Oscillatory structures associated with electron emission in $1–5\text{−}\mathrm{MeV}$ ${\mathrm{H}}^{+}$ collisions with ${\mathrm{N}}_2$ have been investigated. Ratios of experimental molecular ${\mathrm{N}}_2$ to theoretical atomic N cross sections exhibit nearly constant frequency sinusoidal oscillations that do not vary with the electron observation angle or collision velocity. The results suggest suppression of primary Young-type interferences, in sharp contrast to observations for ${\mathrm{H}}_2$, while secondary structures attributed to intramolecular scattering are prominent. Theoretical calculations predict suppression of the primary interferences but not to the extent observed in the measurements.

It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. Asymptotic expansions of this wave function at large interparticle distances are derived, from which is defined a quantity $D$ named three-body scattering hypervolume, which is an analog of the two-body scattering length. Given any finite-range interactions, one can thus predict the effective three-body force from a numerical solution of the Schrödinger equation. In this way, the constant $D$ for hard-sphere bosons is computed, leading to the first complete result for the ground-state energy per particle of a dilute Bose-Einstein condensate (BEC) of hard spheres to order ${\rho }^2$, where $\rho$ is the number density. Effects of $D$ are also demonstrated in the three-body energy in a finite box of size $L$, which is expanded to the order $L^{-7}$, and in the three-body scattering amplitude in vacuum. The three-body scattering amplitude calculated in this paper disagrees with an earlier calculation in the literature, because of the omission of the two-body effective range in that earlier work. Another key prediction is the condensate fractions of dilute BECs, which also disagree with an earlier work in the literature based on the effective field theory (EFT), as a result of short-range physics. An EFT prediction of the BEC ground-state energy, however, is corroborated.

The asymptotic properties of optical waves propagating inside the graded-index waveguide amplifier are studied in the framework of $\left(1+1\right)$-, $\left(2+1\right)$-, and $\left(3+1\right)$-dimensional nonlinear Schrödinger equations. By employing a direct ansatz, we find that the parabolic optical waves can be generated from arbitrary input waves at the asymptotic limit. These waves possess linear chirps and can propagate self-similarly. It is found that the characteristics of the asymptotic parabolic optical waves is not only affected by the input power, but also affected by the inhomogeneity of the graded-index waveguide. Furthermore, the possibility of controlling the shape of output parabolic waves is demonstrated. Specifically, the existence of optical waves with elliptic and ellipsoidal profiles possessing nontrivial but isotropic quadratic phases are predicted. The theoretical results are confirmed by numerical simulations.

In many frontier areas of research it is the distribution of a particular element in the sample which is of crucial interest. This paper proposes a method in which the signal due to the presence of a particular element can be enhanced while signals due to other elements present in the sample are suppressed. Rather than comparing the images measured above and below an absorption edge in conventional absorption contrast technique this method enhances the phase effect due to a particular element by taking multiple-wavelength measurements in the vicinity of its absorption edge of the element of interest. It is shown that the method can be incorporated to various techniques of x-ray phase imaging and therefore promises to have a very wide range of applications.

We demonstrate a simple scheme to achieve fast, accelerating (runaway) evaporative cooling of optically trapped atoms by tilting the optical potential with a magnetic field gradient. Runaway evaporation is possible in this trap geometry due to the weak dependence of vibration frequencies on trap depth, which preserves atomic density during the evaporation process. Using this scheme, we show that Bose-Einstein condensation with $\sim {10}^5$ cesium atoms can be realized in $2–4\mathrm{s}$ of forced evaporation. The evaporation speed and energetics are consistent with the three-dimensional evaporation picture, despite the fact that atoms can only leave the trap in the direction of tilt.

We study macroscopic quantum phenomena for an atomic condensate in a double-well potential as realized in recent experiments by Albiez et al. [Phys. Rev. Lett. 95, 010402 (2005)] and Shin et al. [Phys. Rev. Lett 95, 170402 (2005)]. By keeping the leading correction in the usually adopted mapping to an anisotropic spin model, we find that the topological Berry phase, a parity effect due to the even and odd atom numbers of a condensate, can be observed in the tunnel splitting. Our investigation suggests a cleaner, perhaps significantly improved, alternative for observing macroscopic quantum coherence (MQC) in large spin models.

