The nonconservation of entanglement, when two or more particles interact, sets it apart from other dynamical quantities, like energy and momentum, and does not allow the interpretation of the subtle dynamics of entanglement as a flow of this quantity between the constituents of the system. Nevertheless, we show that when the interaction between a qubit and its environment is described by an amplitude-decay channel, the conservation of the mean excitation number and the inclusion of a third party leads to an invariant expression involving the bipartite entanglement between each of the parties and the other two. We provide an experimental demonstration of this idea using entangled photons and generalize it to $N$-partite Greenberger-Horne-Zeilinger states.

We measure the upper-state lifetime and two ratios of vibrational branching fractions $f_{v^{\prime }v}$ on the $B{}^3{\Pi }_1\left(v^{\prime }\right)-X{}^1{\Sigma }^{+}\left(v\right)$ transition of TlF. We find the $B$-state lifetime to be 99(9) ns. We also determine that the off-diagonal vibrational decays are highly suppressed: $f_{01}/f_{00}<2\times {10}^{-4}$ and $f_{02}/f_{00}=1.10\left(6\right)$%, in excellent agreement with their predicted values of $f_{01}/f_{00}<8\times {10}^{-4}$ and $f_{02}/f_{00}=1.0\left(2\right)$% based on Franck-Condon factors calculated using Morse and Rydberg-Klein-Rees (RKR) potentials. The implications of these results for the possible laser cooling of TlF and fundamental symmetries experiments are discussed.

The exchange-only optimized-effective-potential method is implemented with the use of Slater-type basis functions, seeking an alternative to the standard methods of solution with some computational advantages. This procedure has been tested in a small group of closed-shell atoms and diatomic molecules, for which numerical solutions are available. The results obtained with this implementation have been compared to the exact numerical solutions and to the results obtained when the optimized effective equations are solved using the Gaussian-type basis sets. This Slater-type basis approach leads to a more compact expansion space for representing the potential of the optimized-effective-potential method and to considerable computational savings when compared to both the numerical solution and the more traditional one in terms of the Gaussian basis sets.

The hyperfine-induced $2s2p{}^3{P}_0\to 2s^2{}^1{S}_0$ transition rate in Be-like sulfur was measured by monitoring the decay of isotopically pure beams of ${}^{32}$S${}^{12+}$ and ${}^{33}$S${}^{12+}$ ions in a heavy-ion storage ring. Within the 4$\%$ experimental uncertainty the experimental value of $0.096\left(4\right)$ s${}^{-1}$ agrees with the most recent theoretical results of [Cheng et al. Phys. Rev. A 77, 052504 (2008)] and [Andersson et al. Phys. Rev. A 79, 032501 (2009)]. Repeated experiments with different magnetic fields in the storage-ring bending magnets demonstrate that artificial quenching of the $2s2p{}^3{P}_0$ state by these magnetic fields is negligible.

We present results from numerical calculations in the Coulomb gauge of the first-order self-energy shift of bound hydrogenic states in highly stripped ions. We apply the expressions for the renormalized free-electron self-energy and vertex operators obtained by G. S. Adkins [Phys. Rev. D 27, 1814 (1983); Phys. Rev. D 34, 2489 (1986)] to the evaluation of the zero- and one-potential terms. It is found that in this gauge the contribution from the many-potential term, which limits the overall accuracy, is significantly smaller than in the covariant Feynman gauge. This enables us to improve the accuracy of the self-energy prediction considerably compared to that obtained in the corresponding Feynman-gauge calculations.

The time-dependent close-coupling method is applied to calculate the electron-impact ionization of a diatomic molecule with interior closed subshells. The ionization of the outer $2s\sigma$ subshell of Li${}_2$($1s{\sigma }^{2}2p{\sigma }^{2}2s{\sigma }^2$) is carried out using a standard core orthogonalization method. At the peak of the Li${}_2$ cross section, the nonperturbative time-dependent close-coupling cross sections are found to be lower than perturbative distorted-wave cross sections. The reductions due to electron correlation effects are in keeping with previous reductions of peak cross sections seen in the electron-impact ionization of neutral atoms.

