We study the photoassociative process between cold atoms and a surface. A mechanism to confine free cold atoms in a planar waveguide, characterized by the long-range atom-surface van der Waals potential and based on radiative transitions, is presented. We propose that the vibrational states of this potential can be probed by reflection spectroscopy, giving information about the $C_3$ van der Waals coefficients.

We describe an atom-optical technique for producing large changes in the momentum of cold atoms using a pulsed standing wave of off-resonant light. Experimental results are presented showing how the efficiency and the amount of momentum transfer depend on the parameters of the light field. We also present a theoretical analysis and derive a closed formula which is in excellent agreement with the experimental data.

Experiments are performed on loading cold atoms into a far-off resonance optical dipole trap that is spatially separated from the laser-cooling region. The atoms are delivered using a far-off resonant optical dipole guide and enter the trap through a switchable blue-detuned light sheet or “trap door.” This scheme provides a means to transfer atoms from a dissipative to a non-dissipative trap without a significant loss of phase-space density. We study the dynamics of atoms within the trap and measure their lifetime. Preliminary results on multiple loading are presented. As the technique does not rely on near-resonant light, the atom number limit characteristic of laser-cooling experiments can, in principle, be exceeded.

We analyze systematic (classical) and fundamental (quantum) limitations of the sensitivity of optical magnetometers resulting from ac Stark shifts. We show that in contrast to absorption-based techniques, the signal reduction associated with classical broadening can be compensated in magnetometers based on phase measurements using electromagnetically induced transparency (EIT). However due to ac Stark–associated quantum noise the signal-to-noise ratio of EIT-based magnetometers attains a maximum value at a certain laser intensity. This value is independent on the quantum statistics of the light and defines a standard quantum limit of sensitivity. We demonstrate that an EIT-based optical magnetometer in Faraday configuration is the best candidate to achieve the highest sensitivity of magnetic-field detection and give a detailed analysis of such a device.

We consider a six-port triangular arrangement of beam splitters designed to couple three electromagnetic fields through U(3) unitary transformations. We present conditions for Hong-Ou-Mandel destructive interference of output triple coincidences when single photons are presented, one at each of the three input ports. Unlike the corresponding four-port effect, three-photon Hong-Ou-Mandel interference is sensitive to mixer phases and input-output port reversal.

When the laser medium only partially fills the cavity of a multimode solid-state laser, there are significant changes in the spectral profile of the emission, the intensity fluctuation power spectra, and modulation transfer functions in comparison with lasers which have media that entirely fill the cavity. These effects are computed according to several approximate models for the multimode interactions and compared with experimental measurements. Symmetries and asymmetries in the multimode optical spectrum have corresponding features in the relaxation oscillation spectra. Changes in the laser cavity detuning and laser excitation lead to relatively abrupt changes in some variables (modal intensities, low-frequency relaxation oscillations) while the total intensity and largest relaxation oscillation frequency vary as they would for a single-mode laser.

We consider spontaneous emission in a four-level atomic system driven by three fields. It is shown that by controlling the phase and the amplitude of the driving fields a wide variety of spectral behavior can be obtained, ranging from a very narrow single spectral line to up to six spectral of varying widths.

The unitary operator that transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different timescale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.

An appropriate representation of the apparent generalized oscillator strength (AGOS) permits the demonstration of its general properties. We show that only the zero-angle trajectory connects continuously the threshold energy $E=\omega$ and the high energy $E=\infty$ corresponding to the optical oscillator strength limit of the AGOS. Far-reaching implications, including the normalization of the measured differential cross sections and the identification of their spurious behavior, are discussed and demonstrated using transitions in H, Li, and Ba.

It was shown that the conventional linear-combination-of-atomic-orbitals (LCAO) approximation does not preserve correlation properties of molecular orbitals and a total molecular wave function of the Hartree-Fock (HF) method in the limit of a united atom. On this basis the correct form of the LCAO approximation has been derived for a homonuclear molecule. The Hartree-Fock calculations of the ${\mathrm{H}}_2$ molecule with the new form of the LCAO approximation have given the total energy with the highest numerical precision. Qualitative conclusions about chemical bonds in molecules are derived from an analysis of the exact solution of the HF equation.

