We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of ${}^6\mathrm{Li}.$ To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a ${\mathrm{CO}}_2$ laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for $B=52.8\mathrm{}\pm 0.4\mathrm{mT},$ consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at $\approx 86\mathrm{mT},$ in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 55 mT.

We report on an experiment demonstrating the conservation of the orbital angular momentum in stimulated down-conversion. It has been demonstrated that the orbital angular momentum is not transferred to the individual beams of the spontaneous down-conversion. It is also known that it is conserved when twin photons are taken individually. We observe the conservation law for an individual beam of the down-conversion through cavity-free stimulated emission.

The nonlinear susceptibility of atomic hydrogen interacting with an intense laser field has been investigated using a numerical solution of the time-dependent Schrödinger equation. It was shown that the behavior of the nonlinear susceptibility strongly depends on the intensity; it increases linearly in the low-intensity regime (Kerr regime), then saturates at a higher intensity. Furthermore, it was also shown that the nonlinear susceptibility is substantially induced by the ionization, whose magnitude is simply related to the density of the ionized electrons. By analyzing the calculated refractive index, it was found that the refractive index induced by ionization is 7–20 % smaller than that derived from the plasma frequency.

The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with “superluminality.” A fundamental limitation on the effect is set by nonrelativistic “causality conditions.” We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the “extrapolated phase time,” one of the quantities proposed to characterize the duration of the barrier’s traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to the thresholds of new bound states, the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.

The quantum Fourier transform is a key factor in achieving exponential speedup relative to classical algorithms. We implemented the phase estimation algorithm, which is the very basic application example of the quantum Fourier transform, on a three-bit nuclear magnetic resonance quantum-information processor. The algorithm was applied to one-bit Grover operators to estimate eigenvalues. We also demonstrated the counting algorithm with the same operators to obtain the number of the marked states. The results of projective measurements required by the algorithms were obtained from the split peak positions in the spectra.

We investigate quantum computation with neutral atoms in optical microtraps where the qubit is implemented in the motional states of the atoms, i.e., in the two lowest vibrational states of each trap. The quantum gate operation is performed by adiabatically approaching two traps and allowing tunneling and cold collisions to take place. We demonstrate the capability of this scheme to realize a square root of swap gate, and address the problem of double occupation and excitation to other unwanted states. We expand the two-particle wave function in an orthonormal basis and analyze quantum correlations throughout the whole gate process. Fidelity of the gate operation is evaluated as a function of the degree of adiabaticity in moving the traps. Simulations are based on rubidium atoms in state-of-the-art optical microtraps with quantum gate realizations in the few tens of milliseconds duration range.

Topological features in quantum computing provide controllability and noise error avoidance in the performance of logical gates. While such resilience is favored in the manipulation of quantum systems, it is very hard to identify topological features in nature. This paper proposes a scheme where holonomic quantum gates have intrinsic topological features. An ion trap is employed where the vibrational modes of the ions are coherently manipulated with lasers in an adiabatic cyclic way producing geometrical holonomic gates. A crucial ingredient of the manipulation procedures is squeezing of the vibrational modes, which effectively suppresses exponentially any undesired fluctuations of the squeezing parameter, thus making the gates resilient to control errors.

In this paper we present a scheme in which the amplitude-quadrature difference and phase-quadrature difference of two bright nonclassical beams serve as a pair of observed complementary variables that can be measured directly and can form a new squeezed state. Mixing such two quadrature-difference squeezed-state beams on a beam splitter produces characteristic of the Einstein-Podolsky-Rosen quantum entanglement. The experimental schemes producing such nonclassical beams and its possible applications in quantum information are discussed.

We propose a nonadiabatic scheme for geometric quantum computation with trapped ions. By making use of the Aharonov-Anandan phase, the proposed scheme not only preserves the globally geometric nature in quantum computation, but also provides the advantage of nonadiabaticity that overcomes the problem of slow evolution in the existing adiabatic schemes. Moreover, the present scheme requires only two atomic levels in each ion, making it an appealing candidate for quantum computation.

The $1sns{}^3{S}^e$ Rydberg series in a two-electron system with the charge of the nucleus, $Z\approx 1,$ is treated by means of the quantum-defect theory. Comparison with configuration interaction calculations suggests that the quantum-defect expression for the energy levels becomes asymptotically exact as $\overrightarrow{Z}1.$ This provides an analytic description of the disappearance of the $1sns{}^3{S}^e$ bound states when Z approaches the critical value of 1.

Total and partial photoionization cross sections have been calculated for all inner subshells of atomic magnesium, calcium, and strontium in the relativistic random-phase approximation, the relativistic random-phase approximation modified to include relaxation effects, and the relativistic random-phase approximation modified to include relaxation and Auger decay. Results of the three models are compared with Dirac-Hartree-Fock calculations and with semiempirical results so that the import of various many-body effects can be assessed. Branching ratios and photoelectron angular-distribution asymmetry parameters are also presented for np subshells. Substantial relaxation effects are noted for photoionization of $1s$ and $2s$ subshells.

