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Physics Procedia

Quantum Coherence of Strongly Correlated Defects in Spin Chains

Sylvain Bertaina, Charles‐Emmanuel Dutoit, Johan van Tol, Martin Dressel, B. Barbara, A. A. Stepanov

Published Jan 1, 2015• 3 citations
Publisher

Abstract

Most of qubit systems known to date are isolated paramagnetic centres in magnetically diluted samples since their dilution allows to considerably weaken the dipole-dipole inter-qubit interaction and thus to prevent the decoherence. Here we suggest an alternative approach for spin qubits which are built on spin S = 1/2 defects in magnetically concentrated strongly correlated systems - spin chains. The corresponding qubits are made of spin solitons resulting from local breaking of transitional symmetry associated with point-defects. We provide the first evidence for coherence and Rabi oscillations of spin solitons in isotropic Heisenberg chains, simple antiferromagnetic-Ńeel or spin-Peierls, proving that they can be manipulated as single spin S = 1/2. The entanglement of these many-body soliton states over macroscopic distances along chains gives rise to networks of coupled qubits which could easily be decoupled at will in extensions of this work.

DOI
10.1016/j.phpro.2015.12.004

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Most of qubit systems known to date are isolated paramagnetic centres in magnetically diluted samples since their dilution allows to considerably weaken the dipole-dipole inter-qubit interaction and thus to prevent the decoherence. Here we suggest an alternative approach for spin qubits which are built on spin S = 1/2 defects in magnetically concentrated strongly correlated systems - spin chains. The corresponding qubits are made of spin solitons resulting from local breaking of transitional symmetry associated with point-defects. We provide the first evidence for coherence and Rabi oscillations of spin solitons in isotropic Heisenberg chains, simple antiferromagnetic-Ńeel or spin-Peierls, proving that they can be manipulated as single spin S = 1/2. The entanglement of these many-body soliton states over macroscopic distances along chains gives rise to networks of coupled qubits which could easily be decoupled at will in extensions of this work.
We provide evidence for the coherence and Rabi oscillations of spin solitons pinned by the local breaking of translational symmetry in isotropic Heisenberg chains (simple antiferromagnetic N\'eel or spin Peierls). We show that these correlated spin systems that are made of hundreds of coupled spins bear an overall spin S=1/2S=1/2S=1/2 and can be manipulated as a single spin. This is clearly contrary to known spin qubits which are paramagnetic centers, highly diluted to prevent decoherence. These results offer an alternative approach for spin qubits, paving the way for the implementation of a different type of quantum computer.
Propagation of soliton-like excitations along spin chains has been proposed as a possible way for transmitting both classical and quantum information between two distant parties with negligible dispersion and dissipation. In this work, a somewhat different use of solitons is considered. Solitons propagating along a spin chain realize an effective magnetic field, well localized in space and time, which can be exploited as a means to manipulate the state of an external spin (i.e., a qubit) that is weakly coupled to the chain. We have investigated different couplings between the qubit and the chain, as well as different soliton shapes, according to a Heisenberg chain model. It is found that symmetry properties strongly affect the effectiveness of the proposed scheme, and the most suitable setups for implementing single qubit quantum gates are singled out.
Defects in frustrated antiferromagnetic spin chains are universally present in geometrically frustrated systems. We consider the defects of the one-dimensional, spin-sss XXZ chain with single-ion anisotropy on a periodic chain with NNN sites that was famously studied by Haldane. For NNN odd, the antiferromagnetic model is frustrated, and the ground state must include a soliton defect. We consider the Heisenberg interaction perturbatively and determine the corresponding perturbative solitonic ground state. Then we compute the entanglement spectrum, entanglement entropy (EE), capacity of entanglement (CE), and spin correlations in the solitonic ground state. For weak frustration, we find an algebraic violation of the area law for the EE consistent with recent results on weakly frustrated chains. Our analysis then moves beyond the weak frustration regime, and we obtain a novel extensive scaling law for the EE when strong frustration prevails, signaling large entanglement, and failure of the quasiparticle interpretation in this regime. Enhanced frustration results in less total correlations but relatively more nonlocal correlations.
We consider two distant spin-12\frac{1}{2}21​ particles (or qubits) and a number of interacting objects, all with the same value $S\ensuremath{\gg}1$ of their respective spin, distributed on a one-dimensional lattice (or large-SSS spin chain). The quantum states of the chain are constructed by linearly combining tensor products of single-spin coherent states, whose evolution is determined accordingly, i.e., via classical-like equations of motions. We show that the quantum superposition of the above product states resulting from a local interaction between the first qubit and one spin of the chain evolves so that the second qubit, after having itself interacted with another spin of the chain, can be entangled with the first qubit. Obtaining such an outcome does not imply imposing constraints on the length of the chain or the distance between the qubits, which demonstrates the possibility of generating quantum correlations at a distance by means of a macroscopic system, as far as local interactions with just a few of its components are feasible.
We analyze localization of interacting excitations in a system of qubits or spins. The system is modeled by a spin chain with an anisotropic (XXZ) exchange coupling in a magnetic field. Localization occurs on a defect with an excess on-site spin-flip energy. Such a defect corresponds to a qubit with the level spacing different from other qubits. Because of the interaction, a single defect may lead to multiple localized states. We find energy spectra and localization lengths of the two-excitation states. An excitation remains localized on the defect even where energy conservation allows scattering into extended states. This is due to destructive quantum interference in the two-excitation scattering channels, and it facilitates the operation of a quantum computer. Analytical results are obtained for strong anisotropy and are confirmed by numerical studies.
We show that, in a system with defects, two-particle states may experience destructive quantum interference, or antiresonance. It prevents an excitation localized on a defect from decaying even where the decay is allowed by energy conservation. The system studied is a qubit chain or an equivalent spin chain with an anisotropic (XXZ)(\mathrm{XXZ})(XXZ) exchange coupling in a magnetic field. The chain has a defect with an excess on-site energy. It corresponds to a qubit with the level spacing different from other qubits. We show that, because of the interaction between excitations, a single defect may lead to multiple localized states. The energy spectra and localization lengths are found for two-excitation states. The localization of excitations facilitates the operation of a quantum computer. Analytical results for strongly anisotropic coupling are confirmed by numerical studies.