Topologically protected quantum bits from Josephson junction arrays

All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Proposals based on quantum optics naturally emphasize the aspect of optimal isolation, while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev, holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer liquid groundstate can be used in the construction of topologically stable qubits and discuss their implementation using Josephson junction arrays.Comment: 6 pages, 4 figure

Spin dynamics and disorder effects in the S=1/2 kagome Heisenberg spin liquid phase of kapellasite

We report $^{35}$Cl NMR, ESR, $\mu$SR and specific heat measurements on the $S=1/2$ frustrated kagom\'e magnet kapellasite, $\alpha-$Cu$_3$Zn(OH)$_6$Cl$_2$, where a gapless spin liquid phase is stabilized by a set of competing exchange interactions. Our measurements confirm the ferromagnetic character of the nearest-neighbour exchange interaction $J_1$ and give an energy scale for the competing interactions $|J| \sim 10$ K. The study of the temperature-dependent ESR lineshift reveals a moderate symmetric exchange anisotropy term $D$, with $|D/J|\sim 3$%. These findings validate a posteriori the use of the $J_1 - J_2 - J_d$ Heisenberg model to describe the magnetic properties of kapellasite [Bernu et al., Phys. Rev. B 87, 155107 (2013)]. We further confirm that the main deviation from this model is the severe random depletion of the magnetic kagom\'e lattice by 27%, due to Cu/Zn site mixing, and specifically address the effect of this disorder by $^{35}$Cl NMR, performed on an oriented polycrystalline sample. Surprisingly, while being very sensitive to local structural deformations, our NMR measurements demonstrate that the system remains homogeneous with a unique spin susceptibility at high temperature, despite a variety of magnetic environments. Unconventional spin dynamics is further revealed by NMR and $\mu$SR in the low-$T$, correlated, spin liquid regime, where a broad distribution of spin-lattice relaxation times is observed. We ascribe this to the presence of local low-energy modes.Comment: 15 pages, 11 figures. To appear in Phys. Rev.

Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2

The frustration of antiferromagnetic interactions on the loosely connected kagome lattice associated to the enhancement of quantum fluctuations for S=1/2 spins was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be synthesized and enables a close comparison to theories. We review and classify various experimental results obtained over the past years and underline some of the pending issues.Comment: 23 pages, 16 figures, invited paper in J. Phys. Soc. Jpn, special topics issue on "Novel States of Matter Induced by Frustration", to be published in Jan. 201

RVB description of the low-energy singlets of the spin 1/2 kagome antiferromagnet

{Extensive calculations in the short-range RVB (Resonating valence bond) subspace on both the trimerized and the regular (non-trimerized) Heisenberg model on the kagome lattice show that short-range dimer singlets capture the specific low-energy features of both models. In the trimerized case the singlet spectrum splits into bands in which the average number of dimers lying on one type of bonds is fixed. These results are in good agreement with the mean field solution of an effective model recently introduced. For the regular model one gets a continuous, gapless spectrum, in qualitative agreement with exact diagonalization results.Comment: 10 pages, 13 figures, 3 tables. Submitted to EPJ