We present a temporal characterization of sub-optical-cycle extreme ultraviolet radiation generated in a hollow-core waveguide. This generation scheme permits the use of relatively long $13\text{−}\mathrm{fs}$ driving laser pulses to generate sub-optical-cycle bursts of high-order harmonic light. Using two-color cross-correlation and phase retrieval techniques, we extract the extreme ultraviolet wave form and show that it consists of chirped $470\text{−}\mathrm{as}$ bursts, spaced by $\sim 1.3\mathrm{fs}$, within a $1.4\text{−}\mathrm{fs}$ intensity envelope. The radiation is spectrally narrow and energy tunable, making it a useful tool to investigate state-selective molecular and materials dynamics.

A Lorentz-invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization-sensitive position eigenvector and the photon wave function. It is found that this scalar product is independent of the form chosen for the wave function and that the normalized positive frequency vector potential–electric field pair is a convenient choice of wave function in the presence of matter. The number amplitude describing a localized state is a $\delta$ function at the instant at which localization and detection are seen as simultaneous.

Cluster states are multiparticle entangled states with special entanglement properties particularly suitable for quantum computation. It has been shown that cluster states can exhibit Greenberger-Horne-Zeilinger (GHZ) -type nonlocality even when some of their qubits have been lost. In the present work, we generated a four-photon mixed state, which is equivalent to the partial, qubit-loss state of an $N$-qubit cluster state up to some local transformations. By using this mixed state, we then realize a GHZ-type violation of local realism. Our results not only demonstrate a mixed state’s GHZ-type nonlocality but also exhibit the robustness of cluster states under qubit-loss conditions.

The task of finding a correctable encoding that protects against some physical quantum process is in general hard. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum process, and known algorithmic methods for finding correctable encodings involve operations on exponentially large matrices. However, we show that in some cases it is possible to find such encodings with only partial information about the quantum process. Such useful partial information can be systematically extracted by averaging the channel under the action of a set of unitaries in a process known as twirling. In this paper we prove that correctable encodings for a twirled channel are also correctable for the original channel. We investigate the particular case of twirling over the set of Pauli operators and qubit permutations, and show that the resulting quantum operation can be characterized experimentally in a scalable manner. We also provide a postprocessing scheme for finding unitarily correctable codes for these twirled channels which does not involve exponentially large matrices, and which is robust against uncertainties in the experimental estimates.

Numerical simulations of the interference of a three-way segmented nonrotating Bose-Einstein condensate reveal the production of a honeycomb vortex lattice containing significant numbers of vortices and antivortices. If confined within a trap, the lattice subsequently melts, exhibiting a rich assortment of vortex-antivortex interactions. In contrast with nonlinear vortex production mechanisms previously described for Bose-Einstein condensates, the process here is shown to be primarily one of linear superposition, with initial vortex locations approximately described by a linear theory of wave packet interference.

We study the quantum phase transitions in a two component Bose mixture in a one-dimensional optical lattice. The calculations have been performed in the framework of the extended Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain different phase transitions for the system for integer filling. When the interspecies on-site and the nearest-neighbor interactions are larger than the intraspecies on-site and also the nearest-neighbor interaction, the system exhibits a phase separated charge-density-wave order that is characterized by the two species being spatially separated and existing in the density-wave phases.

We study the effect of quantum motion in a Mach-Zehnder interferometer where ultracold, two-level atoms cross a $\pi ∕2\text{−}\pi \text{−}\pi ∕2$ configuration of separated, laser illuminated regions. Explicit and exact expressions are obtained for transmission amplitudes of monochromatic, incident atomic waves using recurrence relations which take into account all possible paths: the direct ones usually considered in the simple semiclassical treatment, but including quantum motion corrections, and the paths in which the atoms are repeatedly reflected at the fields.

