High-fidelity entanglement of neutral cold atoms can be achieved by combining several already available techniques such as the creation or dissociation of neutral diatomic molecules, manipulating atoms with microfabricated structures (atom chips), and detecting single atoms with almost 100% efficiency. The fidelity of the resulting entanglement is robust against the details of dissociation process. Manipulating this entanglement with integrated or linear atom optics will open a perspective for quantum-information processing with neutral atoms.

In a quasiclassical framework, we formulate the double-energy-differential cross sections for the Coulomb four-body problem. We present results for the triple photoionization from the Li ground state at 115, 50, and $3.8\mathrm{eV}$ excess energies. With the energy of one of the electrons kept fixed, the double-energy-differential cross sections at $115\mathrm{eV}$ excess energy is found to be of “U-shape" (unequal energy sharing), and in very good agreement with ab initio results. At $50\mathrm{eV}$, it seems that a transition starts taking place to more equal energy sharing configurations. Close to threshold, at $3.8\mathrm{eV}$ excess energy, the equal energy sharing configurations are the dominant ones.

We apply the convergent close-coupling formalism to describe direct double photoionization (DPI) of the valence $n{s}^2$ shell of alkaline-earth-metal atoms: beryllium $(n=2)$, magnesium $(n=3)$, and calcium $(n=4)$. We consider the range of photon energies below the onset of resonant and Auger ionization processes where the subvalent and core electrons can be treated as spectators. By comparing alkaline-earth-metal atoms with helium, we elucidate the role of the ground state and final ionized state correlations in DPI of various quasi-two-electron atoms.

We present experimental and theoretical results for the electron-impact-induced ionization of ground-state helium atoms. Using a high-sensitivity toroidal electron spectrometer, we measured cross-section ratios for transitions leading to the first three excited states of the residual helium ion relative to the transition leaving the ion in the ground state. Measurements were performed for both symmetric- and asymmetric-energy-sharing kinematics. By presenting results as a ratio, a direct comparison can be made between theoretical and experimental predictions without recourse to normalization. The experimental data are compared to theoretical predictions employing various first-order models and a second-order hybrid distorted-wave $+$ convergent $R$ matrix with pseudostates (close-coupling) approach. All the first-order models fail in predicting even the approximate size of the cross-section ratios. The second-order calculations are found to describe the experimental data for asymmetric-energy-sharing with reasonable fidelity, although significant disparities are evident for the symmetric-energy-sharing cases. These comparisons demonstrate the need for further theoretical developments, in which all four charged particles are treated on an equal footing.

In this paper, we study nonsequential double ionization in various molecular fragments for laser polarization aligning either parallel or perpendicular to the molecular axis. In the diatomic molecule ${\mathrm{O}}_2$, we find that nonsequential double ionization can be turned on and off when we simply switch the laser polarization between perpendicular and parallel ionization. Furthermore, we find that the dependence of kinetic energy release on intensity can be used to distinguish sequential versus nonsequential ionization in molecules. The results in this paper allow us to gain better understanding of the role of nonsequential ionization in molecular dissociative ionization.

We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms, we have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that these structures can be made stable.

We examine the lowest excitations of one-dimensional few-boson systems trapped in double wells of variable barrier height. Based on a numerically exact multiconfigurational method, we follow the whole pathway from the noninteracting to the fermionization limit. It is shown how, in a purely harmonic trap, the initially equidistant, degenerate levels are split up due to interactions, but merge again for strong enough coupling. In a double well, the low-lying spectrum is largely rearranged in the course of fermionization, exhibiting level adhesion and (anti)crossings. The evolution of the underlying states is explained in analogy to the ground-state behavior. Our discussion is complemented by illuminating the crossover from a single to a double well.

Extending our previous work on time-optimal quantum state evolution [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006)], we formulate a variational principle for finding the time-optimal realization of a target unitary operation, when the available Hamiltonians are subject to certain constraints dictated either by experimental or by theoretical conditions. Since the time-optimal unitary evolutions do not depend on the input quantum state this is of more direct relevance to quantum computation. We explicitly illustrate our method by considering the case of a two-qubit system self-interacting via an anisotropic Heisenberg Hamiltonian and by deriving the time-optimal unitary evolution for three examples of target quantum gates, namely, the swap of qubits, the quantum Fourier transform, and the entangler gate. We also briefly discuss the case in which certain unitary operations take negligible time.

A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one- and two-qubit systems are special cases contained in this class. The design of this quantum network exploits basic algebraic properties which also shed light onto these covariant quantum processes.

Bell-inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state and Bell inequality, both a lower bound and an upper bound on the maximal violation of the inequality. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.

A practical scheme for entanglement creation between distant atoms located inside a single-mode optical cavity is discussed. We show that the degree of entanglement and the time it takes for the entanglement to reach its optimum value is a sensitive function of the initial conditions and the position of the atoms inside the cavity mode. It is found that the entangled properties of the two atoms can readily be extracted from dynamics of a simple two-level system. Effectively, we engineer two coupled qubits whose dynamics are analogous to that of a driven single two-level system. It is found that spatial variations of the coupling constants actually help to create transient entanglement which may appear on the time scale much longer than that predicted for the case of equal coupling constants. When the atoms are initially prepared in an entangled state, they may remain entangled for all times. We also find that the entanglement exhibits an interesting phenomenon of diffraction when the atoms are located between the nodes and antinodes of the cavity mode. The diffraction pattern of the entanglement varies with time and we explain this effect in terms of the quantum property of complementarity, which is manifested as a tradeoff between the knowledge of energy of the exchanged photon versus the evolution time of the system.

