Distillation of continuous-variable entanglement with optical means

We present an event-ready procedure that is capable of distilling Gaussian two-mode entangled states from a supply of weakly entangled states that have become mixed in a decoherence process. This procedure relies on passive optical elements and photon detectors distinguishing the presence and the absence of photons, but does not make use of photon counters. We identify fixed points of the iteration map, and discuss in detail its convergence properties. Necessary and sufficient criteria for the convergence to two-mode Gaussian states are presented. On the basis of various examples we discuss the performance of the procedure as far as the increase of the degree of entanglement and two-mode squeezing is concerned. Finally, we consider imperfect operations and outline the robustness of the scheme under non-unit detection efficiencies of the detectors. This analysis implies that the proposed protocol can be implemented with currently available technology and detector efficiencies.     

Homogeneous catalysts supported on soluble polymers: biphasic Sonogashira coupling of aryl halides and acetylenes using MeOPEG-bound phosphine-palladium catalysts for efficient catalyst recycling

The Sonogashira coupling of various aryl bromides and iodides with different acetylenes was studied under biphasic conditions with soluble, polymer-modified catalysts to allow the efficient recycling of the homogeneous catalyst. For this purpose, several sterically demanding and electron-rich phosphines of the type R(P)PR(2) were synthesised. They are covalently linked to a monomethyl polyethylene glycol ether with a mass of 2000 Dalton (R(P)=MeOPEG(2000)) R(P)PR(2): -PR(2)= -CH(2)C(6)H(4)CH(2)P(1-Ad)(2), -C(6)H(4)-P(1-Ad)(2), -C(6)H(4)-PPh(2). To couple aryl iodides and acetylenes, the catalyst [(MeCN)(2)PdCl(2)]/2 R(P)-C(6)H(4)-PPh(2) was used in CH(3)CN/Et(3)N/n-heptane (5/2/5). The combined yields of coupling product over five reaction cycles are between 80-95 percent. There is no apparent leaching of the catalyst into n-heptane, as evidenced by (1)H NMR spectroscopy. The new catalyst [(MeCN)(2)PdCl(2)]/2 (1-Ad)(2)PBn can be used for room-temperature coupling of various aryl bromides and acetylenes in THF with HNiPr(2) as a base. A closely related catalyst Na(2)[PdCl(4)]/2 R(P)-CH(2)C(6)H(4)CH(2)P(1-Ad)(2) linked to the polymer was used to couple aryl bromides and acetylenes in DMSO or DMSO/n-heptane at 60 degrees C with 0.5 mol percent Na(2)[PdCl(4)], 1 mol percent R(P)PR(2) and 0.33 mol percent CuI. The combined yield of coupling products over five cycles is always greater than 90 percent, except for sterically hindered aryl bromides. The determination of the turnover frequency (TOF) of the catalyst indicates only a small decrease in activity over five cycles. Leaching of the catalyst into the product containing n-heptane solution could not be detected by means of (1)H NMR and TXRF; this is indicative of >99.995 percent catalyst retention in the DMSO solvent.     

