We have developed a simple analytical model describing multiatom signals that are measured in experiments on dipole-dipole interaction at resonant collisions of a few Rydberg atoms. It has been shown that finite efficiency of the selective field-ionization detector leads to the mixing up of the spectra of resonant collisions registered for various numbers of Rydberg atoms. The formulas which help to estimate an appropriate mean Rydberg atom number for a given detection efficiency are presented. We have found that a measurement of the relation between the amplitudes of collisional resonances observed in the one- and two-atom signals provides a straightforward determination of the absolute detection efficiency and mean Rydberg atom number. We also performed a testing experiment on resonant collisions in a small excitation volume of a sodium atomic beam. The resonances observed for 1–4 detected Rydberg atoms have been analyzed and compared with theory.

A general formalism is used to express the long-range potential energies in inverse powers of the separation distance between two like atomic or molecular systems with $P$ symmetries. The long-range molecular interaction coefficients are calculated for the molecular symmetries $\Delta$, $\Pi$, and $\Sigma$, arising from the following interactions: $\mathrm{He}\left(2{}^{1}P\right)–\mathrm{He}\left(2{}^{1}P\right)$, $\mathrm{He}\left(2{}^{1}P\right)–\mathrm{He}\left(2{}^{3}P\right)$, and $\mathrm{He}\left(2{}^{3}P\right)–\mathrm{He}\left(2{}^{3}P\right)$. The electric quadrupole-quadrupole term $C_5$, the van der Waals (dispersion) term $C_6$, and higher-order terms $C_8$ and $C_{10}$ are calculated ab initio using accurate variational wave functions in Hylleraas coordinates with finite nuclear mass effects. A comparison is made with previously published results where available.

Asymptotic levels of the $A$ ${}^1\Sigma _u^{+}$ state of the two isotopomers ${}^{39}\mathrm{K}_2$ and ${}^{39}\mathrm{K}{}^{41}\mathrm{K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a molecular beam. The observed level structure can be reproduced correctly only if a mass dependent correction term is introduced for the interaction potential. The applied relative correction in the depth of the potential is ${10}^{-6}$, which is in the order of magnitude expected for corrections of the Born-Oppenheimer approximation. A similar change in ground state potentials might lead to significant changes of mass-scaled properties describing cold collisions like the $s$-wave scattering length.

Electron emission from LiF, KCl, and KI crystal surfaces during grazing collisions of swift protons is studied using a first-order distorted-wave formalism. Owing to the localized character of the electronic structure of these surfaces, we propose a model that allows us to describe the process as a sequence of atomic transitions from different target ions. Experimental results are presented for electron emission from LiF and KI and energy loss from KI surfaces. Calculations show reasonable agreement with these experimental data. The role played by the charge of the incident particle is also investigated.

The many-body expansion of the interaction potential between atoms and molecules is analyzed in detail for different types of interactions involving up to seven atoms. Elementary clusters of Ar, Na, Si, and, in particular, Au are studied, using first-principles wave-function- and density-functional-based methods to obtain the individual $n$-body contributions to the interaction energies. With increasing atom number the many-body expansion converges rapidly only for long-range weak interactions. Large oscillatory behavior is observed for other types of interactions. This is consistent with the fact that Au clusters up to a certain size prefer planar structures over the more compact three-dimensional Lennard-Jones-type structures. Several Au model potentials and semiempirical PM6 theory are investigated for their ability to reproduce the quantum results. We further investigate small water clusters as prototypes of hydrogen-bonded systems. Here, the many-body expansion converges rapidly, reflecting the localized nature of the hydrogen bond and justifying the use of two-body potentials to describe water-water interactions. The question of whether electron correlation contributions can be successfully modeled by a many-body interaction potential is also addressed.

We discuss the time evolution and matter-wave interference of Fermi condensates on the Bose-Einstein condensate side of Feshbach resonances for $s$- and $p$-wave superfluids, upon release from harmonic traps. In $s$-wave systems, where the order parameter is a complex scalar, we find that the interference patterns depend on the relative phase of the order parameters of the condensates. In $p$-wave systems involving the mixture of two hyperfine states, we show that the interference pattern exhibits a polarization effect depending on the relative orientation of the two vector order parameters. Lastly, we also point out that $p$-wave Fermi condensates exhibit an anisotropic expansion, reflecting the spatial anisotropy of the underlying interaction between fermions and the orbital nature of the vector order parameter. Potential applications of our results include systems of ultracold atoms that exhibit $p$-wave Feshbach resonances, such as ${}^6\mathrm{Li}$ or ${}^{40}\mathrm{K}$.

Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an extremely thin cell (cell thickness $L<1\mu \mathrm{m}$) are investigated experimentally and theoretically. The study is performed on the $D_2$ line $(\lambda =852\mathrm{nm})$ of Cs and concentrates on the two situations $L=\lambda ∕2$ and $L=\lambda$, the most contrasted ones with respect to the length dependence of the coherent Dicke narrowing. For $L=\lambda ∕2$, the Dicke-narrowed absorption profile simply broadens and saturates in amplitude when increasing the light intensity, while for $L=\lambda$, sub-Doppler dips of reduced absorption at the line-center appear on the broad absorption profile. For a fluorescence detection at $L=\lambda$, saturation induces narrow dips, but only for hyperfine components undergoing a population loss through optical pumping. These experimental results are interpreted with the help of the various existing models and are compared with numerical calculations based upon a two-level modeling that considers both a closed and an open system.

Recent progress in the spectroscopy of antiprotonic helium has allowed for measuring the separation between components of the hyperfine structure (hfs) of the (37,35) metastable states with an accuracy of $300\mathrm{kHz}$, equivalent to a relative accuracy of $3\times {10}^{-5}$. The analysis of the uncertainties of the available theoretical results on the antiprotonic helium hfs shows that the accuracy of the value of the dipole magnetic moment of the antiproton (currently known to only 0.3%) may be improved by up to two orders of magnitude by measuring the splitting of appropriately selected components of the hfs of any of the known metastable states. The feasibility of the proposed measurement by means of an analog of the triple resonance method is also discussed.

The properties of cold ion plasmas with large numbers $(>200)$ of laser- and sympathetically cooled species are modeled in detail using molecular dynamics simulations. We describe how to extract temperatures and ion numbers from CCD images. The identification of the ion species by excitation of their oscillation modes is discussed. The sympathetic cooling efficiency, effects of the rf micromotion and of collision heating by a neutral background gas are analyzed, in part experimentally.

Since the early days of quantum physics, the complex behavior of three interacting particles has been the subject of numerous experimental and theoretical studies. In a recent Letter to Nature, Kraemer et al. [Nature (London) 440, 315 (2006)] report on experimental “evidence for Efimov quantum states” in an ultracold gas of cesium atoms. Such quantum states refer to an infinite series of energy levels of three identical Bose particles, accumulating at the threshold for dissociation as the scattering length of each pair is tuned to infinity. Whereas the existence of a single Efimov state has been predicted for three helium atoms, earlier experimental studies concluded that this elusive state had not been found. In this paper we show by an intuitive argument and full numerical calculations that the helium and cesium experiments actually provide evidence of the same, ground state of this trimer spectrum, which the helium experimentalists and pioneering theoretical studies had not associated with Efimov’s effect. Unlike the helium trimer, the observed ${}^{133}\mathrm{Cs}_3$ resonance refers to a Borromean molecular state. We discuss how as yet unobserved, excited Efimov quantum states might be detected in ultracold gases of ${}^{85}\mathrm{Rb}$ and of ${}^{133}\mathrm{Cs}$ at magnetic field strengths in the vicinity of $0.08\mathrm{T}$ $\left(800\mathrm{G}\right)$.

We study analytically the dynamic cancellation of ac Stark shift in the recently proposed pulsed electromagnetically-induced-transparency (EIT-)Raman optical lattice clock based on the wave-function formalism. An explicit expression for the time evolution operator corresponding to the effective two-level interaction Hamiltonian has been obtained in order to explain the atomic phase shift cancellation due to the ac Stark shift induced by the time-separated laser pulses. We present how to determine an optimum value of the common detuning of the driving fields at which the atomic phase shift cancels completely with the parameters for the practical realization of the EIT-Raman optical lattice clock with alkaline-earth-metal atoms.

Experimental studies of a photoinitiated collision in an ultracold Cs Rydberg gas are presented. The process is characterized by measuring the laser intensity dependence of the absorption, the number of particles leaving each collision, and the recoil velocity of the collision fragments. The results of the experiment are compared to ab initio Rydberg pair interaction potentials.