We have simultaneously confined fermionic ${}^{84}\mathrm{Rb}$ and bosonic ${}^{87}\mathrm{Rb}$ atoms in overlapping magneto-optical traps in which radioactive ${}^{84}\mathrm{Rb}$ atoms ${(t}_{1/2}=33\mathrm{}$ d) have been trapped. We investigated ${}^{84}\mathrm{Rb}$ trap loss when overlapped with a cloud of ${}^{87}\mathrm{Rb}$ atoms trapped from a background rubidium vapor. Collision loss measurements were taken with $\sim 5\times {10}^5$ and $\sim 4\times {10}^7$ atoms of trapped ${}^{84}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb},$ respectively. We have found a trapping solution for which there is negligible additional trap loss for ${}^{84}\mathrm{Rb}$ due to the presence of ${}^{87}\mathrm{Rb},$ showing that the mixture can be readily prepared for a sympathetic cooling experiment.

The phases of the circularly polarized harmonics with alternating helicity generated by a bichromatic laser field whose two components are circularly polarized in the same plane but rotate in opposite directions are investigated. Only one trajectory contributes to harmonic generation in the plateau region. The dependence of the harmonic phase on the laser field intensity is weak (with the slope $\sim {0.2U}_p/\omega ).\mathrm{}$ Adjacent harmonics having the same helicity are relatively closely phase locked. As a result, a train of three attosecond pulses per optical cycle of the driving field is generated, each having a width of 80 as. Depending upon whether the two helicity components can be separated the polarization of the pulses is close to circular or close to linear with three different orientations per optical cycle.

Two spatially separated type-I nonlinear crystals are pumped by femtosecond laser pulses to create entangled photon pairs in the process of spontaneous parametric down-conversion. The two-photon entangled state exhibits high-visibility quantum interference for both polarization and space-time variables without the need of stringent spectral postselection by using narrow-band filters. The visibility is insensitive to the thickness of the crystals, unlike in the case of pulse pumped type-II parametric down-conversion; therefore the intensity can be easily increased by using thick nonlinear crystals. This method will be indispensable in experiments that require a pulsed source of entangled photon pairs, such as generation of multiphoton entangled states, quantum teleportation, and quantum communications.

We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential.

We apply the full power of modern electronic band-structure engineering and epitaxial heterostructures to design a transistor that can sense and control a single-donor electron spin. Spin-resonance transistors may form the technological basis for quantum information processing. One- and two-qubit operations are performed by applying a gate bias. The bias electric field pulls the electron wave function away from the dopant ion into layers of different alloy composition. Owing to the variation of the g factor $(\mathrm{Si}:g=1.998,\mathrm{Ge}:g=1.563),$ this displacement changes the spin Zeeman energy, allowing single-qubit operations. By displacing the electron even further, the overlap with neighboring qubits is affected, which allows two-qubit operations. Certain silicon-germanium alloys allow a qubit spacing as large as 200 nm, which is well within the capabilities of current lithographic techniques. We discuss manufacturing limitations and issues regarding scaling up to a large size computer.

Based on our previous calculations of the cross section for photoionization of the excited ${1s}^2{2P(}^2{P}^o)$ state of lithium [H. L. Zhou, S. T. Manson, L. Vo Ky, P. Faucher, F. Bely-Dubau, A. Hibbert, S. Diehl, D. Cubaynes, J.-m. Bizau, L. Journel, and F. J. Wuilleumier, Phys. Rev. A 59, 462 (1999)], an eigenphase derivative technique along with quantum defect theory were employed to obtain the resonance positions and effective quantum numbers $n^{*}=n-\mu$ of the 19 series of ${2l2l}^{\prime }{\mathrm{nl}}^{″}$ resonance up to $n=22.\mathrm{}$ Complicated behaviors due to the interactions among the resonance series were found, leading to series exhibiting dramatic perturbations in positions and strengths along the series, and series whose quantum defects converge only very, very slowly.

