Quantum systems with Hofstadter’s butterfly spectrum are of fundamental interest to many research areas. Based upon slight modifications of existing cold-atom experiments, a cold-atom realization of quantum maps with Hofstadter’s butterfly spectrum is proposed. Connections and differences between our realization and the kicked Harper model are identified. This work also exposes, for the first time, a simple connection between the kicked Harper model and the kicked rotor model, the two paradigms of classical and quantum chaos.

In this paper we study the Coulomb corrections to the Delbrück scattering amplitude. We consider the limit when the energy of the photon is much less than the electron mass. The calculations are carried out in the coordinate representation using the exact relativistic Green function of an electron in a Coulomb field. The resulting relative corrections are of the order of a few percent for a large charge of the nucleus. We compare the corrections with the corresponding ones calculated through the dispersion integral of the pair production cross section and also with the magnetic loop contribution to the $g$ factor of a bound electron. The last one is in a good agreement with our results but the corrections calculated through the dispersion relation are not.

Linear optics is a promising candidate to enable the construction of quantum computers. A number of quantum protocols gates based on linear optics have been demonstrated. However, it is well known that these gates are nondeterministic and that higher order nonlinearity is necessary for deterministic operations. We found the quantum leader election protocol can be operated deterministically only with linear optics, and we have demonstrated the nearly deterministic operation which overcomes classical limit.

We address the general problem of removing correlations from quantum states while preserving local quantum information as much as possible. We provide a complete solution in the case of two qubits by evaluating the minimum amount of noise that is necessary to decorrelate covariant sets of bipartite states. We show that two harmonic oscillators in an arbitrary Gaussian state can be decorrelated by a Gaussian covariant map. Finally, for finite-dimensional Hilbert spaces, we prove that states obtained from most cloning channels (e.g., universal and phase-covariant cloning) can be decorrelated only at the expense of a complete erasure of information about the copied state. More generally, in finite dimension, cloning without correlations is impossible for continuous sets of states. On the contrary, for continuous variables cloning, a slight modification of the customary setup for cloning coherent states allows one to obtain clones without correlations.

We report a simple quantum-key-distribution experiment in which Alice and Bob do not need to share a common polarization direction in order to send information. Logical qubits are encoded into nonseparable states of polarization and first-order transverse spatial modes of the same photon.

We have applied our recent approach [M. Kargarian et al., Phys. Rev. A 76, 060304(R) (2007)] to study the quantum-information properties of the anisotropic $s=1/2$ Heisenberg chain. We have investigated the underlying quantum-information properties such as the evolution of concurrence, entanglement entropy, nonanalytic behaviors, and the scaling close to the quantum critical point of the model. Both the concurrence and the entanglement entropy develop two saturated values after enough iterations of the renormalization of coupling constants. These values are associated with the two different phases, i.e., Néel and spin liquid phases. The nonanalytic behavior comes from the divergence of the first derivative of both measures of entanglement as the size of the system becomes large. The renormalization scheme demonstrates how the minimum value of the first derivative and its position scales with an exponent of the system size. It is shown that this exponent is directly related to the critical properties of the model, i.e., the exponent governing the divergence of the correlation length close to the quantum critical point. We also use a renormalization method based on the quantum group concept in order to get more insight about the critical properties of the model and the renormalization of entanglement.

A number of properties of the low-lying states of the ${\text{Sr}}^{+}$ ion are evaluated by diagonalizing a semiempirical Hamiltonian in a large dimension single electron basis. These properties include the oscillator strengths connecting the low-lying states, the quadrupole moments, and the polarizabilities. In addition, the long-range dispersion coefficients for the states of this ion interacting with a number of atoms are given. The polarizabilities and dispersion coefficients can be used to estimate frequency shifts of the ${\text{Sr}}^{+}$ $5s\to 4d$ clock transition due to background fields, including the blackbody radiation shift, and shifts due to collisions with a buffer gas.

We present a theoretical and experimental study of polarization spectroscopy of rubidium atoms. All of the populations of the magnetic sublevels were calculated from the rate equations and used in the calculation of the polarization spectroscopy spectra. Using this model, we could generate theoretical line shapes of the polarization spectra on the $D_2$ transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.