We describe, analytically and numerically, topologically nontrivial stationary states with azimuthal modulation of density in a repulsive Bose-Einstein condensate (BEC) confined in a harmonic trap. We show that, depending on the number of density peaks and total topological charge, these states can have a sophisticated phase texture associated with a vortex cluster. For a given topological charge, the form of density distribution and the structure of phase singularities are uniquely linked, thus simultaneous phase and density modulation enforces the formation of a vortex cluster both in rotating and in nonrotating BEC clouds.

We study several realistic configurations making it possible to realize an acoustic horizon in the flow of a one-dimensional Bose-Einstein condensate. In each case we give an analytical description of the flow pattern, the spectrum of Hawking radiation, and the associated quantum fluctuations. Our calculations confirm that the nonlocal correlations of the density fluctuations previously studied in a simplified model provide a clear signature of Hawking radiation also in realistic configurations. In addition, we explain by direct computation how this nonlocal signal relates to short-range modifications of the density correlations.

It has recently been shown that the spin-orbit coupling gives rise to topologically nontrivial and thermodynamically stable gapless superfluid phases when the pseudospin populations of an atomic Fermi gas are imbalanced, with the possibility of featuring Majorana zero-energy quasiparticles. In this paper, we consider a Rashba-type spin-orbit coupling, and use the Bogoliubov-de Gennes formalism to analyze a single vortex line along a finite cylinder with a periodic boundary condition. We show that the signatures for the appearance of core- and edge-bound states can be directly found in the density of single-particle states and particle-current density. In particular, we find that the pseudospin components counterflow near the edge of the cylinder, the strength of which increases with increasing spin-orbit coupling.

We study transport of fermions in a system composed of a short optical lattice connecting two finite atomic reservoirs at different filling levels. The average equilibration current through the optical lattice, for strong lattice-reservoir coupling and finite temperatures, is calculated within the Landauer formalism using a nonequilibrium Green's functions approach. We moreover determine quantum and thermal fluctuations in the transport and find significant shot-to-shot deviations from the average equilibration current. We show how to control the atomic current by engineering specific optical lattice potentials without requiring site-by-site manipulations and suggest the realization of a single level model. Based on this model we discuss the blocking effect on the atomic current resulting from weak interactions between the fermions.

Motivated by experiments observing self-organization of cold atoms in optical cavities, we investigate the collective dynamics of the associated nonequilibrium Dicke model. The model displays a rich semiclassical phase diagram of long-time attractors including distinct superradiant fixed points, bistable and multistable coexistence phases, and regimes of persistent oscillations. We explore the intrinsic time scales for reaching these asymptotic states and discuss the implications for finite-duration experiments. On the basis of a semiclassical analysis of the effective Dicke model, we find that sweep measurements over 200 ms may be required in order to access the asymptotic regime. We briefly comment on the corrections that may arise due to quantum fluctuations and states outside of the effective two-level Dicke model description.

We theoretically investigate the flow of electromagnetic waves in complex honeycomb photonic lattices with local $\mathcal{PT}$ symmetries. Such $\mathcal{PT}$ structure is introduced via a judicious arrangement of gain and loss across the honeycomb lattice, characterized by a gain and loss parameter $\gamma$. We found a class of conical diffraction phenomena where the formed cone is brighter and travels along the lattice with a transverse speed proportional to $\sqrt{\gamma }$.

