We provide a detailed analysis of the solubility of the optimized-potential-method (OPM) integral equation for the case of the orbital- and eigenvalue-dependent correlation energy functional $E_{\mathrm{c}}^{\mathrm{MP}2}$ obtained by second-order perturbation theory on the basis of the Kohn-Sham Hamiltonian. For this functional it was shown [Phys. Rev. Lett., 86, 2241 (2001)] that for free atoms no solution of the OPM equation can be found which satisfies the boundary condition $v_{\mathrm{c}}^{\mathrm{MP}2}(r\to \infty )=0$. On the other hand, there exists a proof that $v_{\mathrm{c}}^{\mathrm{MP}2}\left(r\right)$ decays like $1∕r^4$ [J. Chem. Phys., 118, 9504 (2003)]. Here we resolve the obvious contradiction by demonstrating that (i) the OPM equation cannot be solved if continuum states are present, (ii) the OPM equation cannot be solved for a free atom if only a finite number of Rydberg states are included in $E_{\mathrm{c}}^{\mathrm{MP}2}$, and (iii) the OPM equation does allow a solution satisfying $v_{\mathrm{c}}^{\mathrm{MP}2}(r\to \infty )=0$ in the case of finite systems with a countable spectrum (exemplified by an atom in a spherical box), if the complete spectrum is taken into account in the OPM procedure.

The charge transfer of the RNA base uracil by means of ${\mathrm{C}}^{q+}$ ions $(q=2–4)$ has been studied theoretically by means of ab initio quantum-chemistry molecular methods followed by a semiclassical dynamical treatment. The charge-transfer process appears to be highly anisotropic. The theoretical cross sections show different behavior with a strong influence of the electronic structure and charge of the ${\mathrm{C}}^{q+}$ projectile and can be correlated positively with previous experimental studies on the ionization and fragmentation processes in the ${\mathrm{C}}^{q+}$-Uracil collision.

Ultracold molecules can be associated from ultracold atoms by ramping the magnetic field through a Feshbach resonance. A reverse ramp dissociates the molecules. Under suitable conditions, more than one outgoing partial wave can be populated. A theoretical model for this process is discussed here in detail. The model reveals the connection between the dissociation and the theory of multichannel scattering resonances. In particular, the decay rate, the branching ratio, and the relative phase between the partial waves can be predicted from theory or extracted from experiment. The results are applicable to our recent experiment in ${}^{87}\mathrm{Rb}$, which has a $d$-wave shape resonance.

We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions.

Mesoscopic interference effects in multiple scattering of photons depend crucially on the internal structure of the scatterers. In the present paper, we develop the analytical theory of multiple photon scattering by cold atoms with arbitrary internal hyperfine multiplets. For a specific application, we calculate the enhancement factor of elastic coherent backscattering as a function of detuning from an entire hyperfine multiplet of neighboring resonances that cannot be considered isolated. Our theory permits one to understand why atoms behave differently from classical Rayleigh point-dipole scatterers, and how the classical description is recovered for larger but still microscopic objects like molecules or clusters.

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a quasi-one-dimensional cigar-shaped geometry. Due to a strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be bright fermionic solitons in the case of repulsive boson-fermion interactions. However, we demonstrate that stable bright fermionic solitons can be formed for a sufficiently attractive boson-fermion interaction in a boson-fermion mixture. We also consider the formation of fermionic solitons in the presence of a periodic axial optical-lattice potential. These solitons can be formed and studied in the laboratory with present technology.

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.

We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calculate the ground state of the gas using a ground-state auxiliary-field quantum Monte Carlo (QMC) method [Phys. Rev. E 70, 056702 (2004)]. We examine the properties of the gas, such as the energetics, condensate fraction, real-space density, and momentum distribution, as a function of the number of particles and the scattering length. We find that the mean-field Gross-Pitaevskii (GP) approach gives qualitatively incorrect result of the kinetic energy as a function of the scattering length. We present detailed QMC data for the various quantities, and discuss the behavior of GP, modified GP, and the Bogoliubov method under a local density approximation (LDA).

With use of the Kronig-Penney model, we study the excitation spectrum of a Bose-Einstein condensate in a one-dimensional periodic potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum for arbitrary values of the lattice depth. We find that the excitation spectrum is gapless and linear at low energies, and that it is due to the anomalous tunneling of low-energy excitations, predicted by Kagan et al.

We study low-temperature properties of atomic gases in trimerized optical kagomé lattices. The laser arrangements that can be used to create these lattices are briefly described. We also present explicit results for the coupling constants of the generalized Hubbard models that can be realized in such lattices. In the case of a single-component Bose gas the existence of a Mott insulator phase with fractional numbers of particles per trimer is verified in a mean-field approach. The main emphasis of the paper is on an atomic spinless interacting Fermi gas in the trimerized kagomé lattice with two fermions per site. This system is shown to be described by a quantum spin-$1∕2$ model on the triangular lattice with couplings that depend on the bond directions. We investigate this model by means of exact diagonalization. Our key finding is that the system exhibits nonstandard properties of a quantum spin-liquid crystal: it combines planar antiferromagnetic order in the ground state with an exceptionally large number of low-energy excitations. The possibilities of experimental verification of our theoretical results are critically discussed.

