We report on the observation of interspecies Feshbach resonances in an ultracold, optically trapped mixture of Rb and Cs atoms. In a magnetic-field range up to 300 G we find 23 interspecies Feshbach resonances in the lowest spin channel and two resonances in a higher channel of the mixture. The extraordinarily rich Feshbach spectrum suggests the importance of different partial waves in both the open and closed channels of the scattering problem along with higher-order coupling mechanisms. Our results, on one hand, provide fundamental experimental input to characterize the Rb-Cs scattering properties and, on the other hand, identify possible starting points for the association of ultracold heteronuclear RbCs molecules.

We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit $\left(\chi =1\right)$ and Fermi limit $\left(\chi =0\right)$ the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviors from the Bose limit to the Fermi limit.

The unequivocal detection of entanglement between two distinct matter-wave pulses is a significant challenge that has yet to be experimentally demonstrated. We describe a realistic scheme to generate and detect continuous-variable entanglement between two atomic matter-wave pulses produced via degenerate four-wave mixing from an initially trapped Bose-Einstein condensate loaded into a one-dimensional optical lattice. We perform a comprehensive numerical investigation for fixed condensate parameters to determine the maximum violation of separability and Einstein-Podolsky-Rosen inequalities for field quadrature entanglement, and describe and simulate an experimental scheme for measuring the necessary quadratures.

In the presence of a dielectric slab, the modes of the free electromagnetic field comprise traveling modes, consisting of incoming, reflected, and transmitted parts, as well as trapped modes that are subject to repeated total internal reflection and emerge as evanescent field outside the slab. Traveling modes have a continuous range of frequencies, but trapped modes occur only at certain discrete frequencies. We solve the problem of which relative weight to use when summing over all modes, as commonly required in perturbative calculations. We demonstrate the correctness of our method by showing the completeness of electromagnetic field modes in the presence of a dielectric slab. We derive a convenient method of summing over all modes by means of a single contour integral, which is very useful in standard quantum electrodynamic calculations.

Using the approach of coupled wave equations, we consider spontaneous parametric down conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode-overlap integrals for the absolute pair-production rate into single-spatial modes and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and nondegenerate SPDC. We also find a time-domain expression for the correlation function between filtered signal and idler fields.

We study the spectral properties of spontaneous parametric down-conversion (SPDC) in a periodically poled waveguided structure of potassium-titanyl-phosphate (KTP) crystal pumped by ultrashort pulses. Our theoretical analysis reveals a strongly entangled and asymmetric structure of the two-photon spectral amplitude for type-II SPDC. We confirm these predictions experimentally by measuring single-photon spectra, on one hand, and the dependence of Hong-Ou-Mandel interference visibility on the width of spectral filtering, on the other hand.

It is pointed out that a loophole may exist in experimental tests of Bell inequalities using atomic qubits, due to possible errors in the angles defining the observables whose correlation is measured. A sufficient condition is derived for closing the loophole.

It is well established that an entanglement encoded in the Bell states of a two-qubit system with correlated spins exhibits completely different evolution properties from that encoded in states with the anticorrelated spins. A complete and abrupt loss of the entanglement, called the entanglement sudden death, can be found to occur for the spin-correlated states, but the entanglement evolves without any discontinuity or decays asymptotically for the spin-anticorrelated states. We consider the evolution of an initial entanglement encoded in the spin-anticorrelated states and demonstrate that the asymptotic behavior predicted before occurs only in the weak-coupling limit or equivalently when the rotating-wave approximation (RWA) is made on the interaction Hamiltonian of the qubits with the field. If we do not restrict ourselves to the RWA, we find that the entanglement undergoes a discontinuity, the sudden-death phenomenon. We illustrate this behavior by employing an efficient scheme for entanglement evolution between two cold-trapped atoms located inside a single-mode cavity. Although only a single excitation is initially present in the system, we find that the two-photon excited state, which plays the key role for the discontinuity in the behavior of the entanglement, gains a population over a short time of the evolution. When the RWA is made on the interaction, the two-photon excited state remains unpopulated for all times and the discontinuity is absent. We attribute this phenomenon to the principle of complementarity between the evolution time and energy, and the presence of the counter-rotating terms in the interaction Hamiltonian.