We report on the realization of a chip-based multipole ion trap manufactured using microelectromechanical systems technology, requiring minimal manual alignment of the electrodes. It provides ion confinement in an almost field-free volume between two planes of radiofrequency electrodes, deposited on glass substrates, which allows for optical access to the trap. An analytical model of the effective trapping potential is presented and compared with numerical calculations. Stable trapping of argon ions is achieved, and a lifetime of 16 s is measured. Electrostatic charging of the chip surfaces is studied and found to agree with a numerical estimate.

Adapting earlier results that are appropriate in x-ray and perturbative regimes, the double-differential probability of multiphoton ionization by a phase-controlled ultrashort pulse is given. The infinite-pulse-length limit is also discussed. The numerical calculation was carried out in the case of two-photon processes and for a hydrogen-type $1s$ initial state that describes well most inner $\left(K\right)$ shells. The numerical results indicate that the efficiency of multiphoton ionization strongly increases with the shortening of the length of a few-cycle pulse. A moderate carrier-envelope phase dependence of the ionization probability has been found in the one-cycle case only.

We study the formation of vortices in a Bose-Einstein condensate (BEC) that has been prepared by allowing isolated and independent condensed fragments to merge together. We focus on the experimental setup of Scherer et al. [Phys. Rev. Lett. 98, 110402 (2007)], where three BECs are created in a magnetic trap that is segmented into three regions by a repulsive optical potential; the BECs merge together as the optical potential is removed. First, we study the two-dimensional case; in particular, we examine the effects of the relative phases of the different fragments and the removal rate of the optical potential on the vortex formation. We find that many vortices are created by instant removal of the optical potential regardless of relative phases, and that fewer vortices are created if the intensity of the optical potential is gradually ramped down and the condensed fragments gradually merge. In all cases, self-annihilation of vortices of opposite charge is observed. We also find that for sufficiently long barrier ramp times, the initial relative phases between the fragments leave a clear imprint on the resulting topological configuration. Finally, we study the three-dimensional system and the formation of vortex lines and vortex rings due to the merger of the BEC fragments; our results illustrate how the relevant vorticity is manifested for appropriate phase differences, as well as how it may be masked by the planar projections observed experimentally.

The properties of the uniform Bose gas are studied within the optimized variational perturbation theory (Gaussian approximation) in a self-consistent way. It is shown that the atomic Bose-Einstein condensate with a repulsive interaction becomes unstable when the gas parameter $\gamma =\rho a^3$ exceeds a critical value ${\gamma }_{crit}\approx 0.01$. The quantum corrections beyond the Bogoliubov-Popov approximation to the energy density, chemical potential, and pressure in powers of $\sqrt{\gamma }$ expansions are presented.

Two-component equal-mass Fermi gases, in which unlike atoms interact through a short-range two-body potential and like atoms do not interact, are stable even when the interspecies $s$-wave scattering length becomes infinitely large. Solving the many-body Schrödinger equation within a hyperspherical framework and by Monte Carlo techniques, this paper investigates how the properties of trapped two-component gases change if a third or fourth component are added. If all interspecies scattering lengths are equal and negative, our calculations suggest that both three- and four-component Fermi gases become unstable for a certain critical set of parameters. The relevant length scale associated with the collapse is set by the interspecies scattering length and we argue that the collapse is similar to the collapse of an attractive trapped Bose gas, a many-body phenomenon. Furthermore, we consider a three-component Fermi gas in which two interspecies scattering lengths are negative while the other interspecies scattering length is zero. In this case, the stability of the Fermi system is predicted to depend appreciably on the range of the underlying two-body potential. We find parameter combinations for which the system appears to become unstable for a finite negative scattering length and parameter combinations for which the system appears to be made up of weakly bound trimers that consist of one fermion of each species.

