We analyze a simple and feasible practical scheme displaying Zeno, anti-Zeno, and inverse-Zeno effects in the observation of wave-packet spreading caused by free evolution. The scheme is valid both in spatial diffraction of classical optical waves and in time diffraction of a quantum wave packet. In the optical realization, diffraction spreading is observed by placing slits between a light source and a light-power detector. We show that the occurrence of Zeno or anti-Zeno effects depends just on the frequency of observations between the source and detector. These effects are seen to be related to the diffraction mode theory in Fabry-Perot resonators.

A convenient and effective way in the quantum double model to study anyons in a topological space with a tensor product structure is to create and braid anyons using ribbon operators connected to a common base site [A. Kitaev, Ann. Phys. (NY) 303, 2 (2003)]. We show how this scheme can be simulated in a physical system by constructing long ribbon operators connected to a base site that is placed far away. We describe how to move and braid anyons using these ribbon operators, and how to perform measurement on them. We also give the smallest scale of a system that is sufficient for proof-of-principle demonstration of our scheme.

UV-frequency metrology has been performed on the $a^3\Pi$ - $X^1{\Sigma }^{+}$ (0,0) band of various isotopologues of CO using a frequency-quadrupled injection-seeded narrow-band pulsed titanium:sapphire laser referenced to a frequency comb laser. The band origin is determined with an accuracy of 5 MHz ($\delta \nu /\nu =3\times {10}^{-9}$), while the energy differences between rotational levels in the $a^3\Pi$ state are determined with an accuracy of 500 kHz. From these measurements, in combination with previously published radio-frequency and microwave data, a set of molecular constants is obtained that describes the level structure of the $a^3\Pi$ state of ${}^{12}$C${}^{16}$O and ${}^{13}$C${}^{16}$O with improved accuracy. Transitions in the different isotopologues are well reproduced by scaling the molecular constants of ${}^{12}$C${}^{16}$O via the common mass-scaling rules. Only the value of the band origin could not be scaled, indicative of a breakdown of the Born-Oppenheimer approximation. Our analysis confirms the extreme sensitivity of two-photon microwave transitions between nearly degenerate rotational levels of different $\Omega$ manifolds for probing a possible variation of the proton-to-electron mass ratio, $\mu =m_p/m_e$, on a laboratory time scale.

Ground- and excited-state positronium (Ps) formation from the hydrogen atom by positron impact at low and intermediate energies have been studied within the framework of two-center two-channel eikonal final state-continuum initial distorted wave model. A general method for obtaining Ps formation into arbitrary final states has been derived. The present results of Ps (1$s$), Ps $(n=2),$ and total Ps formation cross sections agree very well with previous close-coupling calculations and experimental measurements. The maximum positions of Ps($n$) formation cross sections are found to be in good agreement with the prediction of wave vector matching model introduced by Charlton [J. Phys. B: At. Mol. Opt. Phys. 39, 4575 (2006)]. We also present a scaling law for Ps ($n$) formation cross sections that is valid for all $n$ in the entire energy range.

Xenon clusters were irradiated with plasma soft-x-ray laser pulses (having a wavelength of 13.9 nm, time duration of 7 ps, and intensities of up to 10 GW/cm${}^2$). The laser photon energy was high enough to photoionize 4$d$ core electrons. The cross section is large due to a giant resonance. The interaction was investigated by measuring the electron energy spectra. The photoelectron spectra for small clusters indicate that the spectral width due to the 4$d$ hole significantly broadens with increasing cluster size. For larger clusters, the electron energy spectra evolve into a Maxwell-Boltzmann distribution, as a strongly coupled cluster nanoplasma is generated.

We use a phase-only spatial light modulator to generate light distributions in which the intensity decays as a power law from a central maximum with order ranging from 2 (parabolic) to 0.5. We suggest that a sequence of these can be used as a time-dependent optical dipole trap for all-optical production of Bose-Einstein condensates (BECs) in two stages: efficient evaporative cooling in a trap with adjustable strength and depth, followed by an adiabatic transformation of the trap order to cross the BEC transition in a reversible way. Realistic experimental parameters are used to verify the capability of this approach in producing larger BECs than by evaporative cooling alone.

