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

Abstract

Here we show a direct mapping between waveguide theory and spin chain transport, opening an alternative approach to quantum information transport in the solid-state. By applying temporally varying control profiles to a spin chain, we design a virtual waveguide or 'spin-guide' to conduct individual spin excitations along defined space-time trajectories of the chain. We explicitly show that the concepts of confinement, adiabatic bend loss and beamsplitting can be mapped from optical waveguide theory to spin-guides (and hence 'spin-splitters'). Importantly, the spatial scale of applied control pulses is required to be large compared to the inter-spin spacing, and thereby allowing the design of scalable control architectures. The application of quantum information science to technology promises to make a disruptive change to twenty first century society, comparable to the computer and telecommunications revolutions of the twentieth century. Within this context, there is a pressing need to develop viable quantum networks. There have been many proposals to satisfy this need. Here we wish to focus on just one implementation of quantum communication that is ideally suited to solid-state quantum computing: the one-dimensional spin chain.The physics of spin chains offers a rich phenomenology. There is a comprehensive review of the application of spin chains to quantum information processing due to Bose [1]. In general, a spin chain is a one-dimensional array of spins that are closely spaced to facilitate strong spin-spin interactions, perhaps via dipole-dipole or exchange coupling. As the inter-spin spacing is typically on the atomic or near atomic scale, individual addressability of the spins is either impossible, or unscalable [2][3][4][5]. As a consequence of the restriction on local control, many innovative schemes have been studied to realise spin transport including schemes with uniform spins and control over just the ends of the chains (see Refs. [1,[3][4][5][6][7]), or with carefully designed coupling schemes [8,9]. There has also been related work in transport in coupled cavity systems [10][11][12].Here we outline a distinct alternative to the problem of long-range quantum information transport inspired by optical waveguides. We demonstrate that it is possible to create a virtual waveguide or 'spin-guide' in a one-dimensional spin chain to guide individual spin excitations, magnons [13], as depicted in Fig.

Guided magnon transport in spin chains: Transport speed and correcting for disorder

“…Here we extend our previous analyses of spin guides, explicitly showing the speed limits for QIT in spin guides [12], mechanisms to counteract disorder in the chain, and calculations for achievable spin-guide QIT in realistic media. These calculations are performed for two sets of confining potentials, namely, square-well (SW) and Poschl-Teller (P-T) potentials, although they can be generalized to any other potential.…”

“…In particular in Ref. [12] the analogy of beam splitter and interference was shown, and any achievable refractive index profile should have a corresponding magnetic confining potential. The square well has an abruptly changing profile and therefore can be thought of as analogous to a step index waveguide.…”

“…1. This regime has been considered previously [9,12,30] and under certain circumstances can be viewed as being the magnonic equivalent of a waveguide for light, which we term a spin guide [12]. One of the main imperatives for studying such semilocal control is in the context of phosphorus-in-silicon quantum computing, where it is known that scalable control of qubits spaced at the 20 nm level is problematic given achievable control gate densities [31,32].…”

“…These span the fundamental questions of how quantum information spreads in complicated environments such as random walks [1,2], to more practical issues such as quantum photosynthesis [3], and on-chip quantum communication in solid-state quantum computers [4], Here we concentrate on one aspect of quantum information transport (QIT), namely, transport of information through the Heisenberg chain. This problem has a rich history [5][6][7][8][9][10][11][12][13] and is undergoing renewed investigation due to its importance for certain models of solid-state quantum com putation, especially dopant-in-silicon approaches to quantum computation [8,[14][15][16][17].…”

Electronic transport in Si:Pδ-doped wires

“…The long spin-coherence times and large Bohr radius of the phosphorus donor electron in silicon make this material an interesting candidate for spin-based devices and other nanoscale electronics [21][22][23][24] . Si:P δ-doped wires might be used as the interconnects between stationary and flying qubits 18,25 , low-resistivity source-drain contacts for nanoelectronics 2,26 , or one-dimensional (1D) spin chains for confined magnon transport [27][28][29] . The modern δ-doped wire is a quasi-1D row of phosphorus atoms oriented in the [110] crystallographic direction, with a width of 1.54 nm in the lateral [110] direction which is equivalent to two dimer rows (2DR) on the reconstructed (001) silicon surface 2,11 .…”