We present a complete treatment for the quantum discord of two-qubit $X$ states, by developing a geometric picture of a quantum steering ellipsoid. It is shown that either a von Neumann measurement or a three-element positive-operator-valued measurement is optimal. The condition for the latter is obtained and expressed in geometric language. We show, by using analytical as well as numerical results, that there is a systematic structure in the optimal decomposition which exists in a class of states including the $X$ states. More significantly, we establish the relation to the quantum channel by identifying the steering ellipsoid with the quantum channel ellipsoid. Thus the quantum discord and classical correlation are closely related to the concept of the entanglement entropy of the quantum channel.

We derive an optimal bound for arbitrary entanglement manipulation based on the transmission of a pulse in coherent states over a lossy channel followed by local operations and unlimited classical communication (LOCC). This stands on a theorem to reduce LOCC via a local unital qubit channel to local filtering. We also present an optimal protocol based on beam splitters and a quantum nondemolition (QND) measurement on photons. Even if we replace the QND measurement with photon detectors, the protocol can achieve near-optimal performance, outperforming known entanglement generation schemes.

Negativity in a quasiprobability representation is typically interpreted as an indication of nonclassical behavior. However, this does not preclude states that are non-negative from exhibiting phenomena typically associated with quantum mechanics—the single qubit stabilizer states have non-negative Wigner functions and yet play a fundamental role in many quantum information tasks. We seek to determine what other sets of quantum states and measurements of a qubit can be non-negative in a quasiprobability distribution, and to identify nontrivial groups of unitary transformations that permute the states in such a set. These sets of states and measurements are analogous to the single qubit stabilizer states. We show that no quasiprobability representation of a qubit can be non-negative for more than two bases in any plane of the Bloch sphere. Furthermore, there is a unique set of four bases that can be non-negative in an arbitrary quasiprobability representation of a qubit. We provide an exhaustive list of the sets of single qubit bases that are non-negative in some quasiprobability distribution and are also closed under a group of unitary transformations. This list includes two nontrivial families of three bases that both include the single qubit stabilizer states as a special case. For qudits, we prove that there can be no more than $2^{d^2}$ states in non-negative bases of a $d$-dimensional Hilbert space in any quasiprobability representation. Furthermore, these bases must satisfy certain symmetry constraints, corresponding to requiring the bases to be sufficiently different from each other.

We derive a set of hierarchical equations for qubits interacting with a Lorentz-broadened cavity mode at zero temperature, without using the rotating-wave, Born, and Markovian approximations. We use this exact method to reexamine the entanglement dynamics of two qubits interacting with a common bath, which was previously solved only under the rotating-wave and single-excitation approximations. With the exact hierarchy equation method used here, double excitations due to counter-rotating-wave terms are found to have remarkable effects on the dynamics and the steady-state entanglement.

We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of $N$ particles is initially in the ground state within a hard-wall or a harmonic trap, and then it expands after dropping the trap. We compute the time dependence of the von Neumann and Rényi entanglement entropies and the particle fluctuations of spatial intervals around the original trap in the limit of a large number $N$ of particles. The results for these observables apply to one-dimensional gases of impenetrable bosons as well. We identify different dynamical regimes at small and large times, depending also on the initial condition, i.e., whether it is that of a hard-wall or a harmonic trap. In particular, we show analytically that the expansion from hard-wall traps is characterized by the asymptotic small-time behavior $S\approx (1/3)\ln (1/t)$ of the von Neumann entanglement entropy and the relation $S\approx {\pi }^{2}V/3$ (where $V$ is the particle variance), which are analogous to the equilibrium behaviors whose leading logarithms are essentially determined by the corresponding conformal field theory with central charge $c=1$. The time dependence of the entanglement entropy of extended regions during the expansion from harmonic traps has a remarkable property in that it can be expressed as a global time-dependent rescaling of the space dependence of the initial equilibrium entanglement entropy.

The theoretical and numerical approach used in a recent publication describing a nonperturbative treatment of ionization and simultaneous ionization plus excitation of helium by electron impact [Phys. Rev. Lett. 107, 023203 (2011)] are presented in detail. A variety of comparisons between the present predictions, experimental data, and results from other nonperturbative theories, such as convergent close coupling and time-dependent close coupling, for ionization without excitation are presented. The overall excellent agreement with the other available data provides confidence in using the $B$-spline $R$-matrix-with-pseudostates approach for this benchmark system, as well as extending it to more complex situations for which no other nonperturbative methods are currently available.

