The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number $n_0$ and critical atom number $N_0$ cannot be minimized simultaneously, so that an “optimal” sphere size is taken to be the radius for which the geometric mean $\sqrt{n_0{N}_0},$ is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the $D_2$ transition in atomic cesium at ${\lambda }_0=852\mathrm{}\mathrm{nm}$ using fused-silica microspheres, for which the maximum coupling coefficient $g_a/\left(2\mathrm{}\pi \right)\approx 750\mathrm{MHz}$ occurs for a sphere radius $a=3.63\mathrm{}\mu \mathrm{m}$ corresponding to the minimum for $n_0\approx 6.06\times {10}^{-6}.$ By contrast, the minimum for $N_0\approx 9.00\times {10}^{-6}$ occurs for a sphere radius of $a=8.12\mathrm{}\mu \mathrm{m},$ while the optimal sphere size for which $\sqrt{n_0{N}_0}$ is minimized occurs at $a=7.83\mathrm{}\mu \mathrm{m}.$ On an experimental front, we have fabricated fused-silica microspheres with radii $a\sim 10\mu \mathrm{m}$ and consistently observed quality factors $Q>~0.8\times {10}^7.$ These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.

The absorption spectrum of a weak probe, interacting with a driven degenerate two-level atomic system, whose ground and excited hyperfine states are ${\mathrm{F}}_{g,e},$ can exhibit narrow peaks at line center. When the pump and probe polarizations are different, $F_e{=F}_g+1\mathrm{}$ and $F_g>0,$ the electromagnetically induced absorption (EIA) peak has been shown to be due to the transfer of coherence (TOC) between the excited and ground states via spontaneous decay. We give a detailed explanation of why the TOC that leads to EIA (EIA-TOC) can only take place when ground-state population trapping does not occur, that is, when $F_e{=F}_g+1.\mathrm{}$ We also explain why EIA-TOC is observed in open systems. We show that EIA can also occur when the pump and probe polarizations are identical and $F_e{=F}_g+1.\mathrm{}$ This EIA is analogous to an effect that occurs in simple two-level systems when the collisional transfer of population (TOP) from the ground state to a reservoir is greater than that from the excited state. For a degenerate two-level system, the reservoir consists of the Zeeman sublevels of the ground hyperfine state, and of other nearby hyperfine states that do not interact with the pump. We will also discuss the four-wave mixing spectrum under the conditions where EIA-TOC and EIA-TOP occur.

We investigate the parametric beating of a quantum probe field with a prepared Raman coherence in a far-off-resonance medium, and describe the resulting multiplexing processes. We show that the normalized autocorrelation functions of the probe field are exactly reproduced in the Stokes and anti-Stokes sideband fields. We find that an initial coherent state of the probe field can be replicated to the Raman sidebands, and an initial squeezing of the probe field can be partially transferred to the sidebands. We show that a necessary condition for the output fields to be in an entangled state or, more generally, in a nonclassical state is that the input field state is a nonclassical state.

The Raman interaction of atoms singly traversing a two-mode cavity constitutes a quantum-cloning machine for coherent states. The quality of the two identical output coherent states is independent of the initial, albeit different, coherent state, initially present inside the cavity. The cloning of nonorthogonal states indicates that the entanglement of the output states for an arbitrary initial state is the essence of the no-cloning theorem.

We develop an analytical theory of dark resonances that accounts for the full atomic-level structure, as well as all field-induced effects such as coherence preparation, optical pumping, ac Stark shifts, and power broadening. The analysis uses a model based on relaxation constants, which assumes the total collisional depolarization of the excited state. A good qualitative agreement with the experiments for Cs in Ne is obtained.

The $(p,d,\overline{p},\overline{d})$ molecule, with a proton, a deuteron, and their antiparticles, is stable againt spontaneous dissociation, but none of its three-body subsystems are stable. This molecule should be built by combining two atoms, for instance a protonium $\left(p\overline{p}\right)$ and its heavier analog $\left(d\overline{d}\right).\mathrm{}$ Most other four-body molecules have at least one stable three-body subsystem and thus can be built by adding the constituents one by one.

