Entanglement capabilities of the spin representation of (3+1)D-conformal transformations

Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study the entanglement capabilities of the spin representation of (pseudo-) conformal transformations in (3+1)-dimensional Minkowski space-time. We find that only those tensor product structures can sensibly be introduced in spinor space for which a given spinor is not entangled.Comment: 15 pages LaTeX (v2: minor changes, headings introduced; v3: secs. 1, 5, 6 extended, references [2], [3], [10]-[17], [37], [38] added, final version to appear in Quant. Inf. Comput.

Spectroscopic investigations of a Ti:Tm:LiNbO3 waveguide for photon-echo quantum memory

We report the fabrication and characterization of a Ti$^{4+}$:Tm$^{3+}$:LiNbO$_3$ optical waveguide in view of photon-echo quantum memory applications. In particular, we investigated room- and cryogenic-temperature properties via absorption, spectral hole burning, photon echo, and Stark spectroscopy. We found radiative lifetimes of 82 $\mu$s and 2.4 ms for the $^3$H$_4$ and $^3$F$_4$ levels, respectively, and a 44% branching ratio from the $^3$H$_{4}$ to the $^3$F$_4$ level. We also measured an optical coherence time of 1.6 $\mu$s for the $^3$H$_6\leftrightarrow{}^3$H$_4$, 795 nm wavelength transition, and investigated the limitation of spectral diffusion to spectral hole burning. Upon application of magnetic fields of a few hundred Gauss, we observed persistent spectral holes with lifetimes up to seconds. Furthermore, we measured a linear Stark shift of 25 kHz$\cdot$cm/V. Our results are promising for integrated, electro-optical, waveguide quantum memory for photons.Comment: 11 pages, 14 figure

Conversions between barycentric, RKFUN, and Newton representations of rational interpolants

We derive explicit formulas for converting between rational interpolants in barycentric, rational Krylov (RKFUN), and Newton form. We show applications of these conversions when working with rational approximants produced by the AAA algorithm [Y. Nakatsukasa, O. S\`ete, L. N. Trefethen, arXiv preprint 1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of nonlinear eigenvalue problems

Electron spin coherence in semiconductors: Considerations for a spin-based solid state quantum computer architecture

We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence is dominated by spin-spin interactions, through spectral diffusion and dipolar flip-flop mechanisms. These contributions lead to 1-100 $\mu$s calculated spin coherence times for a wide range of parameters, much higher than former estimates based on $T_{2}^{*}$ measurements.Comment: Role of the dipolar interaction clarified; Included discussion on the approximations employed in the spectral diffusion calculation. Final version to appear in Phys. Rev.