We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single $X$H molecular state when $X$ is one of the bosonic alkali atoms: ${}^7\mathrm{Li}$, ${}^{23}\mathrm{Na}$, ${}^{39}\mathrm{K}$, ${}^{87}\mathrm{Rb}$, or ${}^{133}\mathrm{Cs}$. As a result, the only recombination process is the one that leads to formation of $X$H molecules, $\text{H}+\text{H}+X\to X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for $\text{H}+X\text{H}$ collisions up to a temperature of 0.5 K, including the partial wave contributions from $J^{\Pi }=0^{+}$ to $5^{-}$. We have also found that there is just one three-body bound state for such systems for $J^{\Pi }=0^{+}$ and no bound states for higher angular momenta.

Symmetric charge-transfer cross sections of III$a$ rare-earth-metal elements (Sc, Y, and Gd) in the impact energy range of 30 to 1000 eV were measured for the first time. The experiments were performed with a crossed-beam apparatus that featured primary ion production by photoionization with a tunable dye laser. Comparing the cross sections of III$a$ rare-earth-metal elements (${\sigma }_{\mathrm{Sc}}$, ${\sigma }_Y$, and ${\sigma }_{\mathrm{Gd}}$) with those of alkali metals or helium ${\sigma }_0$, we found that ${\sigma }_0\approx {\sigma }_{\mathrm{Sc}}<{\sigma }_Y<{\sigma }_{\mathrm{Gd}}\approx 2{\sigma }_0$at an impact energy of 1000 eV.

We present a theoretical study of the motion of the antihydrogen atom ($\overline{\mathrm{H}}$) in the gravitational field of Earth above a material surface. We predict that the $\overline{\mathrm{H}}$ atom, falling in the gravitational field of Earth above a material surface, would settle into long-lived quantum states. We point out a method of measuring the difference in the energy of $\overline{\mathrm{H}}$ in such states. The method allows for spectroscopy of gravitational levels based on atom-interferometric principles. We analyze the general feasibility of performing experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force ($\mathit{Mg}$) acting on $\overline{\mathrm{H}}$ and that they might be of interest in the context of testing the weak equivalence principle for antimatter.

X-ray free-electron lasers (FELs) are promising tools for structural determination of macromolecules via coherent x-ray scattering. During ultrashort and ultraintense x-ray pulses with an atomic-scale wavelength, samples are subject to radiation damage and possibly become highly ionized, which may influence the quality of x-ray scattering patterns. We develop a toolkit to treat detailed ionization, relaxation, and scattering dynamics for an atom within a consistent theoretical framework. The coherent x-ray scattering problem including radiation damage is investigated as a function of x-ray FEL parameters such as pulse length, fluence, and photon energy. We find that the x-ray scattering intensity saturates at a fluence of $~$${10}^7$ photon/Å${}^2$ per pulse but can be maximized by using a pulse duration much shorter than the time scales involved in the relaxation of the inner-shell vacancy states created. Under these conditions, both inner-shell electrons in a carbon atom are removed, and the resulting hollow atom gives rise to a scattering pattern with little loss of quality for a spatial resolution $>1$ Å. Our numerical results predict that in order to scatter from a carbon atom 0.1 photon per x-ray pulse, within a spatial resolution of 1.7 Å, a fluence of $1\times {10}^7$ photons/Å${}^2$ per pulse is required at a pulse length of 1 fs and a photon energy of 12 keV. By using a pulse length of a few hundred attoseconds, one can suppress even secondary ionization processes in extended systems. The present results suggest that high-brightness attosecond x-ray FELs would be ideal for single-shot imaging of individual macromolecules.

The generation of photon pairs from randomly poled nonlinear crystals is investigated using an analytically soluble model and numerical calculations. Randomly poled crystals are discovered as sources of entangled ultra broadband signal and idler fields. Their photon-pair generation rates scale linearly with the number of domains. Entanglement times as short as several fs can be reached. A comparison with chirped periodically poled structures is given and reveals close similarity.

