We report the realization of a Bose-Einstein condensate (BEC) in the hydrodynamic regime. The hydrodynamic regime is reached by evaporative cooling at a relatively low density suppressing the effect of avalanches. With the suppression of avalanches a BEC containing more than ${10}^8$ atoms is produced. The collisional opacity can be tuned from the collisionless regime to a collisional opacity of more than 2 by compressing the trap after condensation. In the collisional opaque regime a significant heating of the cloud at time scales shorter than half of the radial trap period is measured, which is a direct proof that the BEC is hydrodynamic.

We theoretically study single and two-qubit dynamics in the circuit QED architecture. We focus on the current experimental design [Wallraff et al., Nature (London) 431, 162 (2004); Schuster et al., Nature (London) 445, 515 (2007)] in which superconducting charge qubits are capacitively coupled to a single high-$Q$ superconducting coplanar resonator. In this system, logical gates are realized by driving the resonator with microwave fields. Advantages of this architecture are that it allows for multiqubit gates between non-nearest qubits and for the realization of gates in parallel, opening the possibility of fault-tolerant quantum computation with superconduting circuits. In this paper, we focus on one- and two-qubit gates that do not require moving away from the charge-degeneracy “sweet spot.” This is advantageous as it helps to increase the qubit dephasing time and does not require modification of the original circuit QED. However, these gates can, in some cases, be slower than those that do not use this constraint. Five types of two-qubit gates are discussed, these include gates based on virtual photons, real excitation of the resonator, and a gate based on the geometric phase. We also point out the importance of selection rules when working at the charge degeneracy point.

A parameter of the $P,T$-odd Hamiltonian characterizing interaction of the nuclear Schiff moment with the gradient of electronic density on the Xe nucleus is calculated for an isolated Xe atom and for liquid xenon. We use a more realistic model of liquid medium than the spherical cell model used by Ravaine and Derevianko [Phys. Rev. A 69, 050101(R) (2004)]. Qualitatively different results for enhancement of the $P,T$-odd effect in liquid xenon are obtained when polarization of the medium is taken into account. Thus, proper choice of the liquid phase model is crucially important even for calculation of the properties dependent mostly on the electronic density near a nucleus.

Few-body systems with large scattering length $a$ have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass $m$ into a shallow dimer scales as $\hslash a^4∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to ${}^4\mathrm{He}$ atoms as a test case.

The static response properties and the structural stability of silver clusters in the size range $1\le n\le 23$ have been studied using a linear combination of atomic Gaussian-type orbitals within the density functional theory in the finite field approach. The Kohn-Sham equations have been solved in conjunction with a generalized gradient approximation (GGA) exchange-correlation functional. A proof that the finite basis set GGA calculation satisfies the Hellmann-Feynman theorem is also included in the Appendix. The calculated polarizabilities of silver clusters are compared with the experimental measurements and the jellium model in the spillout approximation. Despite the fact that the calculated polarizabilities are in good agreement with both of them, we have found that the polarizability appears to be strongly correlated to the cluster shape and the highest occupied–lowest unoccupied molecular-orbital gap.

A laser-cooling experiment with ${\mathrm{Ca}}^{+}$ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled ${\mathrm{Ca}}^{+}$ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.

A nondispersing Rydberg wave packet can be made by applying a weak, linearly polarized field at the Kepler frequency of a Rydberg atom. The field phase locks the electron’s motion to the microwave field, and the wave packet retains its spatial localization for times in excess of a microsecond. The electron’s orbital oscillation leads to an oscillating dipole, which can either oscillate in phase or out of phase with the applied microwave field, creating wave packets analogous to Trojan and anti-Trojan wave packets described theoretically. Our observations can be described in both quantum mechanical and classical terms.

We investigate collective excitations coupled with monopole and quadrupole oscillations in two-component fermion condensates in deformed traps. The frequencies of monopole and dipole modes are calculated using Thomas-Fermi theory and the scaling approximation. When the trap is largely deformed, these collective motions are decoupled to the transverse and longitudinal breathing oscillation modes. As the trap approaches becoming spherical, however, they are coupled and show complicated behaviors.

We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small $q$ and the dynamical instability is caused by the excitations with $q=\pi ∕a$ at their onsets, where $q$ is the quasimomentum of excitation and $a$ is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.

Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic.