We develop an approach, by calculating the autocorrelation function of spins, to derive the magnetic field gradient-induced transverse ($T_2$) relaxation of spins undergoing restricted diffusion. This approach is an extension to the method adopted by McGregor. McGregor's approach solves the problem only in the fast diffusion limit; however, our approach yields a single analytical solution suitable in all diffusion regimes, including the intermediate regime. This establishes a direct connection between the well-known slow diffusion result of Torrey and the fast diffusion result. We also perform free induction decay measurements on spin-exchange optically polarized ${}^3$He gas with different diffusion constants. The measured transverse relaxation profiles are compared with the theory and satisfactory agreement has been found throughout all diffusion regimes. In addition to the transverse relaxation, this approach is also applicable to solving the longitudinal relaxation ($T_1$) regardless of the diffusion limits. It turns out that the longitudinal relaxation in the slow diffusion limit differs by a factor of 2 from that in the fast diffusion limit.

We investigate the dynamics of the photodissociation of the helium hydride ion HeH${}^{+}$ by XUV radiation with the aim to establish a detailed comparison with a recent experimental work carried out at the FLASH free electron laser using both vibrationally hot and cold ions. We determine the corresponding rovibrational distributions using a dissociative charge transfer setup and the same source conditions as in the FLASH experiment. Using a nonadiabatic time-dependent wave-packet method, we calculate the partial photodissociation cross sections for the $n=$1–3 coupled electronic states of HeH${}^{+}$. We find good agreement with the experiment for the cross section into the He + H${}^{+}$ dissociative channel. On the other hand, we show that the experimental observation of the importance of the electronic states with $n>3$ cannot be well explained theoretically, especially for cold ($v=0$) ions. We find a good agreement with the experiment on the relative contribution of the $\Sigma$ and $\Pi$ states to the cross section for the He${}^{+}$ + H channel, but only a qualitative one for the He + H${}^{+}$ channel. We discuss the factors that could explain the remaining discrepancies between theory and experiment.

Velocity map photoelectron imaging was used to study the photoelectron angular distributions of autoionizing Stark states of atomic xenon excited just below the Xe${}^{+}$ ${}^2{P}_{1/2}^o$ threshold at fields ranging from 50 to 700 V/cm. Two-color, two-photon resonant, three-photon excitation via the 6$p^{\prime }$[1/2]${}_0$ level was used to probe the region of interest. The wavelength scans show a similar evolution of structure to that observed in single-photon excitation [Ernst et al., Phys. Rev. A 37, 4172 (1988)]. The photoelectron angular distributions following autoionization of the Stark states provide information on the decay of excited states in electron fields. In the present experiments, the large autoionization width of the $\left({}^2{P}_{1/2}^o\right)nd{[3/2]}_1^o$ series dominates the decay processes, and thus controls the angular distributions. However, the angular distributions of the Stark states also indicate the presence of other decay channels contributing to the decay of these states.

We investigate the geometric phase in a model of a Bose-Einstein condensate coupled to an optical cavity in which both the condensate and the cavity are described with coherent states. When the argument of the atom-cavity coupling term varies in time slowly from zero to $2\pi$, we calculate the geometric phase accumulated by the ground state and obtain its analytic expression in explicit form. We find that the adiabatic geometric phase jumps from zero to nontrivial $\pi$ at a critical value that corresponds to the normal-superradiant phase-transition point. The magneticlike flux interpretation of the geometric phase is also discussed.

We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute the equation of state, double occupancy, entropy, uniform susceptibility, and spin correlations for temperatures that are similar to or below the ones achieved in current optical lattice experiments. We provide a quantitative analysis of adiabatic cooling of trapped fermions in two dimensions, by means of both flattening the trapping potential and increasing the interaction strength.

In Bose superfluids, the single-particle Green's function can be directly related to the superfluid velocity-velocity correlation function in the hydrodynamic regime. An explicit expression for the single-particle spectral density was originally written down by Hohenberg and Martin in 1965, starting from the two-fluid equations for a superfluid. We give a simple derivation of their results. Using these results, we calculate the relative weights of first and second sound modes in the single-particle spectral density as a function of temperature in a uniform Bose gas. We show that the second sound mode makes a dominant contribution to the single-particle spectrum in a relatively high-temperature region. We also discuss the possibility of experimental observation of the second sound mode in a Bose gas by photoemission spectroscopy.

We study the spatial correlations of strongly interacting bosons in a ground state, confined in a two-dimensional square and a three-dimensional cubic lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action in order to calculate the atom-atom correlations’ decay along the principal axis and a diagonal of the lattice-plane direction as a function of distance. Lower tunneling rates lead to quicker decays of the correlations, whose character becomes exponential. Finally, correlation functions allow us to calculate quantities that are directly bound to experimental outcomes, namely time-of-flight absorption images and resulting visibility. Our results contain all the characteristic features present in experimental data (transition from Mott insulating blob to superfluid peaks, etc.), emphasizing the usability of the proposed approach.