We investigate the nonclassicality of photon-added coherent states in the photon-loss channel by exploring the entanglement potential and negative Wigner distribution. The total negative probability defined by the volume of the negative part of the Wigner function reduces with the decay time. The total negative probability and the entanglement potential of pure photon-added coherent states exhibit the similar dependence on the beam intensity. The reduce of the total negative probability is consistent with the behavior of entanglement potential for the dissipative single-photon-added coherent state at short decay times.

We apply direct frequency-comb spectroscopy, in combination with precision cw spectroscopy, to measure the $4s4p{}^{3}P_1\to 4s5s{}^{3}S_1$ transition frequency in cold calcium atoms. A $657\mathrm{nm}$ ultrastable cw laser was used to excite atoms on the narrow $(\gamma \sim 400\mathrm{Hz})$ $4s^2{}^{1}S_0\to 4s4p{}^{3}P_1$ clock transition, and the direct output of the frequency comb was used to excite those atoms from the $4s4p{}^{3}P_1$ state to the $4s5s{}^{3}S_1$ state. The resonance of this second stage was detected by observing a decrease in population of the ground state as a result of atoms being optically pumped to the metastable $4s4p{}^{3}P_{0,2}$ states. The $4s4p{}^{3}P_1\to 4s5s{}^{3}S_1$ transition frequency is measured to be $\nu =489544285713\left(56\right)\mathrm{kHz}$; an improvement by almost four orders of magnitude over the previously measured value. In addition, we demonstrate spectroscopy on magnetically trapped atoms in the $4s4p{}^{3}P_2$ state.

A theoretical study of dipole and quadrupole Cooper minima, along with dipole and nondipole photoelectron angular distribution parameters, in Hg $6s$ has been performed using the relativistic-random-phase approximation methodology. It is found that the Cooper minima affect the angular distribution parameters dramatically. In addition, the results show that the angular distribution parameters are extremely sensitive to both relativistic and correlation effects (interchannel coupling).

The dynamics of the fermion pairing in a nonequilibrium system of trapped Fermi atoms is investigated in the weak coupling region where formation of weakly bound dimmers of fermionic atoms does not occur. Starting from the microscopic Hamiltonian a system of equations for normal and anomalous nonequilibrium Green’s functions beyond the mean-field approximation is derived. The derived equations include the collisions between the uncorrelated atoms and between the correlated (condensate) and uncorrelated atoms as well. It is shown that when the system is out of thermal equilibrium a new order parameter relaxation mechanism associated with the exchange of atoms between the superfluid and normal components caused by collisions appears. The kinetic equations are discussed within different approximations. Particularly, a closed system of quasiclassical equations for the order parameter and the one-particle distribution function of the Fermi liquid is obtained.

Schemes to generate Greenberger-Horne-Zeilinger (GHZ) and $W$ states of three distant atoms are proposed in this paper. The schemes use the effects of quantum statistics of indistinguishable photons emitted by the atoms inside optical cavities. The advantages of the schemes are their robustness against detection inefficiency and asynchronous emission of the photons. Moreover, in Lamb-Dicke limit, the schemes do not require the simultaneous click of the detectors. This makes the schemes more realizable in experiments.

We consider the Casimir effect between two identical (free-electron) metallic plates with emphasis on the influence of their external boundaries on it. We analyze the contributions of different types of the system eigenmodes to the Casimir energy and force paying particular attention to the role of surface plasmon polariton (SP) modes, which are very sensitive to the dielectric properties at the boundaries. Since their contribution to the Casimir energy and force can be easily calculated separately, it is important to determine the conditions under which the contribution of SP modes is sufficient for the interpretation of the Casimir effect. We perform such calculations for a range of system parameters and conclude that, in all cases, the small separation between the metallic plates is a precondition that SP modes have a dominant influence on the Casimir effect. This precondition is sufficient for thick plates, but in the case of thin plates the contribution of SP modes vs that of photonic modes depends significantly on the dielectric (reflection) properties of the medium supporting the plates.

Detailed calculations demonstrate that the quantum capacitances of nonspherical, rodlike molecular wires scale with their dimensions according to a linear law much like that obeyed by classical, macroscopic spherical capacitors. Further, this linear isoperimetric scaling law leads to a particularly simple formula that relates a molecule’s electron affinity directly to its ionization potential and its spatial dimensions.

We extend previous work on applying the $ϵ$ expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio $\xi =\mu ∕{ϵ}_{\mathrm{F}}$ of chemical potential to ideal gas Fermi energy to next-to-next-to-leading-order (NNLO) in $ϵ=4-d$, where $d$ is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.

Using the structure of the Maxwell-Schrödinger equations in two-level systems in the transient domain, we derive both single-soliton and multisoliton ($2n\pi$ pulse) solutions associated with fast light in resonant media. The analytical solutions enable us to understand the nature of fast light, and should open up new investigations of fast light in the form of localized solutions in a variety of media. We also derive the fast-soliton pair in three-level systems with gain.