We study the translational motion of an atom in the vicinity of a weakly driven nanofiber with two fiber-Bragg-grating mirrors. We calculate numerically and analytically the force, the friction coefficients, and the momentum diffusion. We find that the spatial dependences of the force, the friction coefficients, and the momentum diffusion are very complicated due to the evanescent-wave nature of the atom-field coupling as well as the effect of the van der Waals potential. We show that the time development of the mean number of photons in the cavity closely follows the translational motion of the atom through the nodes and antinodes of the fiber-guided cavity standing-wave field even though the cavity finesse is moderate, the cavity is long, and the probe field is weak.

We perform a numeric study (Worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two- and three-dimensional optical lattices. At strong enough interactions and low enough temperatures the system features magnetic ordering. We compute critical temperatures and entropies for the disappearance of the Ising antiferromagnetic and the $\mathit{xy}$-ferromagnetic order and find that the largest possible entropies per particle are $~0.5k_B$. We also estimate (optimistically) the experimental hold times required to reach equilibrium magnetic states to be on a scale of seconds. Low critical entropies and long hold times render the experimental observations of magnetic phases challenging and call for increased control over heating sources.

We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped ${}^{87}\mathrm{Rb}$ atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.

The propagation of polarization-entangled states of light through fluctuating loss channels in the turbulent atmosphere is studied, including the situation of strong losses. We consider violations of Bell inequalities by light, emitted by a parametric down-conversion source, after transmission through the turbulent atmosphere. It is shown by analytical calculations that, in the presence of background radiation and dark counts, fluctuating loss channels may preserve entanglement properties of light even better than standard loss channels, when postselected measurements are applied.

The collective excitation of a gas of highly excited atoms confined to a large spacing ring lattice is studied, where the ground and the excited states are resonantly coupled via a laser field. Attention is focused on the regime where the interaction between the highly excited atoms is very weak in comparison to the Rabi frequency of the laser. In this case, the many-body excitations of the system can be expressed in terms of free spinless fermions. The complex many-particle states arising in this regime are characterized and their properties, for example their correlation functions, are studied. Additional investigation into how some of these many-particle states can actually be experimentally accessed by a temporal variation of the laser parameters is performed.

The conjunction of atom-cavity physics and photonic structures (“solid light” systems) offers new opportunities in terms of more device functionality and the probing of designed emulators of condensed-matter systems. By analogy to the canonical one-electron approximation of solid-state physics, we propose a one-polariton approximation to study these systems. Using this approximation, we apply Bloch states to the uniformly tuned Jaynes-Cummings-Hubbard model to analytically determine the energy-band structure. By analyzing the response of the band structure to local atom-cavity control, we explore its application as a quantum simulator and show phase-transition features absent in mean-field theory. Using this approach for solid light systems, we extend the analysis to include detuning impurities to show the solid light analogy of the semiconductor. This investigation also shows features with no semiconductor analog.

We demonstrate that the characteristics of the high-order harmonic spectra generated by few-cycle carrier-envelope phase-stabilized pulses can be finely adjusted by controlling the time-dependent ellipticity. The experimental measurements show evidence for the generation of single, pairs, and trains of attosecond pulses by controlling the time window of linear polarization of the driving pulses. The influence of the carrier-envelope phase on the generation process in different confinement configurations is interpreted and analyzed using a nonadiabatic stationary phase model. We show that the xuv emission depends critically on particular aspects of the fundamental electric field that allows us to steer the electron trajectories on the time scale of tens of attoseconds.

Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\pi /3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter $t_0$ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\pi /3$.

We propose initial conditions that could facilitate the excitation of rogue waves. Understanding the initial conditions that foster rogue waves could be useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.

Invariant entangled states remain unchanged under simultaneous identical unitary transformations of all their subsystems. We experimentally generate and characterize such invariant two-, four-, and six-photon polarization entangled states. This is done only with a suitable filtering procedure of multiple emissions of entangled photon pairs from a single source without any interferometric overlaps. We get the desired states utilizing bosonic emission enhancement due to indistinguishability. The setup is very stable and gives high interference contrasts. Thus, the process is a very likely candidate for various photonic demonstrations of quantum information protocols.

In this paper, we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.

We present theoretical and experimental studies on quantum path interferences in high-order harmonic generation. Simulations of the single-atom response allow us to calculate the different quantum paths contributions; their relative phases and the resulting interferences can be finely controlled through the laser intensity that provides an efficient means for controlling the electron trajectories with an accuracy on the ten attoseconds time scale. Simulations of the macroscopic response demonstrate the need of spatial and spectral filtering of the harmonic beam in order to observe the interferences between the two shortest quantum paths. Our numerical results are in very good agreement with experimental data. These investigations represent a step toward the full characterization and control of the atomic harmonic dipole.

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)].