We propose a feedback scheme to control the vibrational motion of a single trapped particle based on indirect measurements of its position. It results in the possibility of a motional phase-space uncertainty contraction, corresponding to cool the particle close to the motional ground state.

We consider the case when decoherence is due to the fluctuations of some classical variable or parameter of a system and not to its entanglement with the environment. Under few and quite general assumptions, we derive a model-independent formalism for this nondissipative decoherence, and we apply it to explain the decoherence observed in some recent experiments in cavity QED and on trapped ions.

We have used an electron-beam ion trap to measure the wavelength of the $J=2\mathrm{}–3$ magnetic dipole transition in the ${3d}^4$ ground term of Ti-like ytterbium, tungsten, and bismuth. This fills in a gap in previous measurements along this isoelectronic sequence, as well as extending previous work to the highest Z yet. With the addition of our results, measurements of this line now cover a sufficient range of Z to allow an interpolation of reliable wavelength estimates for the unmeasured members of the isoelectronic sequence from $Z=52\mathrm{}$ to 83. We provide a table of these wavelengths for each member of the sequence in this range, and compare the measured wavelengths to recent calculations. Our results show that a long-standing discrepancy between prediction and experiment disappears in the high-$Z$ limit.

We investigate the influence of electron correlation in the double ionization of a two-electron model atom exposed to an intense laser field. Using the freedom of our model system, we vary in a systematic way the correlation strength between the two electrons. For the case of five-photon ionization, while adjusting the laser frequency according to the correlation charge, we investigate extreme situations of strong and weak two-electron interaction regimes. We monitor the single and double ionization yield and study the variation of the nonsequential ionization.

A different integral form of the Schrödinger equation and some boundedness conditions of the wave functions are proved, which exhibit the origin of some divergences in quantum mechanics. The iterations from the integral equation and the boundedness conditions lead to a method for avoiding the divergence difficulties. The result is extended to the time-dependent and the multidimensional cases. Examples of an electron in the Wigner spherical “box” with a $1/r$ perturbed potential, some heliumlike ions in the ground state, and the Stark effect of the hydrogen atom show that this different perturbation method can give rational multiorder corrections of the wave function and energy.

I prove the security of quantum key distribution against individual attacks for realistic signals sources, including weak coherent pulses and down-conversion sources. The proof applies to the Bennett-Brassard 1984 protocol with the standard detection scheme (no strong reference pulse). I obtain a formula for the secure bit rate per time slot of an experimental setup, which can be used to optimize the performance of existing schemes for the considered scenario.

The full ab initio nonadiabatic approach was successfully applied to calculate energy, radiative, and magnetic properties of strong L-uncoupling $i{}^3{\Pi }_g^{-}$ and $j{}^3{\Delta }_g^{-}$ states of molecular hydrogen isotopes, for the first time, to our knowledge. The concomitant electronic L-uncoupling matrix elements between the $i{}^3{\Pi }_g$ and $j{}^3{\Delta }_g$ as well as the $i{}^3{\Pi }_g–b{}^3{\Sigma }_u^{+},$ $i{}^3{\Pi }_g–e{}^3{\Sigma }_u^{+},$ $i{}^3{\Pi }_g–c{}^3{\Pi }_u,$ and $j{}^3{\Delta }_g–c{}^3{\Pi }_u$ transition dipole moment functions were revised by using an electronic full configuration-interaction calculation together with highly accurate ab initio adiabatic potentials taken from the literature. The ab initio results were borne out by quantum-defect theory estimates. Nonadiabatic rovibronic eigenvalues and eigenfunctions for the bound $i{}^3{\Pi }_g^{-}–j{}^3{\Delta }_g^{-}$ perturbation complex were derived by direct numerical solutions of the two channel-coupling radial equations. The theoretical term values of the complex for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ agree with their experimental counterparts within $0.5–1.5\hspace{0.5em}{\mathrm{cm}}^{-1}.$ For the overwhelming majority of levels, the calculated magnetic g factors coincide with the measured ones within their experimental accuracy. The predicted rovibronic transition probabilities to the lower-lying $b{}^3{\Sigma }_u^{+},$ $c{}^3{\Pi }_u,$ and $e{}^3{\Sigma }_u^{+}$ states completely resolve perplexing problems of the radiative data in experiments: lifetimes, branching ratios of fluorescence decay to the $b{}^3{\Sigma }_u^{+}$ and $c{}^3{\Pi }_u^{+}$ states, and the intensity distribution in rotational structure of the $i{}^3{\Pi }_g^{-}–j{}^3{\Delta }_g^{-}\to c{}^3{\Pi }_u^{\pm }$ transitions.

We present details of our recent calculation of ${\alpha }^2$ corrections to the parapositronium decay into two photons. These corrections are rather small and our final result for the parapositronium lifetime agrees well with the most recent measurement. Implications for orthopositronium decays are briefly discussed.

The vibrational and rotational state dependence of dissociative attachment (DA) in low-energy $e-{\mathrm{H}}_2$ and e-HF collisions is studied within the framework of nonlocal resonance theory. The dynamics of nuclear motion in the nonlocal complex potential is treated by the quasiclassical approach. The resonance energy, width function, and level-shift function are taken from our previous calculations based on the projection operator formalism. Results for all vibrational states up to the dissociative attachment thresholds and selected rotational states are presented. Our cross sections for ${\mathrm{H}}_2$ exhibit a plateau structure in the energy range above the dissociation threshold, and this structure gets more pronounced with higher $v$ or J. The dissociative attachment cross section for vibrationally and rotationally hot HF $(T=1150\mathrm{}$ K) agrees well with available experimental data. For ${\mathrm{H}}_2$ in thermal equilibrium at 1400 K, the agreement between experiment and theory is less satisfactory.