Two-electron sum-momentum distributions from nonsequential double ionization of He in an intense laser field are analyzed. The results of a S-matrix calculation show that the inelastic scattering of the first electron with the residual ion is best considered as a (internal) laser-induced impact ionization. The parallel component of the sum momentum is found to be largest when the prescattering electron energy is close to zero. This is due to the fact that a large momentum transfer between the sum momentum in the final state and the impact momentum in the intermediate state along the polarization axis favors the absorption of field energy by the two-electron system during the scattering process.

We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar invariant under the group realized by the transformations of stochastic local quantum operations and classical communications (SLOCC). This invariant is offered as a candidate entanglement measure for n-qubit states and discussed in relation to measures of quantum state entanglement for certain important classes of two-qubit and three-qubit systems. This invariant can be directly estimated via a quantum network, obviating the need to perform laborious quantum state tomography. We also show that this invariant directly captures the extent of entanglement purification due to SLOCC filters.

We consider an optical lattice potential loaded with a Bose-Einstein condensate in the presence of three-body loss. The dynamics of the atoms in the lattice realizes the Bose-Hubbard model of condensed-matter physics, where on-site number fluctuations are reduced by the atomic repulsion energy but increase with increased tunneling between lattice sites. A range of quantum states with different number fluctuations can therefore be created by varying the amplitude of the optical potential, and will be reflected in the values of the on-site correlation functions $G_n^i=〈b_i^{†n}{b}_i^n〉,$ where $b_i$ is the annihilation operator of the $i\mathrm{th}$ lattice site. The three-body loss rate is shown to be proportional to a sum of the on-site three-body correlation functions and therefore acts as a natural probe of the number fluctuations. The three-body correlation function $G_3^i$ is a sensitive measure of the number fluctuations when site occupation is low. In particular, when the average number at each site is less than $3,$ the number fluctuations in the superfluid phase result in $G_3^i\approx n_i^3$ and give rise to a finite three-body loss, whereas in the insulator phase, $G_3^i{=n}_i{(n}_i-{1\left)\right(n}_i-2)$ and three-body loss ceases to occur.

We generalize to systems with arbitrary finite dimension a measure of quantum fluctuations (the certainty) previously introduced for two-dimensional systems. Using this measure, we study the duality relations satisfied by complementary observables looking for states with minimum joint fluctuations (maximum certainty states). We extend the duality relations to encompass several complementary observables simultaneously.

We trap a single cesium atom in a standing-wave optical dipole trap. Special experimental procedures, designed to work with single atoms, are used to measure the oscillation frequency and the atomic energy distribution in the dipole trap. These methods rely on unambiguously detecting presence or loss of the atom using its resonance fluorescence in the magneto-optical trap.

An one-dimensional optical lattice with rubidium atoms ${(}^{85}\mathrm{Rb})$ is formed inside a ring resonator with a finesse of $1.8\times {10}^5$ and a large mode volume of $2.6{\mathrm{mm}}^3.$ We typically trap several times ${10}^6$ atoms at densities up to ${10}^{12}{\mathrm{cm}}^{-3}$ and temperatures between 25 and $125\mu \mathrm{K}.$ Despite of the narrow bandwidth (17.3 kHz) of the cavity, heating due to intracavity intensity fluctuations is kept at a low level, such that the time evolution of the temperature is determined by evaporative cooling.

This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both nondegenerate as well as degenerate states. Starting with the nondegenerate case, we show that the usual procedure of subtracting the dynamical phase from the total phase to yield the geometric phase for pure states, does not hold for mixed states. To this end, we furnish an expression for the geometric phase that is gauge invariant. The parallelity conditions are shown to be easily derivable from this expression. We also extend our formalism to states that exhibit degeneracies. Here with the holonomy taking on a non-Abelian character, we provide an expression for the geometric phase that is manifestly gauge invariant. As in the case of the nondegenerate case, the form also displays the parallelity conditions clearly. Finally, we furnish explicit examples of the geometric phases for both the nondegenerate as well as degenerate mixed states.

