In an experiment using the odd calcium isotope ${}^{43}\mathrm{Ca}^{+}$, we combine the merits of a high-fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two “clock” states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qubit rotations, and mapping operations, errors smaller than 1% are achieved, whereas the entangling gate adds errors of 2.3%. Based on these operations, we create Bell states with a fidelity of 96.9(3)% in the optical qubit and a fidelity of 96.7(3)% when mapped to the hyperfine states. In the latter case, the entanglement is preserved for $96\left(3\right)\mathrm{ms}$, exceeding the duration of a single gate operation by three orders of magnitude.

We present some general considerations on the properties of a two-component ultracold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the free energy can be written in terms of a single dimensionless function $h(\xi ,\tau )$, where $\xi =-{\left(k_F{a}_s\right)}^{-1}$ and $\tau =T∕T_F$. The function $h(\xi ,\tau )$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the average rf-spectroscopy shift $\overline{\delta \omega }(\xi ,\tau )$ and the molecular fraction $f_c(\xi ,\tau )$ in the closed channel can be expressed in terms of $h(\xi ,\tau )$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.

We rigorously analyze Knill’s Fibonacci scheme for fault-tolerant quantum computation, which is based on the recursive preparation of Bell states protected by a concatenated error-detecting code. We prove lower bounds on the threshold fault rate of $0.67\times {10}^{-3}$ for adversarial local stochastic noise, and $1.25\times {10}^{-3}$ for independent depolarizing noise. In contrast to other schemes with comparable proved accuracy thresholds, the Fibonacci scheme has a significantly reduced overhead cost because it uses postselection far more sparingly.

It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature $300\mathrm{K}$ to sub-Kelvin temperatures, which is much lower than what is achievable in the absence of the parametric amplifier. This is further illustrated in case of a precooled mirror, where one can reach millikelvin temperatures starting with about $1\mathrm{K}$. Our work demonstrates the fundamental dependence of radiation pressure effects on photon statistics.

We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse points with the theoretical predictions, suggests the feasibility of systematic quasienergy band engineering.

Two-photon processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a $\Lambda$-type system, are strongly affected by the ground-state depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of ${}^{87}\mathrm{Rb}$ vapor. Similar to the relaxation-in-the-dark technique, pumping lasers are used to prealign the atomic vapor in a well-defined quantum state. The free propagation of the atomic state is monitored using a Ramsey-like method. Coherence times in the range $1–10\mathrm{ms}$ were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spin-exchange collisions between rubidium atoms.

We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe the simplest case of two membranes in a cavity, in terms of the coupling of the light fields to the breathing and center-of-mass modes of the membrane array. We show that these normal modes can be optically addressed individually and also be cooled, trapped, and characterized, e.g., via quantum nondemolition measurements. The extension to a larger number of membranes is briefly discussed.

We report here experimental evidence of the reflection of a large fraction of a beam of low energy antiprotons by an aluminum wall. This derives from the analysis of a set of annihilations of antiprotons that come to rest in rarefied helium gas after hitting the end wall of the apparatus. A Monte Carlo simulation of the antiproton path in aluminum indicates that the observed reflection occurs primarily via a multiple Rutherford-style scattering on Al nuclei, at least in the energy range $1–10\mathrm{keV}$ where the phenomenon is most visible in the analyzed data. These results contradict the common belief according to which the interactions between matter and antimatter are dominated by the reciprocally destructive phenomenon of annihilation.

We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state $X{{}^1\Sigma }_{\text{g}}^{+}$ of the ${{}^{39}\text{K}}_2$ molecule. The molecules are prepared in a highly collimated particle beam and are interrogated in a $\Lambda$-type excitation scheme of optical transitions to long range levels close to the asymptote of the ground state, using the electronically excited state ${A{}^1\Sigma }_{\text{u}}^{+}$ as the intermediate one. The transition frequencies are measured either by comparison with ${\text{I}}_2$ lines or by absolute measurements using a fs-frequency comb. The determined level energies were used together with Feshbach resonances from cold collisions of ${}^{39}\text{K}$ and ${}^{40}\text{K}$ reported from other authors to fit ground state potentials. Precise scattering lengths are determined and tests of the validity of the Born-Oppenheimer approximation for the description of cold collisions at this level of precision are performed.

The electromagnetic interaction of an atom or ion with an arbitrary spin nucleus is considered. The effective atomic interaction Hamiltonian is derived by a sequence of unitary transformations to separate out the total motion from the internal degrees of freedom. The obtained finite nuclear mass corrections modify the atomic energy levels in the magnetic field. We present resulting contributions to the electron $\mathit{g}$ factor, the NMR shielding factor, and the magnetic susceptibility.

A CCD array is placed facing a chaotic light source and gated by a photon counting detector that simply counts all randomly scattered and reflected photons from an object. A “ghost” image of the object is then observed in the gated CCD. Differing from all published ghost-imaging experiments, this setup captures ghosts from scattered and reflected light of an object, instead of the transmitted ones. This new feature is not only useful for practical applications, but is also important fundamentally. It further explores the nonclassical interference nature of thermal light ghost imaging.

The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work—on thermal-state and biphoton-state imagers—and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross correlations between the two detected fields, plus a background. Because any pair of cross correlations is obtainable with classical Gaussian states, the image does not carry a quantum signature per se. However, if the image characteristics of classical and nonclassical Gaussian-state sources with identical autocorrelation functions are compared, the nonclassical source provides resolution improvement in its near field and field-of-view improvement in its far field.

We have performed a measurement of the Casimir-Polder force using a magnetically trapped ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. By detecting perturbations of the frequency of center-of-mass oscillations of the condensate perpendicular to the surface, we are able to detect this force at a distance $\sim 5\mu \mathrm{m}$, significantly farther than has been previously achieved, and at a precision approaching that needed to detect the modification due to thermal radiation. Additionally, this technique provides a limit for the presence of non-Newtonian gravity forces in the $\sim 1\mu \mathrm{m}$ range.

We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law ${\mathit{I}}_{\mathit{p}}$+3.17${\mathit{U}}_{\mathit{p}}$, where ${\mathit{I}}_{\mathit{p}}$ is the atomic ionization potential and ${\mathit{U}}_{\mathit{p}}$ is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.

Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. An astigmatic optical system may be used to transform a high-order Laguerre-Gaussian mode into a high-order Hermite-Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.