We propose a generation system of continuous-variable (CV) three-color entangled state of bright optical beams based on two cascaded standard nondegenerate optical parametric oscillators (NOPOs) above the threshold. One of signal and idler beams produced by the first NOPO is used for the pump light of the second NOPO. The three-color entanglement among signal and idler beams produced by the second NOPO and the retained another beam of the first NOPO is theoretically demonstrated. The symplectic eigenvalues of the partial transposition covariance matrix of the generated optical entangled state are numerically calculated in terms of experimentally reachable system parameters. The optimal operation conditions of the cascaded NOPOs system for obtaining high entanglement are found. The calculated results explicitly demonstrate that the OPO action can transfer entanglement. Due to that the cavity parameters and the nonlinear crystals of the two NOPOs can be freely chosen, the flexibility of the proposed protocol is relatively good and the system can be also extended to prepare entangled states with more parts easily.

For the example of the $D$${}_1$ line of ${}^{87}$Rb we analyze the experimental parameters that control the transient response of electromagnetically induced transparency. Quantum coherent free-induction decay is observed on time scales exceeding several milliseconds in a buffer-gas vapor cell. Numerical solutions of the quantum master equation and approximate analytical solutions are tested and absolute comparisons of the transient time scales, power broadening, resonance contrast, and frequency shifts are made. Two actively-phase-locked lasers are employed. The effects of laser phase noise that is not fully correlated are studied.

We consider influence of nonlocal (retardation) effects caused by the finite value of the speed of light on collective emission of a single photon by atomic ensembles. Using a fully quantum mechanical description of light and atoms we obtain an evolution equation for the atomic system that takes into account retardation. We found an exact analytical solution of this equation for the atomic slab geometry that yields insight on how the crossover between local and nonlocal dynamics occurs. In particular, it shows that initially nonlocal evolution, accompanied by collective oscillations of atomic population, becomes local at large time. In addition, atomic excitation in some parts of the sample rises above its initial value. We propose an experiment in which the transition between local and nonlocal regimes can be observed by increasing the size of the atomic sample or atomic density.

The time evolution of residual entanglement in a three-qubit system embedded in a photonic crystal is investigated by using a modified conjugate gradient method. In the isotropic photonic crystal the phenomena of entanglement “sudden death” and entanglement “sudden birth” are found due to the decoherence induced by the environment and its memory effect. Compared with the environment of an isotropic photonic crystal, entanglement has a longer lifetime in the anisotropic photonic crystal if the transition frequency is near the band edge. However, once the entanglement disappears, at a finite time in the anisotropic photonic crystal, it cannot revive, which means the phenomenon of entanglement sudden birth cannot happen in the anisotropic photonic crystal. The tripartite entanglement decays faster than bipartite entanglement in both types of photonic crystal, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noise.

We investigate from a theoretical perspective photoelectron angular distributions (PADs) in small $\mathrm{Na}$ clusters in relation to recently available experimental results. We consider various (increasingly refined) levels of theory in order to better understand relevant physical trends. It is found that PADs are extremely sensitive to all details of the modeling such that a detailed description of the final state and the ionic background is necessary. Finally, we compare the theoretical description with recent experimental data on the cluster anion ${\mathrm{Na}}_7^{-}$ and find a satisfying agreement for full time-dependent local-density approximation (TDLDA) with ionic background.

We analytically study the photon generation from vacuum due to the dynamical Casimir effect in a cavity with a two-level atom, initially prepared in an arbitrary pure state. Performing small unitary transformations, we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant and dispersive regimes.

In this Comment we show that the ambiguity of entropic quantities calculated by Montero and Martín-Martínez [Phys. Rev. A 83, 062323 (2011)] for fermionic fields in the context of the Unruh effect is not related to the properties of anticommuting fields, as claimed therein, but rather to wrong mathematical manipulations with them and not taking into account a fundamental superselection rule of quantum field theory.

We show that, contrary to the claims of the preceding Comment [Brádler and Jáuregui, Phys. Rev. A 85, 016301 (2012)], our original work [Phys. Rev. A 83, 062323 (2011)] is devoid of flaws or mistakes. We show that the criticism comes from a misunderstanding of part of our work.