Spin Guides and Spin Splitters: Waveguide Analogies in One-Dimensional Spin Chains

Melissa I. Makin, Jared H. Cole, Charles D. Hill, and Andrew D. Greentree

Phys. Rev. Lett. 108, 017207 – Published 5 January 2012

Abstract

Here we show a mapping between waveguide theory and spin-chain transport, opening an alternative approach to solid-state quantum information transport. By applying temporally varying control profiles to a spin chain, we design a virtual waveguide or “spin guide” to conduct spin excitations along defined space-time trajectories of the chain. We show that the concepts of confinement, adiabatic bend loss, and beam splitting can be mapped from optical waveguide theory to spin guides, and hence to “spin splitters.” Importantly, the spatial scale of applied control pulses is required to be large compared to the interspin spacing, thereby allowing the design of scalable control architectures.

Received 16 September 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.017207

Authors & Affiliations

Melissa I. Makin¹, Jared H. Cole^2,3, Charles D. Hill⁴, and Andrew D. Greentree¹

¹School of Physics, The University of Melbourne, Melbourne 3010, Australia
²Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
³Institut für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures (CFN), Karlsruher Institut für Technologie, 76128 Karlsruhe, Germany
⁴ARC Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Melbourne 3010, Australia

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Issue

Vol. 108, Iss. 1 — 6 January 2012

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Images

Figure 1
(a) Schematic of a spin guide. A one-dimensional line of spins is positioned below a gate array. The gate potentials are varied, breaking the translation symmetry of the chain, to define a spin guide capable of carrying an excitation. The size of the gates is expected to be much larger than the interspin spacing so that individual control of the spins is not possible. (b) A conventional waveguide is defined by a local change in the refractive index of a medium. This can be thought of as defining a two-dimensional pathway. (c) A spin guide is defined by a $1 + 1$ dimensional variation in the spin properties, mimicking the refractive index profile of an optical waveguide.Reuse & Permissions
Figure 2
(a) Fidelity as a function of corner angle $θ$ , for two values of $r$ : $r = 0$ (discontinuous corner, solid line) and $r = 2$ (smooth corner, dashed line). Fidelity decreases with increasing angle $θ$ in accordance with conventional optical bend loss. Four examples of magnon propagation are shown: (b) $r = 0$ , $θ = 0.15$ (fidelity 0.769), (c) $r = 0$ , $θ = 0.5$ (fidelity 0.106), (d) $r = 2$ , $θ = 0.15$ (fidelity 0.979), (e) $r = 2$ , $θ = 0.5$ (fidelity 0.401). In all cases, $t_{f} = 10$ .Reuse & Permissions
Figure 3
Magnon evolution through a spin splitter with parallel component. Oscillatory behavior of the excitation between the spin guides is observed. Here, $r = 0.5$ , $d = 1.2$ , $m = 0.3$ .Reuse & Permissions
Figure 4
(a) Fidelity and reflection and transmission coefficients for an $X$ junction spin splitter as a function of spin-guide angle. The excitation is initialized in the left-to-right spin guide and then evolved for time $t_{f} = x_{l} / \tan (θ / 2)$ ( $x_{l} = 10$ fixed). The reflection and transmission coefficients show oscillations as expected from Landau-Zener theory. The spin-splitting fidelity is less than unity due to nonadiabaticity, although it asymptotes to one in both the small and large angle limits. (b) A $50 / 50$ spin splitter with $θ = 10^{- 0.7976}$ (corresponding to $R \approx T \approx 0.491$ , $F_{tot} \approx 0.982$ , indicated by a circle at the intersection of a horizontal and a vertical line). (c) A nonadiabatic crossing with $θ = 10^{2.2}$ . Note the different time scales in (b) and (c).Reuse & Permissions
Figure 5
Evolution of the spin splitter as a function of induced relative phase. (a)–(e) The magnon is initialized to an equally weighted superposition at time $t = 0$ . The relative phase between spin guides is varied by a localized, time-independent Gaussian perturbation of depth $d$ in the potential in the right-to-left spin guide before the interaction takes place (shown as an inset along the top of the figure). The depths are (a) $d = - 0.147$ , (b) $d = - 0.074$ , (c) $d = 0$ , (d) $d = 0.068$ , (e) $d = 0.136$ . (f) The final spin-guide occupancies in the right-to-left (solid curve) and left-to-right (dashed curve) spin guides as a function of $d$ . The vertical dot-dashed lines correspond to the simulations (a)–(e).Reuse & Permissions

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