Magic numbers predicted by a three-dimensional q-deformed harmonic oscillator with ${\mathrm{u}}_q\mathrm{}\left(3\right)\mathrm{}\supset {\mathrm{so}}_q\mathrm{}\left(3\right)\mathrm{}$ symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, and Cs), noble metals (Cu, Ag, and Au), divalent metals (Zn and Cd), and trivalent metals (Al and In), as well as to theoretical predictions of jellium models, Woods-Saxon and “wine bottle” potentials, and to the classification scheme using the $3n+l$ pseudo quantum number. In alkali-metal clusters, and noble-metal clusters the three-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that ${\mathrm{u}}_q\mathrm{}\left(3\right),$ which is a nonlinear extension of the u(3) symmetry of the spherical (three-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of several metal clusters. The Taylor expansions of angular-momentum-dependent potentials approximately producing the same spectrum as the three-dimensional q-deformed harmonic oscillator are found to be similar to the Taylor expansions of the symmetrized Woods-Saxon potential and wine bottle symmetrized Woods-Saxon potential, which are known to provide successful fits of the Ekardt potentials.

We present a detailed experimental study of the physics involved in transferring atoms from a magneto-optical trap (MOT) to an optical dipole trap. The loading is a dynamical process determined by a loading rate and a density dependent loss rate. The loading rate depends on cooling and the flux of atoms into the trapping volume, and the loss rate is due to excited state collisions induced by the MOT light fields. From this study we found ways to optimize the loading of the optical dipole trap. Key ingredients for maximum loading are found to be a reduction of the hyperfine repump intensity, increased detuning of the MOT light, and a displacement of the optical dipole trap center with respect to the MOT. A factor of 2 increase in the number of loaded atoms is demonstrated by using a hyperfine repump beam with a shadow in it. In this way we load $8\times {10}^6{}^{85}\mathrm{Rb}$ atoms into a 1 mK deep optical dipole trap with a waist of $58\hspace{0.5em}\mu \mathrm{m},$ which is 40% of the atoms initially trapped in the MOT.

We present calculations on the ratio between double and single ionization for He atoms subjected to an intense laser pulse with a wavelength of 0.39 or 0.78 $\mu \mathrm{m}.$ Using a recollision model, we estimate that this ratio reaches a maximum of $5.6\times {10}^{-4},$ four times smaller than the experimental value. This theoretical value is nevertheless a factor of 12 larger than previous recollision values, due to the inclusion of spin factors and a smaller width of the returning wave packet due to the Coulomb field. The recollision mechanism is modified by taking the laser field at the recollision into account, which lowers the required energy for escape from the nucleus. This leads to a lower intensity threshold for the observation of double ionization, and to a factor of 2–3 difference in the probability for double ionization between recollision calculations and experiment. Since this is similar to the expected uncertainty within the recollision model, the calculations support the identification of recollision processes as the main mechanism for double ionization.

We have measured the rate of production of ${\mathrm{Na}}_2^{+}$ ions in collisions of ultracold Na atoms held in a magneto-optical trap (MOT) as a function of probe laser detuning using a single-color probe beam. The ion rate is measured with the atoms mainly in the $3S(f=2\mathrm{})\mathrm{}$ level (“bright MOT”) or the $3S(f=1\mathrm{})\mathrm{}$ level (“dark MOT”). Using recent experimental information about the doubly excited autoionizing states of ${\mathrm{Na}}_2,$ we find that the large structures in the first 5 GHz red of the atomic transition frequency are due to a doubly resonant excitation process with levels in the $0_g^{-}$ potential (asymptotically connected to ${3S}_{1/2}{+3P}_{3/2})$ as the intermediate states, and levels in the $0_u^{-}$ and $1_u$ potentials (asymptotically connected to ${3P}_{3/2}{+3P}_{3/2})$ as the final autoionizing states. We can account for nearly all of the observed structure in this region of the spectra for both the bright and dark MOT.