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arXiv:1402.5664 · Physical Review B

Rabi oscillations of pinned solitons in spin chains: A route to quantum computation and communication

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

Published Aug 20, 2014• 24 citations
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Abstract

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 $S=1/2$ 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.

DOI
10.1103/physrevb.90.060404

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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.
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.
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.
Macroscopic quantum coherence oscillations of the N\'eel vector are proved to appear in the antiferromagnetic nuclear spin chain of eight 129Xe{}^{129}\mathrm{Xe}129Xe atoms placed on a magnetic surface. The oscillation period at zero temperature is calculated numerically as a function of the chain constant. The environmental decoherence effects at finite temperature are accounted assuming a dipole coupling between the spin chain and the fluctuating magnetic field of the surface. With this coupling the N\'eel vector oscillations are damped by a rate $(N\ensuremath{-}1)/\ensuremath{\tau},$ where N is the number of spins and $\ensuremath{\tau}$ is the relaxation time of a single spin.
Many proposals for quantum devices are based on qubits that are physically realized by the spin magnetic moment of some quantum object. In this case, one of the most often adopted strategies for manipulating qubits is that of using external magnetic fields. However, selectively applying a field just to one qubit may be a practically unattainable goal, as it is, for instance, in most solid-state based setups. In this work, we present a proposal for using nonlinear excitations of solitonic type to accomplish the above task. Our scheme entails the generation of a dynamical soliton in a classical spin-chain which is locally coupled with one qubit: as the soliton runs through, the qubit behaves, due to its interaction with the chain, as if it were subject to a magnetic field with a time dependence that follows from the soliton's features. We here present results for the time evolution of the qubit density-matrix induced by the overall dynamics of the above scheme.
We propose a method for acting on the spin state of a spin- localized particle, or qubit , by means of a magnetic signal effectively generated by the nearby transit of a magnetic soliton, there conveyed through a transmission line. We first introduce the specific magnetic soliton of which we will make use, and briefly review the properties that make it apt to represent a signal. We then show that a Heisenberg spin chain can serve as transmission line, and propose a method for injecting a soliton into the chain by acting just on one of its ends. We finally demonstrate that the resulting magnetic pulse can indeed cause, just passing by the spin- localized particle embodying the qubit, a permanent change in its spin state, thus realizing the possibility of getting through to a single, localized qubit, and manipulating its state. A thorough analysis of how the overall dynamical system operates depending on the setting of its parameters demonstrates that fine tuning is not necessary as there exists an extended region in the parameters space that corresponds to effective functioning. Moreover, we show that possible noise on the transmission line does not invalidate the scheme.
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.