We study various properties of an ultracold two-dimensional (2D) Bose gas that are beyond a mean-field description. We first derive the effective interaction for such a system as realized in current experiments, which requires the use of an energy dependent $T$ matrix. Using this result, we then solve the mean-field equation of state of the modified Popov theory, and compare it with the usual Hartree-Fock theory. We show that even though the former theory does not suffer from infrared divergences in both the normal and superfluid phases, there is an unphysical density discontinuity close to the Berezinskii-Kosterlitz-Thouless transition. We then improve upon the mean-field description by using a renormalization group approach and show how the density discontinuity is resolved. The flow equations in two dimensions, in particular, of the symmetry-broken phase, already contain some unique features pertinent to the 2D $XY$ model, even though vortices have not been included explicitly. We also compute various many-body correlators, and show that correlation effects beyond the Hartree-Fock theory are important already in the normal phase as criticality is approached. We finally extend our results to the inhomogeneous case of a trapped Bose gas using the local-density approximation and show that close to criticality, the renormalization group approach is required for the accurate determination of the density profile.

We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging $s$-wave scattering length. Using the fixed-node diffusion Monte Carlo method, the energies of the “normal state” are determined as functions of the population imbalance and the number of particles. The energies of the trapped system follow, to a good approximation, a universal curve even for fairly small systems. A simple parametrization of the universal curve is presented and related to the equation of state of the bulk system.

Omnidirectional zero-$\overline{n}$ gaps in one-dimensional photonic crystals with a Fibonacci basis containing frequency dependent metamaterials are examined. In this study, the band structure and band gaps are determined by an explicit band-edge equation rather than by a traditional dispersion equation. We find that the present method has better numerical stability than traditional methods, especially for calculating the zero-$\overline{n}$ gap in the photonic crystals with metamaterials. We observe that the change in the width and location of the omnidirectional zero-$\overline{n}$ gap is limited for the Fibonacci photonic crystals with different generation orders. However, the width of the omnidirectional gap in the Fibonacci photonic crystals is significantly affected by the filling factor of the metamaterials. We also find that the width of the gap will be maximum at an optimum filling factor. The gap will vanish if the filling factor is greater than a critical value. Moreover, for a given filling factor and a metamaterial, it is interesting that the gap will be enlarged as the refractive index of the traditional layer increases.

We show that the Rényi uncertainty relations give a good description of the dynamical behavior of wave packets and constitute a sound approach to revival phenomena by analyzing three model systems: the simple harmonic oscillator, the infinite square well, and the quantum bouncer. We prove the usefulness of entropic uncertainty relations as a tool for identifying fractional revivals by providing a comparison in different contexts with the usual Heisenberg uncertainty relation and with the common approach in terms of the autocorrelation function.

In this work we consider the permutational properties of multipartite entanglement monotones. Based on the fact that genuine multipartite entanglement is a property of the entire multiqubit system, we argue that ideal definitions for its characterizing quantities must be permutation invariant. Using this criterion, we examine the three four-qubit entanglement monotones introduced by Osterloh and Siewert [Phys. Rev. A 72, 012337 (2005)]. By expressing them in terms of quantities whose permutational properties can be easily derived, we find that one of these monotones is not permutation invariant. We propose a permutation-invariant entanglement monotone to replace it, and show that our new monotone properly measures the genuine four-qubit entanglement in four-qubit cluster-class states. Our results provide some useful insights in understanding multipartite entanglement.

We construct general schemes for multipartite quantum secret sharing using multilevel systems, and find that the consistency conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using very high-dimensional mutually unbiased bases can in principle achieve perfect security against intercept-resend attack; and for the scheme using mutually biased bases, it reaches the optimal but nonperfect security at the four-level system. We also address the security issue against general attacks in the context of our multilevel schemes. In particular, we propose a protocol to enhance both the efficiency and the security against an entanglement-assisted participant’s attack by incorporating quantum-key-distribution and measurement-basis-encrypted schemes so that its security is as robust as quantum-key distribution.

We report on the implementation of an interferometric scheme that allows the generation of photon pairs entangled in the time-energy degree of freedom. This scheme does not require any kind of temporal postselection on the generated pairs and can be used even with lasers with short coherence time.