We study a superfluid in a rotating anharmonic trap and explicate a rigorous proof of a transition from a vortex lattice to a giant vortex state as the rotation is increased beyond a limiting speed determined by the interaction strength. The transition is characterized by the disappearance of the vortices from the annulus where the bulk of the superfluid is concentrated due to centrifugal forces while a macroscopic phase circulation remains. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and reveals significant differences between “soft” anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary: in the latter case the transition takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus, whereas in soft traps the vortex lattice persists until the width of the annulus becomes comparable to the vortex cores. Moreover, the density profile in the annulus where the bulk is concentrated is, in the soft case, approximately Gaussian with long tails and not of the Thomas-Fermi type like in a trap with a fixed boundary.

We consider an ultrasmall system of polarized bosons on an optical lattice with a ring topology, interacting via long-range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions between different density-wave phases. As the strength of the dipolar interactions is varied, the behavior of the transitions is first-order-like. For dipoles polarized in the plane of the ring, the transitions between possible phases show pronounced sensitivity to the lattice depth. The abundance of possible configurations may be useful for quantum-information applications.

We use a Green's tensor method to investigate the spontaneous emission rate of a molecule and the energy-transfer rate between molecules placed in two types of layered geometries: a slab geometry and a planar waveguide. We focus especially on the role played by surface-plasmon polaritons in modifying the spontaneous emission and energy-transfer rates as compared to free space. In the presence of more than one interface, the surface-plasmon polariton modes split into several branches, and each branch can contribute significantly to modifying the electromagnetic properties of atoms and molecules. Enhancements of several orders of magnitude both in the spontaneous emission rate of a molecule and the energy-transfer rate between molecules are obtained and, by tuning the parameters of the geometry, one has the ability to control the range and magnitude of these enhancements. For the energy-transfer rate interference effects between contributions of different plasmon-polariton branches are observed as oscillations in the distance dependence of this rate.

We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a dual-periodically-poled crystal. Compared with the usual forward-wave-type source, this source, in the backward-wave way, has a much narrower bandwidth. With a 2-cm-long bulk crystal, the bandwidths of the example sources are estimated to be $3.6$ GHz, and the spectral brightnesses are more than 100 pairs$/$(s GHz mW). Two concurrent quasi-phase-matched spontaneous parametric down-conversion processes in a single crystal enable our source to be compact and stable. This scheme does not rely on any state projection and applies to both degenerate and nondegenerate cases, facilitating applications of the entangled photons.

We study the generation of intensity quantum correlations using four-wave mixing in a rubidium vapor. The absence of cavities in these experiments allows to deal with several spatial modes simultaneously. In the standard amplifying configuration, we measure relative intensity squeezing up to 9.2 dB below the standard quantum limit. We also theoretically identify and experimentally demonstrate an original regime where, despite no overall amplification, quantum correlations are generated. In this regime, a four-wave mixing setup can play the role of a photonic beam splitter with nonclassical properties, that is, a device that splits a coherent state input into two quantum-correlated beams.

We present a diagrammatic method for complete characterization of multiphoton processes in three-level atomic systems. By considering the interaction routes of the coupling and probe photons for a ladder-type, three-level, noncycling (or cycling) atomic system, we are able to completely discriminate between the pure one-photon and the pure two-photon resonance effects, and the effect of their combination in electromagnetically induced transparency (EIT) using our diagrammatic method. We show that the proposed diagrammatic method is very useful for the analysis of multiphoton processes in ladder-type EIT.

Interaction and motion of multiple solitons in passively-mode-locked (PML) fiber lasers are investigated numerically. Three types of relative motions of two solitons are found in PML fiber lasers. The numerical results show that the relative motion of solitons attributes to the phase shift, which corresponds to the instantaneous frequency at pulse peak to be nonzero. Different from the classical dynamics of billiard balls, the interaction of solitons is similar to the Feynman diagram which is a pictorial way to represent the interaction of particles. After solitons interact with one another, their shapes do not change, but their phases shift and relative motions change. The theoretical results demonstrate that the separation of neighboring solitons in the laser cavity is about several hundred picoseconds to several nanoseconds. The theoretical predictions are in good agreement with the experimental results.