How can one discriminate different inequivalent classes of multiparticle entanglement experimentally? We present an approach for the discrimination of an experimentally prepared state from the equivalence class of another state. We consider two possible measures for the discrimination strength of an observable. The first measure is based on the difference of expectation values, the second on the relative entropy of the probability distributions of the measurement outcomes. The interpretation of these measures and their usefulness for experiments with limited resources are discussed. In the case of graph states, the stabilizer formalism is employed to compute these quantities and to find sets of observables that result in the most decisive discrimination.

We study a scheme for state-insensitive trapping of neutral atoms by using light with two independent wavelengths. In particular, we describe the use of trapping and control lasers to minimize the variance of the potential experienced by a trapped Rb atom in ground and excited states. We present calculated values of wavelength pairs for which the $5s$ and $5p_{3/2}$ levels have the same ac Stark shifts in the presence of two laser fields.

In this addendum to our paper [D. Burgarth and V. Giovannetti, Phys. Rev. Lett. 99, 100501 (2007)] we prove that during the transformation that allows one to enforce control by relaxation on a quantum system, the ancillary memory can be kept at a finite size, independently from the fidelity one wants to achieve. The result is obtained by introducing the quantum analog of defragmentation algorithms which are employed for efficiently reorganizing classical information in conventional hard disks.

Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed.

We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and the time-convolutionless generator as well as the Nakajima-Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important differences.

We study the capacity of antiferromagnetic lattices of varying geometries to entangle two additional spin-$1/2$ probes. Analytical modeling of the quantum Monte Carlo data shows the appearance of a robust gap, allowing a description of entanglement in terms of probe-only states, even in cases where the coupling to the probes is larger than the gap of the spin lattice and cannot be treated perturbatively. We find a considerable enhancement of the temperature at which probe entanglement disappears as we vary the geometry of the bus and the coupling to the probes. In particular, the square Heisenberg antiferromagnet exhibits the best thermal robustness of all systems, whereas the three-leg ladder chain shows the best performance in the natural quantum ground state.

We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines the Wentzel-Kramers-Brillouin (WKB) treatment of the long-range attraction with the Fraunhofer model treatment of the short-range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey et al. [Phys. Rev. Lett. 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two-dimensional “hard core” of the potential, is essential for obtaining a correct imaginary part of the refractive index.

We present a systematic theoretical study to deal with linear and nonlinear light propagations in a Doppler-broadened three-level $\Lambda$ system via electromagnetically induced transparency (EIT), with incoherent population exchange between two lower energy levels taken into account. Through a careful analysis of base state and linear excitation, we show that the EIT condition of the system is given by $\left|{\Omega }_c\right|{}^2{\gamma }_{31}\gg 2{\gamma }_{21}\Delta {\omega }_D^2$, where ${\Omega }_c$ is half the Rabi frequency of the control field, $\Delta {\omega }_D$ is the Doppler width, and ${\gamma }_{\mathit{jl}}$ is the decay rate of the coherence between states $|j\rangle$ and $|l\rangle$. Under this condition, the effect of incoherent population exchange is insignificant, while dephasing dominates the decoherence of the system. This condition also ensures the validity of the weak nonlinear perturbation theory used in this work for solving the Maxwell-Bloch equations with inhomogeneous broadening. We then investigate the nonlinear propagation of the probe field and show that it is possible to form temporal optical solitons in the Doppler-broadened medium. Such solitons have ultraslow propagating velocity and can be generated in very low light power. The possibility of realizing ($1+1$)-dimensional and ($2+1$)-dimensional spatial optical solitons in the adiabatic regime of the system is also discussed.

We investigate the use of coherent optical fields as a means of dynamically controlling the resonant behavior of a variety of composite metamaterials, wherein the metamaterial structures are embedded in a dispersive dielectric medium. Control and switching are implemented by coherently driving the resonant permittivity of the embedding medium with applied optical radiation. The effect of embedding split ring resonators in a frequency-dispersive medium with Lorentz-like dispersion or with dispersion engineered by electromagnetically induced transparency (EIT) is manifested in the splitting of the negative-permeability band, the modified (frequency-dependent) filling fractions, and the dissipation factors. The modified material parameters are strongly linked to the resonant frequencies of the medium, and for an embedding medium exhibiting EIT also to the strength and detuning of the control field. The robustness of control against the deleterious influence of dissipation associated with the metallic structures as well as the inhomogeneous broadening due to structural imperfections is demonstrated. Studies on plasmonic metamaterials that consist of metallic nanorods arranged in loops and exhibit a collective magnetic response at optical frequencies are presented. Control and switching in this class of plasmonic nanorod metamaterials is shown to be possible, for example, by embedding these arrays in a Raman-active liquid like ${\mathrm{CS}}_2$ and utilizing the inverse Raman effect.