We report an experimental study of guided transmission of low-energy $(200–350\mathrm{eV})$ electrons through highly ordered ${\mathrm{Al}}_2{\mathrm{O}}_3$ nanocapillaries with large aspect ratio ($140\mathrm{nm}$ diameter and $15\mathrm{\mu }\mathrm{m}$ length). The nanochannel array was prepared using self-ordering phenomena during a two-step anodization process of a high-purity aluminum foil. The experimental results clearly show the existence of the guiding effect, as found for highly charged ions. The guiding of the electron beam was observed for tilt angles up to $12°$. As seen for highly charged ions, the guiding efficiency increases with decreasing electron incident energy. The transmission efficiency appeared to be significantly lower than observed for highly charged ions and, moreover, the intensity of transmitted electrons significantly decreases with decreasing impact energy.

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening. The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.

In this paper, we propose a way to achieve protected universal computation in a neutral-atom quantum computer subject to collective dephasing. Our proposal relies on the existence of a decoherence-free subspace (DFS), resulting from symmetry properties of the errors. After briefly describing the physical system and the error model considered, we show how to encode information into the DFS and build a complete set of safe universal gates. Finally, we provide numerical simulations for the fidelity of the different gates in the presence of time-dependent phase errors and discuss their performance and practical feasibility.

Spin components for the Grassmann product of the one-electron reduced density matrix with itself are compared with those of the two-electron reduced density matrix for the same state. It is found that the Grassmann product introduces some inappropriate behaviors which must be removed by the cumulant but are not what is usually thought of as correlation.

The Hellmann-Feynman theorem in a pure ensemble is extended to a quasidegenerate mixed ensemble (canonical) as an ensemble average value. The theorem is also extended to a grand canonical ensemble wherein average particle number is conserved. Connections with the thermodynamic observables are made. An approximate relation between $\partial {\left[\widehat{H}\right]}_C∕\partial \lambda$ and $\partial {\left[\widehat{H}\right]}_G∕\partial \lambda$ is established at the leading order of the saddle-point approximation.

Xenon multiphoton double ionization pathways are studied in a reaction microscope using a pump-probe arrangement of extreme ultraviolet high harmonic and infrared laser radiation. The momentum of photoelectrons is recorded in coincidence with singly or doubly charged ions. Among all possible routes to multiphoton double ionization, sequential processes using ionic excited states as intermediate steps are clearly identified.

We calculate the ground states and ground state phase diagrams of Bose-Einstein condensates of spin-3 atoms under the assumption of conserved magnetization. We especially concentrate on the ground states of a ${}^{52}\mathrm{Cr}$ condensate. In ${}^{52}\mathrm{Cr}$ the magnetic dipole-dipole interaction enables magnetization changing collisions, but in a strong magnetic field these are suppressed. In the calculation of the phase diagrams we neglect the contribution from the dipole-dipole interaction, but discuss its effects at the end of the paper. We show that the ground state of a ${}^{52}\mathrm{Cr}$ condensate does not seem to depend on whether or not the dipole-dipole interaction is taken into attention.

We describe a nonlocal method for generating entangled coherent states of a two-mode field wherein the field modes never meet. The proposed method is an extension of an earlier proposal [C. C. Gerry, Phys. Rev. A 59, 4095 (1999)] for the generation of superpositions of coherent states. A single photon injected into a Mach-Zehnder interferometer with cross-Kerr media in both arms coupling with two external fields in coherent states produces entangled coherent states upon detection at one of the output ports. We point out that our proposal can be alternatively viewed as a “which path” experiment, and in the case of only one external field, we describe the implementation of a quantum eraser.

We describe gapped single-particle and collective excitations across a superfluid to insulator quantum phase transition of particles (bosons or fermions) in a periodic potential, with an even number of particles per unit cell. We demonstrate that the dynamics are controlled by a quantum impurity problem of a localized particle interacting with the bulk critical modes. Critical exponents are determined by a renormalization group analysis. We discuss applications to spin oscillations of ultracold atoms in optical lattices and to the electronic phases in the cuprate and related compounds.

We derive an alternative representation for the relativistic nonlocal kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and does not depend on an expansion in terms of local operators. We have used the relativistic harmonic oscillator problem to test our formula and we have found that arbitrarily precise results are obtained, simply increasing the number of grid points. More difficult problems have also been considered, observing in all cases the convergence of the numerical results. Using these results we have also derived a new representation for the quantum mechanical Green’s function and for the corresponding path integral. We have tested this representation for a free particle in a box, recovering the exact result after taking the proper limits, and we have also found that the application of the Feynman-Kac formula to our Green’s function yields the correct ground state energy. Our path integral representation allows us to treat Hamiltonians containing nonlocal operators and it could provide to the community a new tool to deal with such class of problems.