We show that atomic interference in the reflection from two suitably polarized evanescent waves is sensitive to retardation effects in the atom-surface interaction for specific experimental parameters. We study the limit of short and long atomic de Broglie wavelengths. The former case is analyzed in the semiclassical approximation (Landau-Zener model). The latter represents a quantum regime and is analyzed by solving numerically the associated coupled Schrödinger equations. We consider a specific experimental scheme and show the results for rubidium (short wavelength) and the much lighter metastable helium atom (long wavelength). The merits of each case are then discussed.

The damping of collective modes and the relaxation of temperature anisotropies in a trapped Bose gas is determined at temperatures above the Bose-Einstein condensation temperature in the collisionless regime. We demonstrate for both cases how the effects of collisions may be treated perturbatively and calculate relaxation rates from a variational principle. Our results are compared with experiment and with previous theoretical calculations.

We discuss an experimental scheme to create a low-dimensional gas of ultracold atoms, based on inelastic bouncing on an evanescent-wave mirror. Close to the turning point of the mirror, the atoms are transferred into an optical dipole trap. This scheme can compress the phase-space density and can ultimately yield an optically driven atom laser. An important issue is the suppression of photon scattering due to “cross talk” between the mirror potential and the trapping potential. We propose that for alkali-metal atoms the photon scattering rate can be suppressed by several orders of magnitude if the atoms are decoupled from the evanescent-wave light. We discuss how such dark states can be achieved by making use of circularly polarized evanescent waves.

The dynamical behavior of semiconductor lasers subject to external optical feedback is analyzed using an approach based on the theory of whole-universe laser modes [R. Lang, M.O. Scully, and W. Lamb, Phys. Rev. A 7, 1788 (1972)]. The system is modeled as a coupled cavity formed by the laser diode and an external reflector. The leakage of each optical mode out of the cavity is characterized by its mode lifetime. The variation of the cavity mode lifetimes is the dominant mechanism which determines the regime of operation. The method yields the expected range of phenomena observed when a laser diode is subjected to optical feedback, without a priori assumptions of the regime of behavior or of the resulting mode wavelengths. For strong optical feedback the imbalance of the lifetimes ensures that a single mode dominates. At other feedback levels the system exhibits chaotic dynamics or stable, multimode operation.

We solve the Gross-Pitaevskii equation to study energy transfer from an oscillating “object” to a trapped Bose-Einstein condensate. Two regimes are found: for object velocities below a critical value, energy is transferred by excitation of phonons at the motion extrema; while above the critical velocity, energy transfer is via vortex formation. The second regime corresponds to significantly enhanced heating, in agreement with a recent experiment.

We propose a scheme for preparing an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated trapped atoms. The scheme utilizes the entangled light fields output from a nondegenerate optical parametric amplifier. Quantum-state exchange between these fields and the motional states of the trapped atoms is accomplished via interactions in cavity QED.

Electron excitation and loss of relativistic ion projectiles colliding with atomic targets are studied within the framework of the first order of the plane-wave Born approximation. General expressions are derived for the elastic and electron-electron contributions to the electron excitation and loss cross sections. In the limit of nonrelativistic collision velocities these expressions go over into known nonrelativistic formulas. In ultrarelativistic collisions shielding effects are shown to be very important for the excitation and loss cross sections even for collisions of highly charged projectiles with light atomic targets. Results of our calculations for the electron loss cross sections are in reasonable agreement with available experimental data on projectile-electron loss in relativistic collisions.

We consider a mixture of a single-component Bose gas and a two-component Fermi gas at temperatures where the Bose gas is almost fully condensed. In such a mixture, two fermionic atoms can interact with each other by exchanging a phonon that propagates through the Bose condensate. We calculate the interaction potential due to this mechanism, and determine the effective s-wave scattering length for two fermions that interact, both directly by the interatomic potentials as well as by the above-mentioned exchange mechanism. We find that the effective scattering length is quite sensitive to changes in the condensate density, and becomes strongly energy dependent. In addition, we consider the mechanical stability of these mixtures, and also calculate the dispersion and the damping of the various collisionless collective modes of the gas.

We find a limit cycle in a quasiequilibrium model of evaporative cooling of a two-component trapped fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively $\beta \mu \sim O\left(1\right).$ We speculate that one may be able to cool an atomic Fermi gas further by photoassociating dimers near the bottom of the Fermi sea.

In “interaction-free” measurements, one typically wants to detect the presence of an object without touching it with even a single photon. One often imagines a bomb whose trigger is an extremely sensitive measuring device whose presence we would like to detect without triggering it. We point out that all such measuring devices have a maximum sensitivity set by the uncertainty principle, and thus can only determine whether a measurement is “interaction-free” to within a finite minimum resolution. We further discuss exactly what can be achieved with the proposed “interaction-free” measurement schemes.

Integrated optical elements can simplify the linear optics used to simulate quantum circuits. These linear optical simulations of quantum circuits have been developed primarily in terms of the free space optics associated with single-photon interferometry. For an L-bit simulation the number of required free-space optical elements is $\propto 2^L$ if 50/50 beam splitters are used. The implementation (construction and alignment) of these circuits with these free-space elements is nontrivial. On the other hand, for the cases presented in this paper in which linear integrated optics (e.g., $2^L\times 2^L$ fiber couplers) are used, the number of optical devices does not grow exponentially with L. The problem is changed from having an exponential growth of the number of devices to having devices with an exponential growth in the number of ports. In addition to simplifying the construction, the association of an $N\times N$ fiber coupler with the discrete Fourier transform suggests alternative formulations for the circuits. Several examples of circuit reductions are given.