HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Hilbert scheme topological invariants of plane curve singularities are identified to framed threefold stable pair invariants. As a result, the conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve singularities is given a Calabi-Yau threefold interpretation. The motivic Donaldson-Thomas theory developed by M. Kontsevich and the third author then yields natural motivic invariants for algebraic knots. This construction is motivated by previous work of V. Shende, C. Vafa and the first author on the large $N$ duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition improved, proofs expanded, results unchanged, to appear in Comm. Num. Th. Phy

Steady-State Two Atom Entanglement in a Pumped Cavity

In this paper we explore the possibility of a steady-state entanglement of two two-level atoms inside a pumped cavity by taking into account cavity leakage and the spontaneous emission of photons by the atoms. We describe the system in the dressed state picture in which the coherence is built into the dressed states while transitions between the dressed states are incoherent. Our model assumes the vacuum Rabi splitting of the dressed states to be much larger than any of the decay parameters of the system which allows atom-field coherence to build up before any decay process takes over. We show that, under our model, a pumping field cannot entangle two closed two-level atoms inside the cavity in the steady-state, but a steady-state entanglement can be achieved with two open two-level atoms.Comment: 19 pages, 5 figure

Classification of free actions on complete intersections of four quadrics

In this paper we classify all free actions of finite groups on Calabi-Yau complete intersection of four quadrics in ℙ 7, up to projective equivalence. We get some examples of smooth Calabi-Yau three-folds with large nonabelian fundamental groups. We also observe the relation between some of these examples and moduli of polarized abelian surfaces. © 2011 International Press.postprin

Insulating state and the importance of the spin-orbit coupling in Ca3_3CoRhO6_6

We have carried out a comparative theoretical study of the electronic structure of the novel one-dimensional Ca$_3$CoRhO$_6$ and Ca$_3$FeRhO$_6$ systems. The insulating antiferromagnetic state for the Ca$_3$FeRhO$_6$ can be well explained by band structure calculations with the closed shell high-spin $d^5$ (Fe$^{3+}$) and low-spin $t_{2g}^{6}$ (Rh$^{3+}$) configurations. We found for the Ca$_3$CoRhO$_6$ that the Co has a strong tendency to be $d^7$ (Co$^{2+}$) rather than $d^6$ (Co$^{3+}$), and that there is an orbital degeneracy in the local Co electronic structure. We argue that it is the spin-orbit coupling which will lift this degeneracy thereby enabling local spin density approximation + Hubbard U (LSDA+U) band structure calculations to generate the band gap. We predict that the orbital contribution to the magnetic moment in Ca$_3$CoRhO$_6$ is substantial, i.e. significantly larger than 1 $\mu_B$ per formula unit. Moreover, we propose a model for the contrasting intra-chain magnetism in both materials.Comment: 7 pages, 4 figures, and 1 tabl

Generation of frequency multiplexed entangled single photons assisted by the entanglement

We present a scheme to generate the frequency multiplexed entangled (FME) single photons based on the entanglement between two species atomic mixture ensemble. The write and reads fields driven according to a certain timing sequence, the generation of FME single photons can be repeated until success is achieved. The source might have significant applications in wavelength division multiplexing quantum key distribution.Comment: 4 pages, 4 figures, submitted to PR