We introduce a model for spatiotemporal solitons in a symmetric system of parallel linearly coupled planar optical waveguides carrying a transverse grating. It also applies to the description of two-dimensional matter-wave solitons in parallel two-dimensional disk–shaped traps combined with a one-dimensional optical lattice. Using the variational approximation and numerical methods, we demonstrate that attenuation of the linear coupling between the cores causes reduction in the stable part of the family of symmetric solitons. Eventually, this family detaches from the asymmetric one and becomes entirely unstable. Close to the symmetry-breaking bifurcation (SBB), unstable symmetric solitons evolve into asymmetric quasisolitons, being destroyed far from the bifurcation. Unlike previously studied models, in the present setting the SBB is of the backward type, giving rise to an unstable branch of asymmetric solitons. Near the bifurcation, they transform into robust breathers.

We demonstrate the generation of supercontinuum with controllable cutoff extension in ultraviolet spectral region through femtosecond filamentation in parallel aligned ${\text{CO}}_2$ molecules. The additional cross-focusing effect from the quantum wake of impulsive molecular alignment and the subsequently enhanced self-phase-modulation as well as self-steepening and space-time focusing play important roles for the observed supercontinuum generation, which also result in a self-cleaned beam profile by attracting almost all the energy into a single core.

Anomalous dispersion is at the heart of superluminal pulse propagation in dispersive media. Most earlier analyses of these effects have been confined to discussions of pulse shapes or group velocity and group-velocity dispersion, while experiments typically measure the absorbed energy. We investigate the transport of energy in causal dispersive media including superluminal effects, via the time moments of the Poynting vector. We find that superluminal and negative traversal times are invariably accompanied by an initial temporal compression of the pulse. We predict a crossover distance at which superluminal behavior becomes subluminal even when the spectral width of the initial pulse lies well within the anomalous dispersion region. This effect is generic and we offer a theoretical basis for the experimental results of Talukder et al. [Phys. Rev. Lett. 86, 3546 (2001)]. As the pulse propagates, a strong spectral modification due to dissipation (gain) results in the dominance of normally dispersive spectral components that suffer from lower dissipation (higher gain) and is responsible for this crossover.

Far-off-resonant pulsed laser fields produce negligible excitation between two atomic states but may induce considerable phase shifts. The acquired phases are usually calculated by using the adiabatic-elimination approximation. We analyze the accuracy of this approximation and derive the conditions for its applicability to the calculation of the phases. We account for various sources of imperfections, ranging from higher terms in the adiabatic-elimination expansion and irreversible population loss to couplings to additional states. We find that as far as the phase shifts are concerned, the adiabatic elimination is accurate only for a very large detuning. We show that the adiabatic approximation is a far more accurate method for evaluating the phase shifts, with a vast domain of validity; the accuracy is further enhanced by superadiabatic corrections, which reduce the error well below ${10}^{-4}$. Moreover, owing to the effect of adiabatic population return, the adiabatic and superadiabatic approximations allow one to calculate the phase shifts even for a moderately large detuning and even when the peak Rabi frequency is larger than the detuning; in these regimes the adiabatic elimination is completely inapplicable. We also derive several exact expressions for the phases using exactly soluble two-state and three-state analytical models.

We analyze the performance of a quantum repeater protocol based on single trapped ions. At each node, single trapped ions embedded into high-finesse cavities emit single photons whose polarization is entangled with the ion state. A specific detection of two photons at a central station located half-way between two nodes heralds the entanglement of two remote ions. Entanglement can be extended to long distances by applying successive entanglement swapping operations based on two-ion gate operations that have already been demonstrated experimentally with high precision. Our calculation shows that the distribution rate of entanglement achievable with such an ion-based quantum repeater protocol is higher by orders of magnitude than the rates that are achievable with the best known schemes based on atomic-ensemble memories and linear optics. The main reason is that for trapped ions the entanglement swapping operations are performed deterministically, in contrast to success probabilities below 50% per swapping with linear optics. The scheme requires efficient collection of the emitted photons, which can be achieved with cavities, and efficient conversion of their wavelength, which can be done via stimulated parametric down-conversion. We also suggest how to realize temporal multiplexing, which offers additional significant speed ups in entanglement distribution, with trapped ions.

We propose a simple scheme to establish entanglement among stationary qubits based on the mechanism of resonance scattering between them and a single-spin-flip wave packet in designed spin network. It is found that through the natural dynamical evolution of an incident single-spin-flip wave packet in a spin network and the subsequent measurement of the output single-spin-flip wave packet, multipartite entangled states among $n$ stationary qubits, Greenberger-Horne-Zeilinger (GHZ), and $W$ states can be generated with success probabilities $P_{\text{GHZ}}=2/{\left|1+t^{-n}\right|}^2$ and $P_W={\left|t\right|}^2/n$, respectively, where $t$ is the transmission amplitude of the near-resonance scattering.