The singlet state of two spin-$\frac{3}{2}$ particles allows a proof of Bell’s theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.

The creation of specified quantum states is important for most, if not all, applications in quantum computation and communication. The quality of the state preparation is therefore an essential ingredient in any assessment of a quantum-state gun. We show that the fidelity, under the standard definitions, is not sufficient to assess quantum sources, and we propose a measure of suitability that necessarily depends on the application for the source. We consider the performance of single-photon guns in the context of quantum key distribution (QKD) and linear optical quantum computation. Single-photon sources for QKD need radically different properties than sources for quantum computing. Furthermore, the suitability for single-photon guns is discussed explicitly in terms of experimentally accessible criteria.

Sub-eV collisions between protons and atomic deuterium targets are studied by utilizing the very slow dissociation of ${\mathrm{HD}}^{+}$ from its electronic ground state. Studying the resulting ${\mathrm{H}}^{+}+\mathrm{D}\mathrm{}\left(1s\right)\mathrm{}$ “half” collisions accesses energies more than an order of magnitude lower, and with better energy resolution, than previous measurements. The collision energy is determined a posteriori via three-dimensional momentum imaging. New results for energies near the threshold for charge transfer, incorporating an improved approach to the key problem of subtracting the ${\mathrm{H}}_2^{+}$ background, are presented along with a discussion of the experimental technique.

Reionization rates of Rydberg states $(n\gg 1$ and $l=0,1,$ and $2)$ of multiply charged ionic projectiles escaping solid surfaces are calculated. These rates are obtained in an analytic form as a function of the ion-surface distance R. A phenomenological model of the reionization process, based on two-state quantum dynamics, is adopted for the vicinity of the potential barrier top. The results of calculations show that ionization rates for different Rydberg states are strictly localized and relatively separated. Universality of the reionization rate as a function of the scaling parameter $\alpha ,$ describing the turning point configurations, is demonstrated. The reionization is discussed within the framework of a nonresonant population-reionization process at intermediate ionic velocities $(v\sim 1$ a.u.). The influence of reionization on the population of ionic Rydberg states is expressed in terms of a renormalized neutralization rate. It is demonstrated that the reionization effect significantly changes the population curves for all Rydberg states. The population curves obtained correlate with beam-foil experimental data concerning the S VI, Cl VII, and Ar VIII ions.

A limited equivalence between microscopic and macroscopic quantizations of the electromagnetic field in a dielectric is established. We demonstrate that macroscopic canonical quantization of the electromagnetic field in an idealized absorptionless dielectric is equivalent to microscopic quantization followed by the elimination of the material degrees of freedom in the limit of an adiabatic response of the oscillators averaged over a quantization volume. We demonstrate that a loss of generality and extensibility accompanies the reduction of the full microscopic theory.

The measurement of time durations or instants of occurrence of events has been frequently modeled “operationally” by coupling the system of interest to a “clock.” According to several of these models, the operational approach is limited at low energies because the perturbation of the clock does not allow to reproduce accurately the corresponding ideal time quantity, defined for the system in isolation. We show that, for a time-of-flight measurement model that can be set to measure dwell or arrival times, these limitations may be overcome by extending the range of energies where the clock works properly using pulsed couplings rather than continuous ones.

We propose a method to implement cavity QED and quantum-information processing in high-$Q$ cavities with a single trapped but nonlocalized atom. The system is beyond the Lamb-Dicke limit due to the atomic thermal motion. Our method is based on adiabatic passages, which make the relevant dynamics insensitive to the randomness of the atom position with an appropriate interaction configuration. The validity of this method is demonstrated from both approximate analytical calculations and exact numerical simulations. We also discuss various applications of this method based on the current experimental technology.