We report on systematic numerical and experimental investigations of electromagnetically induced transparency (EIT) to determine temperatures in an ultracold atomic gas. The technique relies on the strong dependence of EIT on atomic motion (i.e., Doppler shifts), when the relevant atomic transitions are driven with counterpropagating probe and control laser beams. Electromagnetically induced transparency permits thermometry with satisfactory precision over a large temperature range, which can be addressed by the appropriate choice of Rabi frequency in the control beam. In contrast to time-of-flight techniques, thermometry by EIT is fast and nondestructive, i.e., essentially it does not affect the ultracold medium. In an experimental demonstration we apply both EIT and time-of-flight measurements to determine temperatures along different symmetry axes of an anisotropic ultracold gas. As an interesting feature we find that the temperatures in the anisotropic atom cloud vary in different directions.

The ring dark solitons in spin-1 ${}^{23}$Na and ${}^{87}$Rb Bose-Einstein condensates are studied numerically in the framework of the time-dependent Gross-Pitaevskii equations. By simulating the phase engineering technique in real experiments, we explore the roles of the parameters characterizing the far-off resonant laser pulse which can be used to generate the ring dark solitons. The variations of these parameters have a dramatic effect on the lifetime and the decay profiles of the ring dark solitons. If only one ring dark soliton is generated in one component of the condensate, then ring dark solitons in other components are inclined to be induced, resulting in a coexistence state composed of interdependent ring dark solitons coming from different components of the condensate. Ring dark solitons in this coexistence state exhibit dynamical oscillations for hundreds of milliseconds. By studying the lifetime and decaying profiles of ring dark solitons, we explore the similarities and differences of ${}^{23}$Na and ${}^{87}$Rb condensates. In addition, taking into account the fact that the center of the ring may not coincide with that of the trap, we study the dynamics and decaying profiles of the off-centered ring dark solitons in the presence of the symmetry-breaking effect.

We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture ${}^{87}$Rb-${}^{40}$K for different values of the density imbalance. We then analyze the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.

We consider a model consisting of two subsystems with crossing linear dispersion curves that describes, for example, light propagation in binary waveguide arrays. This model admits bright-dark gap solitons in both the discrete and the continuous (long-wavelength) limits, in spite of the absence of a gap in the linear (i.e., plane-wave) spectrum. We find that these solitons are always modulationally unstable in the continuous limit, whereas they can be stable in the discrete system if the amplitude of the background component exceeds a certain threshold.

We study the geometrical phase when multiple exceptional points (EPs) are involved. In an optical microcavity of a stadium shape, we find two EPs, connected through three interacting modes, in a two-dimensional parameter space. It is shown that the geometrical phase imprinted on wave functions becomes zero when the two EPs are encircled three times in the parameter plane. In addition, we examine geometrical phases when three EPs are involved in a $3\times 3$ matrix model, and show that single- and double-loop return modes have the geometrical phase of $\pm \pi$ or zero, depending on the type of the three EPs encircled.

We study the quantum nonequilibrium dynamics of ultracold three-level atoms trapped in an optical lattice, which are excited to their Rydberg states via a two-photon excitation with non-negligible spontaneous emission. Rich quantum phases, including the uniform phase, the antiferromagnetic phase, and the oscillatory phase are identified. We map out the phase diagram and find these phases can be controlled by adjusting the ratio of intensity of the pump light to the control light and that of two-photon detuning to the Rydberg interaction strength. When the two-photon detuning is blueshifted and the latter ratio is less than 1, bistability exists among the phases. Actually, this ratio controls the Rydberg-blockade and Rydberg-antiblockade effects, thus, the phase transition in this system can be considered as a possible approach to study both effects.

In this Brief Report the extended Bose-Hubbard model with local two- and three-body interactions is studied by the exact diagonalization approach. The shapes of the first two insulating lobes are discussed and the values of the critical tunneling for which the insulating phase loses stability for repulsive and attractive three-body interactions are predicted.

We are able to clearly distinguish the processes responsible for enhanced low-intensity atomic Kerr nonlinearity, namely coherent population trapping and coherent population oscillations in experiments performed on the Rb $D_1$ line, where one or the other process dominates under appropriate conditions. The potential of this approach based on wave mixing for probing coherent atomic media is discussed. It allows the new spectral components to be detected with sub-kHz resolution, which is well below the laser linewidth limit. Spatial selectivity and enhanced sensitivity make this method useful for testing dilute cold atomic samples.