Comparison between our close-coupling many-channel quantum calculations based on a model potential for the description of the interaction between atoms and accurate experiments of disalignment and destruction of alignment of the ${\text{Ne}}^{\ast }\left(2p_i\left[J=1\right]\right)$ atoms induced by collisions with $\text{He}\left(1s^2\right)$ atoms in a gaseous mixture at thermal equilibrium is reported for temperatures between 10 and 3000 K. Our analysis leads to the conclusion that a good agreement with the various experiments is achieved when the dipole polarizability of the ${\text{Ne}}^{\ast }\left(2p_i\left[J=1\right]\right)$ states is added to the long-range potentials proposed in Phys. Rev. A 56, 1305 (1997) by Bahrim et al. Dipole polarizabilities for all the ${\text{Ne}}^{\ast }\left(2p_i\left[J=1\right]\right)$ states of the $2p^{5}3p$ electronic configuration are calculated.

High-resolution Fourier transform spectroscopy was used to record fluorescence progressions of KLi formed in a heat pipe. Lithium isotope effects were used to derive the adiabatic correction to the Born-Oppenheimer potential for the electronic ground state over a wide range of internuclear separations. With a short extrapolation from the experimentally determined potential functions of the coupled states $X{{}^1\Sigma }^{+}$ and $a{{}^3\Sigma }^{+}$ toward their common atomic asymptote, we have improved the modeling of recently observed Feshbach resonances for the fermionic atom pair ${}^6\text{L}\text{i}$ and ${}^{40}\text{K}$. Predictions for cold collisions between different isotopologues are presented using mass scaling with or without Born-Oppenheimer corrections. Predictions for Feshbach resonance positions differ by up to 0.5 G within reach of current experimental verification.

A class of Coulomb radial functions is defined for use in atomic or molecular Rydberg multichannel quantum-defect calculations. The associated accumulated radial phase parameters $\beta \left(ϵ\right)$ have a simple functional dependence on the energy, analogous to the familiar Rydberg relation where $\beta \left(ϵ\right)=\pi \left(n^{\ast }-l\right)$, with $n^{\ast }={\left(-ϵ\right)}^{-1/2}$, enabling easy use in the empirical fitting of complex multichannel spectra. However, “false roots” at low-energy and strong energy dependences of the quantum defects are largely avoided in the approach, which also may be implemented in the framework of ab initio $R$-matrix calculations in a straightforward manner. The method is illustrated with one-channel and multichannel examples relating to atomic potassium, nitric oxide, and molecular hydrogen.

Generalized squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing the properties of such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples we deal with nonlinear generalizations of quadrature squeezed states and deformed nonlinear squeezed states, which may be useful for optimized measurements at a reduced level of quantum noise. The realization of such states is studied for the quantized center-of-mass motion of a trapped ion.

Optic Tamm states (OTSs) in one-dimensional photonic crystal (PhC) heterostructures are studied via a Bloch-wave-expansion method (BWEM). We show that by considering both the periodicity and the finiteness, the propagation of electromagnetic wave in a finite one-dimensional PhC can be characterized by three parameters—two Bloch impedances and the Bloch-wave vector—in the framework of the BWEM. Applying the BWEM, we give a criterion of optic Tamm states at the interfaces inside finite heterostructures. It is demonstrated that the criterion is applicable for the OTSs at the interface inside both finite PhC-PhC heterostructures and PhC-metal heterostructures. In addition, we also discuss the importance of the number and the element order of the unit cells in the occurrence of optic Tamm states.

We introduce two classes of spatial optical breathers in strongly nonlocal nonlinear media: multiringed breathers and rotating breathers, which can be created as results of the superposition of off-waist input Laguerre-Gaussian beams. Their width “breathes” sinusoidally during propagation under the off-waist incident condition, whatever the input power is. Only when the beam is inputted at the waist and the input power equals the critical power simultaneously would the multiringed (rotating) breather reduce to a multiringed (rotating) soliton. For a rotating breather, the azimuthal orientation of the intensity pattern is determined by the indices of the constituent beams and varies periodically in propagation. This property together with the breath of the beam width yields novel trajectories which the points within the beam cross section undergo.