The photoabsorption cross section for ${\mathrm{Ni}}^{14+}$ has been calculated using an intermediate-coupling frame-transformation technique, together with the R-matrix method and multichannel quantum-defect theory. We find the interesting result that, in addition to the usual geometric frame transformation, dynamic frame transformations involving term coupling in both the ${\mathrm{Ni}}^{15+}$ target states and the ${\mathrm{Ni}}^{14+}$ initial ground state are important. These computed cross sections are virtually indistinguishable from those obtained with the more elaborate Breit-Pauli R matrix method, validating the applicability of frame-transformation methods to open-shell systems.

Observation of nonthermal, light-induced desorption of Cs and Rb atoms from paraffin coating is reported. Buffer-gas-free paraffin-coated cells containing Cs and Rb were exposed to laser light of various intensities and frequencies, and the change of the vapor densities as a function of time was investigated. Because atomic polarization relaxes very slowly in paraffin-coated cells (spin-relaxation times can be $\gtrsim 1\mathrm{s}),$ they are applied in a variety of precision measurements (e.g., magnetometry, discrete symmetry tests, etc.). Light-induced desorption may be useful in such measurements as a method to control atomic density without changing the temperature of the cell.

The interactions of charged particles with cylindrical tubules are studied within the framework of the dielectric theory. Elementary excitations on a tubule are modeled by an infinitesimally thin layer of free-electron gas, uniformly distributed over the surface of the tubule. The dielectric function of such a system, obtained from the random-phase approximation, exhibits a dimensional crossover from two-dimensional to one-dimensional electron gas, when the radius of the tubule decreases. Energy loss of a charged particle, moving paraxially in a tubule, can be divided into a single-particle excitation part and a resonant excitation part. It is shown that the resonant excitation modes on a tubule, which dominate the energy loss in the high-velocity regime, are quite different from those in a cylindrical cavity in a solid, described by a bulk dielectric function of the surrounding three-dimensional electron gas.

We present a model for sympathetic cooling of a mixture of fermionic and bosonic atomic gases in harmonic traps, based on a three-fluid description. The model confirms the experimentally observed cooling limit of about ${0.2T}_F$ when only bosons are pumped. We propose sequential cooling—pumping first of bosons and afterward fermions—as a way to obtain lower temperatures. For this scheme, our model predicts that temperatures less than ${0.1T}_F$ can be reached.

The multiphoton selective dissociation of a HF molecule is studied by means of the Lie-algebra method using a quadratic anharmonic Hamiltonian. The averaged absorbed energy in a shaped laser pulse is calculated. The selective dissociation of the target states in chirped and shaped infrared laser fields is discussed. The paper shows that Lie algebra can be employed to discuss multiphoton dissociation.

Photoassociation and the Feshbach resonance are, in principle, feasible means for creating a molecular Bose-Einstein condensate from an already-quantum-degenerate gas of atoms; however, mean-field shifts and irreversible decay place practical constraints on the efficient delivery of stable molecules using either mechanism alone. We therefore propose Feshbach-stimulated Raman photoproduction, i.e., a combination of magnetic and optical methods, as a means to collectively convert degenerate atoms into a stable molecular condensate with near-unit efficiency.

We present results of calculations on Bose-Einstein-condensed ${}^{87}\mathrm{Rb}$ atoms subjected to a moving standing-wave light potential of the form $V_L{\mathrm{}(z,t)=V}_0\mathrm{}\left(t\right)\mathrm{}\cos \left(qz-\omega t\right).\mathrm{}$ We calculate the mean-field dynamics (the order parameter) of the condensate and determine the resulting condensate momentum in the z direction, $P_z(q,\omega {,V}_0{,t}_p),$ where $V_0$ is the peak optical potential strength and $t_p$ is the pulse duration. Although the local-density approximation for the Bogoliubov excitation spectral distribution is a good approximation for very low optical intensities, long pulse duration and sufficiently large values of the wave vector q of the light potential, for small q, short duration pulses, or for not-so-low intensities, the local-density perturbative description of the excitation spectrum breaks down badly, as shown by our results.

We report on a backaction-evading (BAE) measurement of the photon number of fiber-optical solitons operating in the quantum regime. We employ a recently proposed different detection scheme based on spectral filtering of colliding optical solitons. The measurements of the BAE criteria demonstrate significant quantum state preparation and transfer of the input signal to the signal and probe outputs exiting the apparatus, displaying the quantum-nondemolition behavior of the experiment.

Long et al. first used an SO(3) picture to study Grover’s general algorithm. The present paper gives the formulas of the rotation angle and the rotation axis of the rotation $R_{u_0}\in \mathrm{SO}\mathrm{}\left(3\right)\mathrm{}$ in the space simply by means of the invariants of Grover’s general algorithm. Thus it avoids computing $R_{u_0}$ and solving the eigenvalue problem $R_{u_0}\xi =\xi$ for the rotation angle and the rotation axis of the rotation $R_{u_0}$ as Long et al. did. So it saves much space and time. Conversely by means of the rotation angle in the space we can describe the nature of Grover’s algorithm.