We study two-photon absorption in a three-level ladder atomic system driven by a pair of bichromatic fields of equal frequency differences. The high-frequency component of one bichromatic field and the low-frequency component of the other are on two-photon resonance. The transition probability is calculated by employing the method of harmonic expansion and matrix inversion. Unexpectedly, when the sums of the phases of the different pairs of field components on the two-photon resonance are equal to each other, two-photon absorption is dramatically suppressed and the atomic system becomes transparent against two-photon absorption. Physically, due to dynamical Stark splitting, the two-photon transitions induced by the different pairs of field components experience different dressed states with phase difference of $\pi$. As a result, destructive interference occurs between the two pathways and leads to the inhibition of two-photon absorption.

We propose a scheme for implementing a controlled unitary gate between two distant atoms directly communicating through a quantum transmission line. To achieve our goal, only a series of several coherent pulses are applied to the atoms. Our scheme thus requires no ancilla atomic qubit. The simplicity of our scheme may significantly improve the scalability of quantum computers based on trapped neutral atoms or ions.

The condensation produced in supersonic expansions of $\mathrm{C}{\mathrm{O}}_2$ is studied quantitatively combining Rayleigh and Raman scattering. The cluster number density $n_c$ and the mean cluster size $\overline{N}$ are obtained for five expansions with stagnation pressures $P_0=1–5\text{bars}$, and temperature $T_0=294\mathrm{K}$, along axial and radial directions; $n_c$ and $\overline{N}$ are determined from the condensation onset up to a terminal size ${\overline{N}}_{\infty }$, verifying the empirical law ${\overline{N}}_{\infty }\propto P_0^{2.23}$. A maximum growth rate $d\overline{N}∕dt\approx 8\times {10}^8{\mathrm{s}}^{-1}$ is estimated for the $5\text{−}\text{bar}$ expansion. The Raman spectra show a coexistence of solid and liquidlike phases in the jet, with a progressive transition from the liquid to the solid fraction as the clusters increase their size.

We present experimental data to demonstrate coherently driven population inversion by retroreflection-induced bichromatic adiabatic passage in metastable helium atoms. Complete and robust population transfer from an initial to a target state is induced by coherent interaction of the atoms in a supersonic beam with two counterpropagating and temporally delayed laser pulses of different intensities. The radiation fields intersect the atomic beam slightly tilted away from normal incidence, thereby inducing Doppler shifts of the atomic resonance between the initial and the target state. Thus the laser pulses produce a bichromatic field in the rest frame of each atom, which induces complete coherent population transfer by an adiabatic passage process.

We report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et al. for long-distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. The theory includes the Zeeman structure of the atomic hyperfine levels used in the experiment, and the polarization of both excitation fields and detected photons. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground-state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than $10\mu \mathrm{s}$, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.

We experimentally measure the propagation delays for chirped optical pulses with asymmetric temporal envelope functions, through a resonantly absorbing dye solution. The transmitted pulses suffer a strong deformation and the arrival times are dramatically modified by the interaction between the chirp and the absorption effect of the sample. It is shown that the arrival time, represented by the centroid of energy of the transmitted pulse, can be well described by the reshaping delay and has a greater significance than the peak of the pulse.

The nonlocal electrodynamics of uniformly rotating systems is presented and its predictions are discussed. In this case, due to paucity of adequate experimental data, the nonlocal theory cannot be directly confronted with observation at present. The approach adopted here is therefore based on the correspondence principle: the nonrelativistic quantum physics of electrons in circular “orbits” is studied. The helicity dependence of the photoeffect from the circular states of atomic hydrogen is explored as well as the resonant absorption of a photon by an electron in a circular “orbit” about a uniform magnetic field. Qualitative agreement of the predictions of the classical nonlocal electrodynamics with quantum-mechanical results is demonstrated in the correspondence regime.

We consider two three-dimensional isotropic harmonic oscillators with the same frequency and interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-type transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift, the nonperturbative Casimir–Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expression of the far zone Casimir–Polder potential in terms of the polarizabilities of the oscillators is recovered.

We present a universal analyzer for the three-particle Greenberger-Horne-Zeilinger (GHZ) states with quantum nondemolition parity detectors and linear-optics elements. In our scheme, all of the three-photon GHZ states can be discriminated with nearly unity probability in the regime of weak nonlinearity feasible at the present state of the art experimentally. We also show that our scheme can be easily extended to the analysis of the multi-particle GHZ states.

Partial single-differential ionization cross sections (PSDICSs) of a multiply ionized xenon atom (${\mathrm{Xe}}^{n+}$, $n=1–7$) are measured for impact of $10–28\mathrm{keV}$ electrons with xenon by performing coincidences between the produced recoil ions and the electrons of indiscriminated energies detected at 90° with respect to the incident electron beam direction. Values of relative PSDICSs for doubly charged ions are found to be about 25% larger than those for singly charged ions in the considered impact energy range. The examination of charge-state fractions and relative cross-section fractions of multiply charged ions as a function of incident electron energy suggests that the multiply charged ions are produced via creation of an inner-shell vacancy followed by Auger and shakeoff processes. The mean charge state of the ions produced in the collisions is found to be independent of the impact energy and reaches a constant value close to 2.6. The Fano-Bethe plots of the PSDICSs suggest that higher charge states of the ions are weakly produced via optical transitions; moreover, the latter process becomes a dominant channel for producing the doubly charged ions that are correlated with the electrons detected at 90°.