We derive simple practical tests revealing the quantum nature of states by the violation of classical upper bounds on the statistics of multiple outcomes of an observable. These criteria can be expressed in terms of the Kullback-Leibler divergence (or relative entropy). Nonclassicality tests for multiple outcomes can be satisfied by states that do not fulfill the corresponding single-outcome criteria.

The nonradiative charge-transfer processes in ${\mathrm{Be}}^{2+}(1s^2)+\mathrm{H}(1s)$ and ${\mathrm{B}}^{3+}(1s^2)+\mathrm{H}(1s)$ collisions are investigated by the quantal molecular orbital close-coupling method in the energy range of ${10}^{-5}$eV/u–$10$ keV/u and by the two-center atomic-orbital close-coupling method in the energy range of 0.1–100 keV/u. The radiative charge-transfer cross sections are calculated by using the optical potential and semiclassical methods in the energy range ${10}^{-5}$–$100$ eV/u. For both collision systems, the nonradiative charge-transfer cross sections in the low-energy region show an increasing behavior with decreasing energy. The nonradiative process is the dominant charge-transfer process in the ${\mathrm{Be}}^{2+}(1s^2)+\mathrm{H}(1s)$ collision in the entire eV and sub-eV energy region. In the ${\mathrm{B}}^{3+}(1s^2)+\mathrm{H}(1s)$ collision case, however, the cross section for radiative decay to $1{\hspace{0.5em}}^2$${\Sigma }^{+}$ and $2{\hspace{0.5em}}^2$${\Sigma }^{+}$ molecular states significantly exceeds that for the nonradiative process for energies below 30 eV/u.

The Siegert states of atoms in a static uniform electric field, defined as the solutions to the stationary Schrödinger equation satisfying the regularity and outgoing-wave boundary conditions, are discussed. An efficient method to calculate not only the complex energy eigenvalue, but also the eigenfunction for a general class of one-electron atomic potentials is introduced. An exact expression for the transverse momentum distribution of the ionized electrons in terms of the Siegert eigenfunction in the asymptotic region is derived. The method is illustrated by calculations of the energy, ionization width, and transverse momentum distribution as functions of the electric field for several lowest states of H, outer $p$ shells of Ne, Ar, Kr, and Xe, and the active electron in ${\mathrm{H}}^{-}$. We also discuss the ionization of Ar by the pulse of a unidirectional time-dependent electric field, which illustrates the role of the Siegert states in the recently developed adiabatic theory of ionization of atoms by intense laser pulses [O. I. Tolstikhin et al., Phys. Rev. A 81, 033415 (2010)].

We study the dynamics of an optically injected quantum-dot laser accounting for excited states. Mapping of the bifurcations in the plane frequency detuning vs. injection strength shows that the relaxation rate scales the regions of locking and single- and double-period solutions, while the capture rate has a minor effect. Within the regions of time-periodic solutions, close to the saddle-node bifurcation boundary, we identify subregions where the output signal resembles excitable pulses as a result of the bottleneck phenomenon. We show that such emission is determined mainly by fluctuations in the occupation of the excited states. The interpulse time follows an inverse square root scaling law as a function of the detuning. In a deterministic system the pulses are periodic regardless of the detuning, but in the presence of noise, close to the locking region, the interpulse time follows a positively skewed normal distribution. For a fixed frequency detuning, increasing the noise strength can shift the mean of the interpulse time distribution and make the pulsations more periodic.

We have investigated correlation patterns generated by a frequency-comb laser in a dispersive unbalanced Michelson interferometer and apply the developed formalism to the case of distance metrology. Due to group velocity dispersion, the position of the brightest fringe of the correlation pattern, which is used for distance determination, cannot be derived by simply using the definition of group refractive index of the dispersive medium. It is shown that the discrete spectrum of the optical frequency comb gives rise to correlation functions which can be represented by a series, namely a discrete correlation series. We have developed a general formalism, valid for any pulse train, extending the discrete model to a continuous model of cross-correlation functions using the Poisson summation. Our model is relevant for any offset and repetition frequency of the frequency comb. From the continuous cross-correlation model we show that, even for a homogeneous dispersive medium the position of the brightest fringe varies nonlinearly for small delay distances and stabilizes for longer ones. We have compared the theoretical results to measurements of pulse propagation in air for path-lengths up to 200 m.

