives. Other combinations of these pathways represent spontaneous density fluctuations and the response of such fluctuations to an external field. The resolution of the causality paradox of time-dependent density-functional theory (TDDFT) is shown to be intimately connected with the nonretarded nature of fluctuations.

A projectile traveling inside a metal can excite bulk plasmons (collective oscillations of the electron gas) that eventually decay. The two main decay mechanisms are the excitation of a Bloch electron and the excitation of a pair of interacting free electrons. In recent publications we developed a model to study these mechanisms for proton impact. In this Brief Report, we extend that model in order to consider an electron as the projectile and deal with the numerical difficulties this projectile choice brings along.

We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the complete evolution of the combined qubit-EMF system, thus allowing for the coherent backaction from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find nonexponential decay for both the diagonal and nondiagonal matrix elements of the qubit’s reduced density matrix in the pointer basis. The former shows the qubit relaxing to thermal equilibrium with the bath, while the latter shows the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero-temperature value as the qubit and bath become entangled. The decoherence and relaxation rates are comparable, as in the zero-temperature case. On the entanglement of a qubit with the EMF we calculated the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.

We investigate bipartite entanglement in spin-$1∕2$ systems on a generic lattice. For states that are an equal superposition of elements of a group $G$ of spin flips acting on the fully polarized state ${\mid 0⟩}^{\otimes n}$, we find that the von Neumann entropy depends only on the boundary between the two subsystems $A$ and $B$. These states are stabilized by the group $G$. A physical realization of such states is given by the ground state manifold of the Kitaev’s model on a Riemann surface of genus $\mathfrak{g}$. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem $A$ and is equal to the perimeter (up to an additive constant) when $A$ is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i.e., no partition has zero entanglement. We also provide several examples for the square lattice.