We study the problem of cooling a mechanical oscillator using the photothermal (bolometric) force. Contrary to previous attempts to model this system, we take into account the noise effects due to the granular nature of photon absorption. We achieve this by developing a Langevin formalism for the motion of the cantilever, valid in the bad-cavity limit, which includes both photon absorption shot noise and the noise due to radiation pressure. This allows us to tackle the cooling problem down to the noise-dominated regime and to find reasonable estimates for the lowest achievable phonon occupation in the cantilever.

We propose a scheme to teleport a superposition of squeezed coherent states from one mode of a lossy cavity to one mode of a second lossy cavity. Based on current experimental capabilities, we present a calculation of the fidelity demonstrating that accurate quantum teleportation can be achieved for some parameters of the squeezed coherent states superposition. The signature of successful quantum teleportation is present in the negative values of the Wigner function.

We conducted photodetachment spectroscopy near the lowest detachment threshold from ${\mathrm{O}}^{-}$ in a 1-T field with sufficient resolution to observe a magnetic field structure similar to that observed in experiments conducted at the threshold of the electron affinity. These observations included not only cyclotron structure but also, to a smaller degree, individual Zeeman thresholds. The experiment was conducted in a Penning ion trap and with a single-mode, tunable, amplified diode laser. Finally, analysis of our results yielded a measurement of the lowest threshold energy.

We report on a simple trapping scheme for the generation of Bose-Einstein condensates of ${}^{87}\mathrm{Rb}$ atoms. This scheme employs a near-infrared single-beam optical dipole trap combined with a weak magnetic quadrupole field as used for magneto-optical trapping to enhance the confinement in axial direction. Efficient forced evaporative cooling to the phase transition is achieved in this weak hybrid trap via reduction of the laser intensity of the optical dipole trap at constant magnetic field gradient.

The statistical properties of patch electric fields due to a polycrystalline metal surface are calculated. The fluctuations in the electric field scale like $1/z^2$ when $z\gg w$, where $z$ is the distance to the surface and $w$ is the characteristic length scale of the surface patches. For typical thermally evaporated gold surfaces these field fluctuations are comparable to the image field of an elementary charge, and scale in the same way with distance to the surface. Expressions for calculating the statistics of the inhomogeneous broadening of Rydberg-atom energies due to patch electric fields are presented. Spatial variations in the patch fields over the Rydberg orbit are found to be insignificant.

We have found an exact analytical solution of the Bogoliubov–de Gennes equations for the Tkachenko modes of the vortex lattice in the lowest Landau level (LLL) in the thermodynamic limit (geometry of an infinite plane) at any momenta and calculated their damping rates. At finite temperatures both Beliaev and Landau damping leads to momentum-independent damping rates in the low-energy limit, which shows that, at sufficiently low energies, Tkachenko modes become strongly damped. We then found that the mean-square fluctuations of the density grow logarithmically at large distances, which indicates that the state is ordered in the vortex lattice only on a finite (although exponentially large) distance scale and introduces a low-momentum cutoff. Using this circumstance we showed that at finite temperatures the one-body density matrix undergoes an exponential decay at large distances.

We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity that is used to amplify a dispersively coupled input signal. Focusing on an operating regime that is near a bifurcation point, we derive simple asymptotic expressions describing the cavity’s noise and response. We show that the cavity’s backaction and imprecision noise allow for quantum-limited linear amplification and position detection only if one is able to utilize the sizable correlations between these quantities. This is possible when one amplifies a nonresonant signal but is not possible in quantum nondemolition qubit detection. We also consider the possibility of using the nonlinear cavity’s backaction for cooling a mechanical mode.