A geometrical description of open quantum systems is presented. This is based on a connection on a vector bundle over a Grassmann manifold, as well as the Anandan geometric phase for pure states [J. Anandan, Phys. Lett. A 133, 171 (1988)]. The geometric phase proposed here also naturally includes the geometric phase in adiabatic open quantum systems proposed by Sarandy and Lidar [Phys. Rev. A 73, 062101 (2006)]. The present geometrical description can be applied to all the quantum systems described by time-local master equations for density operators.

We develop a method to determine spatial configurations to realize decoherence-free subspaces for spatially extended multiparticle systems. We have assumed normal reservoir behavior including translational invariance of the reservoir and preparation in stationary states or mixture thereof and weak Markovian system-reservoir coupling that requires energy transfer. One important outcome of our method is a proof that there does not exist a multiparticle decoherence-free subspace in such systems except in the limit that the spatial extent of the system becomes infinitesimal.

Interference effects for electron emission in collisions between molecules and fast highly charged ions are studied using a nonperturbative semiclassical approach. Angle- and energy-differential results are presented and analyzed as a function of the projectile charge and velocity, as well as the geometric characteristics of the molecular target. They agree qualitatively with the available experimental data and validate the observed primary interference patterns. Contrary to previous theoretical predictions a strong backward-forward asymmetry of the interference structures is found and discussed in detail.

Rapidly oscillating potentials with a vanishing time average have been used for a long time to trap charged particles in source-free regions. It has been argued that the motion of a particle inside such a potential can be approximately described by a time independent effective potential, which does not depend upon the initial phase of the oscillating potential. However, here we show that the motion of a particle and its trapping condition significantly depend upon this initial phase for arbitrarily high frequencies of the potential’s oscillation. We explain this phenomenon by showing that the motion of a particle is determined by the effective potential stated in the literature only if its initial conditions are transformed according to a transformation which we show to significantly depend on the potential’s initial phase for arbitrarily high frequencies. We confirm our theoretical findings by numerical simulations. Further, we demonstrate that the found phenomenon offers different ways to manipulate the dynamics of particles which are trapped by rapidly oscillating potentials. Finally, we propose a simple experiment to verify the theoretical findings of this work.

We describe the full-time dynamics of modulational instability in $F=1$ spinor Bose-Einstein condensates for the case of the integrable three-component model associated with the matrix nonlinear Schrödinger equation. We obtain an exact homoclinic solution of this model by employing the dressing method which we generalize to the case of the higher-rank projectors. This homoclinic solution describes the development of modulational instability beyond the linear regime, and we show that the modulational instability demonstrates the reversal property when the growth of the modulated amplitude is changed by its exponential decay.

We demonstrate sub-shot-noise photon-number correlations in a (temporal) multimode mesoscopic ($\sim {10}^3$ detected photons) twin beam produced by picosecond-pulsed spontaneous nondegenerate parametric down-conversion. We have separately detected the signal and idler distributions of photons collected in twin coherence areas and found that the variance of the photon-count difference goes below the shot-noise limit by $3.25\mathrm{dB}$. The number of temporal modes contained in the twin beam, as well as the size of the twin coherence areas, depends on the pump intensity. Our scheme is based on spontaneous down-conversion and thus does not suffer from limitations due to the finite gain of the parametric process. Twin beams are also used to demonstrate the conditional preparation of a nonclassical (sub-Poissonian) state.

The propagation of guided electromagnetic waves in open elliptical metamaterial waveguide structures is investigated. The waveguide contains a negative-index media core, where the permittivity $\epsilon$ and permeability $\mu$ are negative over a given bandwidth. The allowed mode spectrum for these structures is numerically calculated by solving a dispersion relation that is expressed in terms of Mathieu functions. By probing certain regions of parameter space, we find the possibility exists to have extremely localized waves that transmit along the surface of the waveguide.

The statistical properties of the fluorescence lifetime of single emitters in disordered systems are discussed. The contribution of radiative and nonradiative processes to the spontaneous decay rate is analyzed using a simple analytical model, in full agreement with exact numerical simulations. The relative fluctuations of the decay rate are shown to exhibit two well-defined regimes dominated either by near-field scattering or by absorption processes. In both regimes, the averaged apparent quantum yield remains high enough to permit practical measurements. Lifetime fluctuations could thus be used a probe of the local environment in complex systems at the nanometer scale.