Closed formula for the relative entropy of entanglement

The long-standing problem of finding a closed formula for the relative entropy of entanglement (REE) for two qubits is addressed. A compact-form solution to the inverse problem, which characterizes an entangled state for a given closest separable state, is obtained. Analysis of the formula for a large class of entangled states strongly suggests that a compact analytical solution of the original problem, which corresponds to finding the closest separable state for a given entangled state, can be given only in some special cases. A few applications of the compact-form formula are given to show additivity of the REE, to relate the REE with the Rains upper bound for distillable entanglement, and to show that a Bell state does not have a unique closest separable state.Comment: 7 pages, the title was modified as suggested by the PRA editor

Ultrafast nematic-orbital excitation in FeSe

The electronic nematic phase is an unconventional state of matter that spontaneously breaks the rotational symmetry of electrons. In iron-pnictides/chalcogenides and cuprates, the nematic ordering and fluctuations have been suggested to have as-yet-unconfirmed roles in superconductivity. However, most studies have been conducted in thermal equilibrium, where the dynamical property and excitation can be masked by the coupling with the lattice. Here we use femtosecond optical pulse to perturb the electronic nematic order in FeSe. Through time-, energy-, momentum- and orbital-resolved photo-emission spectroscopy, we detect the ultrafast dynamics of electronic nematicity. In the strong-excitation regime, through the observation of Fermi surface anisotropy, we find a quick disappearance of the nematicity followed by a heavily-damped oscillation. This short-life nematicity oscillation is seemingly related to the imbalance of Fe 3dxz and dyz orbitals. These phenomena show critical behavior as a function of pump fluence. Our real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice

Momentum dependence of the energy gap in the superconducting state of optimally doped Bi2(Sr,R)2CuOy (R=La and Eu)

The energy gap of optimally doped Bi2(Sr,R)2CuOy (R=La and Eu) was probed by angle resolved photoemission spectroscopy (ARPES) using a vacuum ultraviolet laser (photon energy 6.994 eV) or He I resonance line (21.218 eV) as photon source. The results show that the gap around the node at sufficiently low temperatures can be well described by a monotonic d-wave gap function for both samples and the gap of the R=La sample is larger reflecting the higher Tc. However, an abrupt deviation from the d-wave gap function and an opposite R dependence for the gap size were observed around the antinode, which represent a clear disentanglement between the antinodal pseudogap and the nodal superconducting gap.Comment: Submitted as the proceedings of LT2

Doping-dependence of nodal quasiparticle properties in high-TcT_{\rm c} cuprates studied by laser-excited angle-resolved photoemission spectroscopy

We investigate the doping dependent low energy, low temperature ($T$ = 5 K) properties of nodal quasiparticles in the d-wave superconductor Bi$_{2.1}$Sr$_{1.9}$CaCu$_2$O$_{8+\delta}$ (Bi2212). By utilizing ultrahigh resolution laser-excited angle-resolved photoemission spectroscopy, we obtain precise band dispersions near $E_{F}$, mean free paths and scattering rates ($\Gamma$) of quasiparticles. For optimally and overdoped, we obtain very sharp quasiparticle peaks of 8 meV and 6 meV full-width at half-maximum, respectively, in accord with terahertz conductivity. For all doping levels, we find the energy-dependence of $\Gamma \sim |\omega |$, while $\Gamma$($\omega =0$) shows a monotonic increase from overdoping to underdoping. The doping dependence suggests the role of electronic inhomogeneity on the nodal quasiparticle scattering at low temperature (5 K \lsim 0.07T_{\rm c}), pronounced in the underdoped region

Orbital-dependent modifications of electronic structure across magneto-structural transition in BaFe2As2

Laser angle-resolved photoemission spectroscopy (ARPES) is employed to investigate the temperature (T) dependence of the electronic structure in BaFe2As2 across the magneto-structural transition at TN ~ 140 K. A drastic transformation in Fermi surface (FS) shape across TN is observed, as expected by first-principles band calculations. Polarization-dependent ARPES and band calculations consistently indicate that the observed FSs at kz ~ pi in the low-T antiferromagnetic (AF) state are dominated by the Fe3dzx orbital, leading to the two-fold electronic structure. These results indicate that magneto-structural transition in BaFe2As2 accompanies orbital-dependent modifications in the electronic structure.Comment: 13 pages, 4 figures. accepted by Physical Review Letter

Influence of aggregation and measurement scale on ranking a compromise alternative in AHP

Author's pre-print version dated 20. December 2009 deposited in Munich Personal RePEc Archive. Final version published by Palgrave Macmillan; available online at http:// www.palgrave-journals.com/Analytic Hierarchy Process (AHP) is one of the most popular multi-attribute decision aid methods. However, within AHP, there are several competing preference measurement scales and aggregation techniques. In this paper, we compare these possibilities using a decision problem with an inherent trade-off between two criteria. A decision-maker has to choose among three alternatives: two extremes and one compromise. Six different measurement scales described previously in the literature and the new proposed logarithmic scale are considered for applying the additive and the multiplicative aggregation techniques. The results are compared with the standard consumer choice theory. We find that with the geometric and power scales a compromise is never selected when aggregation is additive and rarely when aggregation is multiplicative, while the logarithmic scale used with the multiplicative aggregation most often selects the compromise that is desirable by consumer choice theory