Electromagnetic induced transparency (EIT) can be produced in a four-level atomic system in the W scheme using a linearly polarized optical field for simultaneously slowing down two $\sigma {}^{+}$ and $\sigma {}^{-}$ circularly polarized optical fields. This four-level atomic system can be set up with a $|{}^1{S}_0\rangle$ ground state and three Zeeman levels of the $|{}^1{P}_1\rangle$ excited state of any alkali-metal atom placed in a weak magnetic field. We apply our W scheme to ultracold magnesium atoms for neglecting the collisional dephasing. Atomic coherences are reported after solving a density matrix master equation including radiative relaxations from Zeeman states of the $|{}^1{P}_1\rangle$ multiplet to the $|{}^1{S}_0\rangle$ ground state. The EIT feature is analyzed using the transit time between the normal dispersive region and the EIT region. The evolution of the EIT feature with the variation of the coupling field is discussed using an intuitive dressed-state representation. We analyze the sensitivity of an EIT feature to pressure broadening of the excited Zeeman states.

Quantitative spectroscopy has been used to measure accurately the Doppler broadening of atomic transitions in ${}^{85}\mathrm{Rb}$ vapor. By using a conventional platinum resistance thermometer and the Doppler thermometry technique, we were able to determine $k_B$ with a relative uncertainty of $4.1\times {10}^{-4}$ and with a deviation of $2.7\times {10}^{-4}$ from the expected value. Our experiment, using an effusive vapor, departs significantly from other Doppler-broadened thermometry (DBT) techniques, which rely on weakly absorbing molecules in a diffusive regime. In these circumstances, very different systematic effects such as magnetic sensitivity and optical pumping are dominant. Using the model developed recently by Stace and Luiten, we estimate the perturbation due to optical pumping of the measured $k_B$ value was less than $4\times {10}^{-6}$. The effects of optical pumping on atomic and molecular DBT experiments is mapped over a wide range of beam size and saturation intensity, indicating possible avenues for improvement. We also compare the line-broadening mechanisms, windows of operation and detection limits of some recent DBT experiments.

Hollow-core photonic-crystal waveguides filled with cold atoms can support giant optical nonlinearities through nondispersive propagation of light tightly confined in the transverse direction. Here we explore electromagnetically induced transparency is such structures, considering a pair of counterpropagating weak quantum fields in the medium of coherently driven atoms in the ladder configuration. Strong dipole-dipole interactions between optically excited, polarized Rydberg states of the atoms translate into a large dispersive interaction between the two fields. This can be used to attain a spatially homogeneous conditional phase shift of $\pi$ for two single-photon pulses, realizing a deterministic photonic phase gate, or to implement a quantum nondemolition measurement of the photon number in the signal pulse by a coherent probe, thereby achieving a heralded source of single- or few-photon pulses.

We theoretically study nonlinear optical frequency conversion with time-frequency entangled paired photons whose sum frequency is on two-photon resonance of an atomic ensemble. Assisted by a strong coupling laser, two paired photons with wide spectrum are converted into a single monochromatic photon. The on-resonance nonlinear process is made possible due to the electromagnetically induced transparency that not only eliminates the on-resonance absorption but also enhances the nonlinear interaction between the single photons and atoms. Compared to this quantum-nonlinear conversion, the classical corresponding single-photon counts from accidental two-photon coincidence has a wide spectrum and experiences large absorption. As a result, the system can be used as an efficient two-photon quantum correlator in which the classical accidental coincidences can be suppressed. We perform numerical simulations basing on a Rb atomic vapor cell with realistic operating parameters.

Photon-added coherent states have been realized in optical parametric down-conversion by Zavatta et al. [Science 306, 660 (2004)]. In this report, it is established that the states generated in the process are ideal photon-added coherent states. It is shown that the scheme can generate higher-order photon-added coherent states. A comparative study of the down-conversion process and atom-cavity interaction in generating the photon-added coherent states is presented.

Employing a short-range two-channel description, we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a parametrization of the energy-dependent scattering length that differs from the one previously employed. We validate the model by comparison to full numerical calculations for ${}^6\mathrm{Li}$-${}^{87}\mathrm{Rb}$ and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.