The branching ratios between the single and double electron radiative transitions to empty K shell in He-like ions with 2s2p configuration are evaluated for 15 ions with $4\le Z\le 26$ using fully relativistic multiconfiguration Dirac-Fock wavefunctions in the active space approximation. The effects of configuration interaction and Breit contributions on the transition parameters have been analyzed in detail. Though the influence of Breit interaction on the electric dipole allowed one-electron radiative transitions is negligible, it substantially changes the spin-forbidden rates and the two-electron one-photon transition probabilities. Also, while the single electron transition rates are gauge independent, the correlated double-electron probabilities are found to be gauge sensitive. The probable uncertainties in the computed transition rates have been evaluated by considering the line strengths and the differences between the calculated and experimental transition energies as accuracy indicators. The present results are compared with other available experimental and theoretical data.

The simplest iterative complement (SIC) calculations starting from Hartree-Fock and giving full configuration interaction (CI) at convergence were performed using regular and inverse Hamiltonians. Each iteration step is variational and involves only one variable. The convergence was slow when we used the regular Hamiltonian, but became very fast when we used the inverse Hamiltonian. This difference is due to the Coulomb singularity problem inherent in the regular Hamiltonian; the inverse Hamiltonian does not have such a problem. For this reason, the merit of the inverse Hamiltonian over the regular one becomes even more dramatic when we use a better-quality basis set. This was seen by comparing the calculations due to the minimal and double-ζ basis sets. Similar problematic situations exist in the Krylov sequence and in the Lanczos and Arnoldi methods.

A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential and that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the fermionic or bosonic symmetry in the case of indistinguishable particles.

We investigate the properties of impenetrable bosons confined in a one-dimensional lattice at finite temperature in the presence of an additional incommensurate periodic potential. Relying on the exact Fermi-Bose mapping, we study the effects of temperature on the one-particle density matrix and related quantities such as the momentum distribution function and the natural orbitals. We found evidence of a finite-temperature crossover related to the zero-temperature superfluid-to-Bose-glass-transition that induces a delocalization of the lowest natural orbitals.

We discuss dynamical enhancement of entanglement in a driven Bose-Hubbard model and find an enhancement of two orders of magnitude from the ground state value which is robust against fluctuations in experimental parameters.

We investigate an ultracold Fermi gas at unitarity confined in a periodic box $V=L^3$ using renormalization group techniques. Within this approach we can quantitatively assess the long-range bosonic order parameter fluctuations, which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finite-size and particle-number effects present in Monte Carlo simulations of ultracold Fermi gases.

We display a photonic embodiment of the Demkov-Ostrovsky solution to the crossing of two manifolds made of equidistant modes thanks to broad periodic waveguides. We find clearly narrowing resonances that signal the singular, flat dispersion case that we had termed “critical coupling.” The reconciliation of band-edge confinement and cavity confinement, two pillars of photonics, appear from the guide length dependence of spectra. We suggest the generality of the Demkov-Ostrovsky or critical coupling flat dispersion across all kinds of waves, e.g., electronic and acoustic.

We show an alternative path to efficient second- and third-harmonic generation in proximity of the zero crossing points of the dielectric permittivity in conjunction with low absorption. Under these circumstances, any material, either natural or artificial, will show similar degrees of field enhancement followed by strong harmonic generation, without resorting to any resonant mechanism. The results presented in this paper provide a general demonstration of the potential that the zero-crossing-point condition holds for nonlinear optical phenomena. We investigate a generic Lorentz medium and demonstrate that a singularity-driven enhancement of the electric field may be achieved even in extremely thin layers of material. We also discuss the role of nonlinear surface sources in a realistic scenario where a 20-nm layer of CaF${}_2$ is excited at 21 μm, where ε ∼ 0. Finally, we show similar behavior in an artificial composite material that includes absorbing dyes in the visible range, provide a general tool for the improvement of harmonic generation using the ε ∼ 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.

We study the simplest optomechanical system in the presence of laser phase noise (LPN) using the covariance matrix formalism. We show that for any LPN model with a finite correlation time, the destructive effect of the phase noise is especially strong in the bistable regime. This explains why ground-state cooling is still possible in the presence of phase noise, as it happens far away from the bistable regime. We also show that the optomechanical entanglement is strongly affected by phase noise.

It is a well-known fact that a single nanoparticle placed in the evanescent field of an optical microdisk leads to coherent backscattering of light between counterpropagating whispering-gallery modes. This backscattering lifts the spectral degeneracy giving rise to a doublet of standing-wave modes. Here, we show that the evanescent coupling of two or more nanoparticles leads in general to asymmetric backscattering (i.e., the strength of the scattering of light from the clockwise to the counterclockwise propagation direction is different than the other way around). Even if the strength of the backscattering is weak its asymmetry can have a dramatic impact on the mode structure. In the regime of overlapping resonances the modes do not have a standing-wave character. Instead nonorthogonal pairs of mainly copropagating modes are formed. In the extreme case the pair of optical modes coalesce at a so-called exceptional point. We derive an effective Hamiltonian within a two-mode approximation which reveals that this unexpected behavior is due to interference of the scattered waves which can be destructive or constructive depending on the propagation direction of the light.

We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.

We analyze the effect of the filling factor on the imaging performance of metallic nanorod lenses. We observe that thicker nanorods allow lower reflection in the canalization regime and we find optimal values of the filling factor to achieve a transfer function with the characteristics of a perfect lens in a wide range of spatial frequencies.