Optically and redox-active ferroceneacetylene polymers and oligomers

The palladium-catalyzed Sonogashira reaction can be used to build optically active, oligomeric 1,2,3-substituted ferrocenes up to the tetramer, as well as polymers, by sequential coupling of optically active (ee > 98 %), planar chiral iodoferroceneacetylenes and ferroceneacetylenes. (SFC)-1-Iodoferrocene-2-carbaldehyde (1) was reduced to the alcohol and methylated to give the corresponding methyl ether, which was Sonogashira-coupled with HC(triple bond)CSiEt3, resulting in (RFc)-1-(C(triple bond)CSiEt3)-2-methoxymethylferrocene (4) (79%, three steps). Orthometalation with tBuLi followed by quenching with 1,2-diodoethane gave (RFc)-1-(C(triple bond)CSiEt3)-2-methoxymethyl-3-iodoferrocene (5). Deprotection of the acetylene with nBu4NF resulted in (RFc)-1-ethynyl-2-methoxymethyl-3-iodoferrocene (6), which was Sonogashira-coupled with itself to produce an optically active polymer. Deprotection of 4 with nBu4NF and Sonogashira coupling of the product with 5 resulted in the dinuclear ferrocene 9. Deprotection of 9 and coupling with 5, followed by deprotection of the resulting acetylene 11, gave the trinuclear ferrocene 12. Another such sequence involving 11 and 5 produced a tetranuclear ferrocene 13. To study the electronic communication in such oligomers in more detail, two symmetrical, closely interrelated, trinuclear ferrocenes 18 and 19 were synthesized. The redox potentials of all the ferrocenes and the ferroceneacetylene polymer were determined by cyclic and square-wave voltammetry. All the metallocenes were investigated by UV/Vis spectroscopy. A linear relationship was found between lambdamax and l/n (n=number of ferrocene units in the oligomer). The polymer displayed two redox waves in the cyclic voltammogram, at 0.65 and 0.795 V. The corresponding mixed-valence oligoferrocene cations were synthesized from four ferroceneacetylenes, and their metal-metal charge transfer bands were examined by UV/Vis-NIR. The resonance exchange integrals Had, calculated on the basis of spectral information from the metal - metal charge transfer (MMCT) bands, were between 290 and 552 cm-1.     

Ferrocene-cyclam: a redox-active macrocycle for the complexation of transition metal ions and a study on the influence of the relative permittivity on the coulombic interaction between metal cations

The reaction of 1,1'-ferrocene-bis(methylenepyridinium) salt with 1,4,8,11-tetraazacyclotetradecane-5,12-dione, followed by LiAlH4 reduction results in the formation of FcCyclam. Metal complexes of FcCyclam with M2+ = Co2+, Ni2+, Cu2+, and Zn2+ were synthesized from FcCyclam and the respective metal triflates. The complexation of Cu2+ and FcCyclam in CH3CN is preceeded by a rapid electron transfer, followed by a slower complex formation reaction and a reverse electron transfer. The protonation constants of FcCyclam and the stability constants for the Cu2+ complex of FcCyclam (logK = 9.26(4) for the formation of the [Cu(FcCyclam)]2+ complex) were determined in 1,4-dioxane/water 70:30 v/v, 0.1 moldm(-3), KNO3, 25 degrees C. By using FcCyclam one can selectively sense the presence of Cu2+ ions in the presence of Ni2+, Zn2+, Cd2+, Hg2+, and Pb2+ with a very large deltaE approximately 200 mV, depending on pH. The X-ray crystal structures of FcCyclam and of complexes with Co2+, Ni2+, Cu2+, and Zn2+ were determined and Fe-M2+ distances obtained: Fe-Co2+ 395.9, Fe-Ni2+ 385.4, Fe-Cu2+ 377.7, and Fe-Zn2+ 369.0 pm. The redox potential of FcCyclam is influenced in a characteristic manner by the complexation of M2+. A linear correlation of 1/r approximately/= deltaE [r = distance Fe-M2+ from crystal data, deltaE=-E1/2([M(FcCyclam)]2+) - E1/2(FcCyclam)] was found; this is indicative of a mainly Coulomb type interaction between the two metal centers. The nature of the Fe...M2+ interaction was also investigated by determining deltaE in several solvents (mixtures) of different dielectric constants epsilon. The expected relation of deltaE approximately/= 1/epsilon was only found at very high values of epsilon. At epsilon < 40 increased ion-pairing appears to reduce the effective positive charge at M2+ leading to progessively smaller values of deltaE with lowered epsilon. The dependence of deltaE and epsilon can be calculated semiquantitatively by combining the Fuoss ion-pairing theory with the Coulomb model.     

Entropy, entanglement, and area: analytical results for harmonic lattice systems

We revisit the question of the relation between entanglement, entropy, and area for harmonic lattice Hamiltonians corresponding to discrete versions of real free Klein-Gordon fields. For the ground state of the d-dimensional cubic harmonic lattice we establish a strict relationship between the surface area of a distinguished hypercube and the degree of entanglement between the hypercube and the rest of the lattice analytically, without resorting to numerical means. We outline extensions of these results to longer ranged interactions, finite temperatures, and for classical correlations in classical harmonic lattice systems. These findings further suggest that the tools of quantum information science may help in establishing results in quantum field theory that were previously less accessible.