The dwell time is calculated within the framework of time-dependent weak measurement considering dissipative interaction between a spin-$\frac{1}{2}$ system and the environment. Caldirola and Montaldi's method of retarded Schrödinger equation is used to study the dissipative system. The result shows that inclusion of dissipative interaction prevents zero time tunneling.

Decoherent histories quantum theory is reformulated with the assumption that there is one “real” fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one. As we will show, this construction implies that the real history is not completely accessible to experimental or other observational discovery. However, sufficiently and appropriately coarse-grained sets of alternative histories have standard probabilities providing information about the real fine-grained history that can be compared with observation. We recover the probabilities of decoherent histories quantum mechanics for sets of histories that are recorded and therefore decohere. Quantum mechanics can be viewed as a classical stochastic theory of histories with extended probabilities and a well-defined notion of reality common to all decoherent sets of alternative coarse-grained histories.

We investigate the problem of teleporting unknown qudit states via pure quantum channels with nonmaximal Schmidt rank. This process is mapped to the problem of discriminating among nonorthogonal symmetric states which are linearly dependent and equally likely. It is shown that by applying an optimized maximum-confidence (MC) measurement for accomplishing this task, one reaches the maximum possible teleportation fidelity after a conclusive event in the discrimination process, which in turn occurs with the maximum success probability. In this case, such fidelity depends only on the Schmidt rank of the channel and it is larger than the optimal one achieved, deterministically, by the standard teleportation protocol. Furthermore, we show that there are quantum channels for which it is possible to apply a $k$-stage sequential MC measurement in the discrimination process such that a conclusive event at any stage leads to a teleportation fidelity above the aforementioned optimal one and, consequently, increases the overall success probability of teleportation with a fidelity above this limit.

Charge-state-specific spectra produced from charge exchange collisions between xenon ions and helium target atoms using an ECR (electron cyclotron resonance) source have been recorded in extreme ultraviolet (EUV). At low target gas pressures, the spectra were produced after a single collision event involving electron capture by the projectile ion and in each case intense emission near 11 nm was observed. The spectra of Xe${}^{16+}$ to Xe${}^{20+}$ are compared with atomic structure calculations and the possible mechanisms for electron capture are discussed. There is some evidence that for lower charged ions the spectra in the 10–15 nm region result mainly from transfer excitation or ionization processes rather than direct single electron capture into high $nl$ states.

The Perdew-Zunger self-interaction correction (SIC) to local and semilocal density functionals systematically underestimates molecular bond lengths, yet improves many other ground-state properties. An alternative definition of a SIC is reached by using the Perdew-Zunger energy with a global, multiplicative Kohn-Sham potential instead of the orbital-specific potentials of traditional SIC. Due to the unitary variance of the SIC energy, the most general construction of the SIC Kohn-Sham potential involves a unitary transformation of the Kohn-Sham orbitals. We systematically investigate the Kohn-Sham version of the SIC, in particular with respect to the bond-length question, and present a detailed analysis of the influence of different unitary transformations. Using a complex-valued energy-minimizing transformation appears to be the most favorable approach, and we explain this result by analyzing orbital densities. We discuss how to calculate the transformations efficiently.

Experiments and ab initio calculations of the differential and integral cross sections for the electronic excitation from the ground state ${}^1{A}_1$ to the ${}^3{B}_2$ and ${}^3{A}_1$ states of gas-phase furan molecules by low-energy electron impact were performed. Experimental differential cross sections were measured at incident electron energies between 5 and 15 eV and for scattering angles from 10${}^{\circ }$ to 130${}^{\circ }$. The calculated cross sections were obtained using the Schwinger multichannel method implemented with pseudopotentials. The influence of channel-coupling and polarization effects is investigated through the comparison between three different models of scattering calculations, each one considering a distinct channel-coupling scheme. The comparison of experimental and calculated cross sections for electronically inelastic electron scattering by C${}_4$H${}_4$O molecules is found to be mostly reasonable. The existing discrepancies in this combined theoretical and experimental study help to illustrate difficulties in readily establishing reliable electronic excitation cross sections of polyatomic molecules by low-energy electrons.