Temporal evolution of a macroscopic condensate of ultracold atoms is usually driven by mean-field potentials, either due to scattering between atoms or due to coupling to external fields; and coherent quantum dynamics of this type have been observed in various cold atom experiments. In this paper, we report results of studies of a class of quantum spin dynamics which are purely driven by zero point quantum fluctuations of spin collective coordinates. Unlike the usual mean-field coherent dynamics, quantum-fluctuation-controlled spin dynamics (or QFCSD) studied here are very sensitive to variation of quantum fluctuations and the corresponding driving potentials induced by zero point motions can be tuned by four to five orders of magnitude using optical lattices. These dynamics have unique dependence on optical lattice potential depths and quadratic Zeeman fields. We also find that thermal fluctuations generally can further enhance the induced potentials although the enhancement in deep optical lattices is much less substantial than in traps or shallow lattices. QFCSD can be potentially used to calibrate quantum fluctuations and investigate correlated fluctuations and various universal scaling properties near quantum critical points.

We study vortex-lattice phases for a Bose gas trapped in a rotating optical-lattice near the superfluid–Mott-insulator transition. We find a series of abrupt structural phase transitions where vortices are pinned with their cores only on plaquettes or only on sites. We discuss connections between these vortex structures and the Hofstadter-butterfly spectrum of free particles on a rotating lattice.

We present a theoretical model for the propagation of non-self-interacting atom laser beams. We start from a general propagation integral equation and we use the same approximations as in photon optics to derive tools to calculate the atom-laser-beam propagation. We discuss the approximations that allow one to reduce the general equation whether to a Fresnel-Kirchhoff integral calculated by using the stationary phase method, or to the eikonal. Within the paraxial approximation, we also introduce the $ABCD$ matrices formalism and the beam quality factor. As an example, we apply these tools to analyze the recent experiment by Riou et al. [Phys. Rev. Lett. 96, 070404 (2006)].

A pair of optical cavities are designed and set up so as to be insensitive to both temperature fluctuations and mechanical vibrations. With the influence of these perturbations removed, a fundamental limit to the frequency stability of the optical cavity is revealed. The stability of a laser locked to the cavity reaches a floor $<2\times {10}^{-15}$ for averaging times in the range $0.5-100$ s. This limit is attributed to Brownian motion of the mirror substrates and coatings.

We discuss propagation effects in realistic, transparent, metallodielectric photonic band gap structures in the context of negative refraction and super-resolution in the visible and near infrared ranges. In the resonance tunneling regime, we find that for transverse-magnetic incident polarization, field localization effects contribute to a waveguiding phenomenon that makes it possible for the light to remain confined within a small fraction of a wavelength, without any transverse boundaries, due to the suppression of diffraction. This effect is related to negative refraction of the Poynting vector inside each metal layer, balanced by normal refraction inside the adjacent dielectric layer: The degree of field localization and material dispersion together determine the total momentum that resides within any given layer, and thus the direction of energy flow. We find that the transport of evanescent wave vectors is mediated by the excitation of quasistationary, low group velocity surface waves responsible for relatively large losses. As representative examples we consider transparent metallodielectric stacks such as $\mathrm{Ag}∕{\mathrm{TiO}}_2$ and $\mathrm{Ag}∕\mathrm{GaP}$ and show in detail how to obtain the optimum conditions for high transmittance of both propagating and evanescent modes for super-guiding and super-resolution applications across the visible and near IR ranges. Finally, we study the influence of gain on super-resolution. We find that the introduction of gain can compensate the losses caused by the excitation of surface plasmons, improves the resolving characteristics of the lens, and leads to gain-tunable super-resolution.

Electromagnetic wave propagation in rotationally symmetric bianisotropic structures is investigated. Spherical solutions are presented in compact tensor (matrix) form with separated angle and radial variables. The separation is achieved by applying tensor functions $F_{lm}\left(\theta ,\phi \right)$ based on ordinary scalar and vector spherical harmonics. Such tensor functions describe the angle dependences of partial spherical waves. The scattering problem for a multilayered bianisotropic spherical particle is solved using an impedance tensor and evolution operator (transfer matrix). These quantities have been previously defined for planar and cylindrical structures. The approach developed is applied to computing the differential cross section of a plane wave from a two-layer bianisotropic sphere.

We show how the effects of vacuum-induced coherence can be realized by studying photon-photon correlation in the $\pi$-polarized fluorescence in the $j=1/2$ to $j=1/2$ transition. These effects should thus be observable in measurements of photon statistics in, for example, Hg and Ba ion traps.