The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.

We theoretically analyze the roles of initial correlations between a two-qubit system and a structured environment on entanglement dynamics of these two qubits. Considering two initial system-environment correlations, we show that the system-environment quantum correlation can initially increase the two-qubit entanglement, and the system-environment classical correlation would lead to the initially decreased two-qubit entanglement. Different two-qubit entanglement dynamics can be induced by these two initial system-environment correlations. However, under a certain condition, the roles of these two initial system-environment correlations on the two-qubit entanglement are the same.

A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.

The Kitaev honeycomb model with a topological phase transition at zero temperature is studied using the quantum-information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two bonds with the greatest distance are obtained. It is found that the mutual information shows some singularities at the critical point where the system transits from the gapless phase to the gapped phase. Finite-size effects and scaling behavior are also studied. Our results indicate that the mutual information can serve as a good indicator of the topological phase transition. This is because the mutual information is believed to be able to catch some global correlation properties of the system. Meanwhile, this method has the advantages that the phase transition can be determined easily and the order parameters, which are hard to obtain for some topological phase transitions, are not necessarily known.

In the present work, an alternative approach for the evaluation of the equilibrium $K$-, $L$-, and $M$-shell ionizations and the mean charge state $\overline{q}$ for projectiles passing through various targets has been proposed. The approach is based on measured $K$ x-ray energy shifts and line intensity ratios and utilizes the theoretical analysis of projectile spectra using multiconfiguration Dirac-Fock calculations. It was applied for the satellite and hypersatellite $K$ lines in the x-ray spectra emitted by sulfur projectiles passing with energies of 9.6–122 MeV through carbon, aluminium, titanium, and iron targets, recorded by a Si(Li) detector. It was found that only in the high projectile energy region there was significant dependence of mean equilibrium $K$-shell ionization on the target atomic number. The equilibrium $L$-shell ionization rises with the increase of sulfur energy until 32 MeV, but for higher energies the changes are very weak. The equilibrium $M$-shell ionization changes very weakly for low projectile energy while for higher energies this ionization is practically constant. For each target, the estimated value of $\overline{q}$ rises with the increase of the sulfur energy value. The dependence of the sulfur charge state on the target atomic number was discussed by taking into account the cross sections for ionization, decay, and electron capture processes. The data were compared with the experimental data measured by other authors and with the predictions of Shima’s and Schiwietz and Grande’s semiempirical formulas. The presented good agreement points out that this alternative approach delivers quantitative results.

The dissociation pathways of HeH${}^{+}$ have been investigated below the first ionization continuum by photoabsorption at 32 nm, using fragment momentum imaging in a crossed-beams experiment at the free-electron laser in Hamburg (FLASH). Investigations were done both for ions with several vibrational levels excited in the ion source and for ions vibrationally cooled in an electrostatic ion trap prior to the irradiation. The product channels ${\text{He}}^{+}(1s)+\text{H}(\mathit{nl})$ and $\text{He}(1\mathit{snl})+{\text{H}}^{+}$ were separated and the $\text{He}(1\mathit{snl})+{\text{H}}^{+}$ channel was particularly studied by coincidence detection of the He and ${\mathrm{H}}^{+}$ fragments on two separate fragment detectors. At 32 nm excitation, the branching ratio between the product channels was found to be ${\sigma }_{{\mathrm{He}}^{+}+\mathrm{H}}/{\sigma }_{\mathrm{He}+{\mathrm{H}}^{+}}=0.96\pm 0.11$ for vibrationally hot and $1.70\pm 0.48$ for vibrationally cold ions. The spectra of kinetic energy releases for both channels revealed that photodissociation at 32 nm leads to high Rydberg states ($n\gtrsim 3$–4) of the emerging atomic fragments irrespective of the initial vibrational excitation of HeH${}^{+}$. The fragment angular distributions showed that dissociation into the $\text{He}+{\text{H}}^{+}$ channel mostly ($~70\%$) proceeds through ${}^1\Pi$ states, while for the ${\text{He}}^{+}+\text{H}$ channel ${}^1\Sigma$ and ${}^1\Pi$ states are of about equal importance.