We present a theoretical analysis of rf association of Efimov trimers in a two-component Bose gas with short-range interactions. Using the adiabatic hyperspherical formalism to solve the quantum three-body problem, we obtain universal expressions for three-body rf association rates as a function of the $s$-wave scattering length $a>0$. We find that the association rates scale as $a^{-2}$ in the limit of large $a$, and diverge as $a^3{a}_{ad}^3$ whenever an Efimov state crosses the atom-dimer threshold (where $a_{ad}$ stands for the atom-dimer scattering length). Our calculations show that trimer formation rates as large as $\sim$10${}^{-21}$ cm${}^6$/s can be achieved with rf Rabi frequencies on the order of 1 MHz, suggesting that direct rf association is a powerful tool for making and probing few-body quantum states in ultracold atomic gases.

Quantum escape of a particle from an end of a one-dimensional finite region to $N$ semi-infinite leads is discussed from a scattering theory approach. Depending on the potential barrier amplitude at the junction, the probability $P\left(t\right)$ for a particle to remain in the finite region at time $t$ shows two different decay behaviors at long times; one is proportional to $N^2/t^3$ and another is proportional to $1/\left(N^{2}t\right)$. In addition, the velocity $V\left(t\right)$ for a particle to leave the finite region, defined from a probability current of the particle position, decays asymptotically as a power of time $\sim$$1/t$, independent of the number of leads and the initial wave function. For a finite time, the probability $P\left(t\right)$ decays exponentially in time with a smaller decay rate for a greater number of leads, and the velocity $V\left(t\right)$ shows a time oscillation whose amplitude is larger for a greater number of leads. Particle escapes from the both ends of a finite region to multiple leads are also discussed using a different boundary condition.

We apply the fully quantum-mechanical convergent close-coupling method to the calculation of antiproton scattering on the ground state of helium. The helium target is treated as a three-body Coulomb system using frozen-core and multiconfiguration approximations. The electron-electron correlation of the target is fully treated in both cases. Though both calculations yield generally good agreement with experiment for the total ionization cross sections, the multiconfiguration results are substantially higher at the lower energies than the frozen-core ones. Calculated longitudinal ejected electron and recoil-ion momentum distributions for the single ionization of helium are in good agreement with the experiment.

Organosilicon compounds are of current interest due to the numerous applications of these species in industries. Some of these applications require the knowledge of electron collision cross sections, which are scarce for such compounds. In this work, we report absolute values of differential, integral, and momentum-transfer cross sections for elastic electron scattering by tetramethylsilane (TMS) measured in the 100–1000 eV energy range. The relative-flow technique is used to normalize our data. In addition, the independent-atom-model (IAM) and the additivity rule (AR), widely used to model electron collisions with light hydrocarbons, are also applied for $e^{-}$-TMS interaction. The comparison of our measured results of cross sections and the calculated data shows good agreement, particularly near the higher-end of incident energies.

The Landau-Zener-Stückelberg-Majorana (LZSM) model is widely used for estimating transition probabilities in the presence of crossing energy levels in quantum physics. This model, however, makes the unphysical assumption of an infinitely long constant interaction, which introduces a divergent phase in the propagator. This divergence remains hidden when estimating output probabilities for a single input state insofar as the divergent phase cancels out. In this paper we show that, because of this divergent phase, the LZSM model is inadequate to describe the evolution of pure or mixed superposition states across a level crossing. The LZSM model can be used only if the system is initially in a single state or in a completely mixed superposition state. To this end, we show that the more realistic Demkov-Kunike model, which assumes a hyperbolic-tangent level crossing and a hyperbolic-secant interaction envelope, is free of divergences and is a much more adequate tool for describing the evolution through a level crossing for an arbitrary input state. For multiple crossing energies which are reducible to one or more effective two-state systems (e.g., by the Majorana and Morris-Shore decompositions), similar conclusions apply: the LZSM model does not produce definite values of the populations and the coherences, and one should use the Demkov-Kunike model instead.

The weak-coupling many-polaron formalism is applied to the case of the polaronic system consisting of impurities in a Bose-Einstein condensate. This allows investigating the ground-state properties and the response of the system to Bragg spectroscopy. Then, this theory is applied to the system of spin-polarized fermionic lithium-6 impurities in a sodium condensate. The Bragg spectrum reveals a peak that corresponds to the emission of Bogoliubov excitations. Both the ground-state properties and the response spectrum show that the polaronic effect vanishes at high densities. We also look at two possibilities to define the polaronic effective mass and observe that this results in a different quantitative behavior if multiple impurities are involved.

We study the propagation of cold-atom wave packets in an interferometer with a Mach-Zehnder topology based on the dynamical phase of Bloch oscillation in a weakly forced optical lattice with a narrow potential barrier that functions as a cold-atom wave-packet splitter. We calculate analytically the atomic wave function, and show that the expected number of atoms in the two outputs of the interferometer oscillates rapidly as a function of the angle between the potential barrier and the forcing direction with period proportional to the external potential difference across a lattice spacing divided by the lattice band energy scale. The interferometer can be used as a high-precision force probe whose principle of operation is different from current interferometers based on the overall position of Bloch oscillating wave packets.

We propose to employ the storage of light in a dynamically tuned add-drop resonator to realize an optical gyroscope of ultrahigh sensitivity and compact size. Taking the impact of the linewidth of incident light on the sensitivity into account, we investigate the effect of rotation on the propagation of a partially coherent light field in this dynamically tuned slow-light structure. It is demonstrated that the fundamental trade-off between the rotation-detection sensitivity and the linewidth will be overcome and the sensitivity-linewidth product will be enhanced by two orders of magnitude in comparison to that of the corresponding static slow-light structure. Furthermore, the optical gyroscope employing the storage of light in the dynamically tuned add-drop resonator can acquire ultrahigh sensitivity by extremely short fiber length without a high-performance laser source of narrow linewidth and a complex laser frequency stabilization system. Thus the proposal in this paper provides a promising and feasible scheme to realize highly sensitive and compact integrated optical gyroscopes by slow-light structures.