We present a numerical study of the ultrafast ionization dynamics of $\text{H}_2{}^{+}$ exposed to attosecond extreme ultraviolet (xuv) pulses that goes beyond the Born-Openheimer approximation. The four-dimensional, time-dependent Schrödinger equation was solved using a generalization of the finite-element discrete-variable-representation/real-space–product technique used in our previous calculations to include the dynamical motion of the nuclei. This has enabled us to expose the target to any polarized light at arbitrary angles with respect to the molecular axis. Calculations have been performed at different angles and photon energies ($\hslash \omega =50\text{eV}$ up to 630 eV) to investigate the energy and orientation dependence of the photoionization probability. A strong orientation dependence of the photoionization probability of $\text{H}_2{}^{+}$ was found at a photon energy of $\hslash \omega =50\text{eV}$. At this energy, we found that the ionization probability is three times larger in the perpendicular polarization than in the parallel case. These observations are explained by the different geometric “cross sections” seen by the photoejected electron as it leaves the molecule. This ionization anisotropy vanishes at the higher-photon energy of $\hslash \omega \ge 170\text{eV}$. When these higher-energy xuv pulses are polarized perpendicular to the internuclear axis, a “double-slit-like” interference pattern is observed. However, we find that the diffraction angle only approaches the classical formula ${\varphi }_n={\text{sin}}^{-1}\left(n{\lambda }_{\text{e}}/R_0\right)$, where $n$ is the diffraction order, ${\lambda }_{\text{e}}$ is the released electron wavelength, and $R_0$ is the internuclear distance, when $n{\lambda }_{\text{e}}$ becomes less than 65% of $R_0$. These results illustrate the possibility of employing attosecond pulses to perform photoelectron microscopy of molecules.

We present the experimental demonstration of nondestructive probing of the ${{}^{1}S}_0\text{−}{{}^{3}P}_0$ clock transition probability in an optical lattice clock with ${}^{87}\text{S}\text{r}$ atoms. It is based on the phase shift induced by the atoms on a weak off-resonant laser beam. The method we propose is a differential measurement of this phase shift on two modulation sidebands with opposite detuning with respect to the ${{}^{1}S}_0\text{−}{{}^{1}P}_1$ transition, allowing a detection limited by the photon shot noise. We have measured an atomic population of ${10}^4$ atoms with a signal-to-noise ratio of 100 per cycle, while keeping more than 95% of the atoms in the optical lattice with a depth of 0.1 mK. The method proves simple and robust enough to be operated as part of the whole clock setup. This detection scheme enables us to reuse atoms for subsequent clock state interrogations, dramatically reducing the loading time and thereby improving the clock frequency stability.

We examine the phase relationships between different packets of a beam of light emitted from a cavity through a partially transmitting mirror. We find that the beam has a pronounced phase coherence even when the intracavity field has a completely indeterminate phase such as, for example, when it is in a pure photon number state. In this case, the phase coherence can be directly attributed to entanglement caused by the partially transmitting mirror and, even though the external light has phase coherence, it has no identifiable phase. Consequently there is no phase diffusion but there is diffusion of the phase difference between a packet and the intracavity field. Remarkably, we find that the phase coherence of the beam is almost independent of the intracavity state, provided this has a reasonably narrow number-state distribution about a large mean value.

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

The transition from a superfluid to a Mott-insulator (MI) phase has been observed in a Bose-Einstein condensate (BEC) of ytterbium (Yb) atoms in an optical lattice. An all-optically produced BEC of ${}^{174}\text{Y}\text{b}$ atoms was loaded into three-dimensional optical lattices produced by a 532 nm laser beam. The interference pattern was measured after releasing the quantum gas from the trapping potential. As increasing the optical lattice depth, we observed the disappearance of the interference patterns, which is a signature of entering the MI regime. This result is an important step into studies by using a combination of the MI state and the ultranarrow optical transition of ultracold alkaline-earth-metal-like atoms.

Linear mechanical oscillators have been applied to measure very small forces, mostly with the help of noise suppression. In contrast, adding noise to nonlinear oscillators can improve the measurement conditions. Here, this effect of stochastic resonance is demonstrated in a macroscopic torsion oscillator, for an optomechanical nonlinear potential. The signal output is enhanced for a subthreshold electronic signal. This nonlinear oscillator serves as a model system for the enhancement of signal-to-noise ratio in high precision optomechanical experiments.

We discuss the dynamics of a Bose-Einstein condensate in a double-well trap subject to phase noise and particle loss. The phase coherence of a weakly interacting condensate, experimentally measured via the contrast in an interference experiment, as well as the response to an external driving becomes maximal for a finite value of the dissipation rate matching the intrinsic time scales of the system. This can be understood as a stochastic resonance of the many-particle system. Even stronger effects are observed when dissipation acts in concurrence with strong interparticle interactions, restoring the purity of the condensate almost completely and increasing the phase coherence significantly. Our theoretical results are backed by Monte Carlo simulations, which show a good qualitative agreement and provide a microscopic explanation for the observed stochastic resonance effect.

We report on precision laser spectroscopy of the ${{}^{2}S}_{1/2}\left(F=0\right)\text{−}{{}^{2}F}_{7/2}\left(F=3,m_F=0\right)$ clock transition in a single ion of ${{}^{171}\text{Y}\text{b}}^{+}$. A linewidth of $<40\text{Hz}$ is observed and frequency instability due to fluctuation of the ac Stark shift is reduced through improved stability of the beam alignment. The absolute value of the transition frequency, determined using an optical frequency comb, is $642121496772657\pm 12\text{Hz}$ with a fractional uncertainty of $2\times {10}^{-14}$. This is a factor of 50 better than the previously published value [Hosaka et al., IEEE Trans. Instrum. Meas. 54, 759 (2005)].

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.