Rare-earth solid-state qubits

Quantum bits (qubits) are the basic building blocks of any quantum computer. Superconducting qubits have been created with a 'top-down' approach that integrates superconducting devices into macroscopic electrical circuits [1-3], whereas electron-spin qubits have been demonstrated in quantum dots [4-6]. The phase coherence time (Tau2) and the single qubit figure of merit (QM) of superconducting and electron-spin qubits are similar -- Tau2 ~ microseconds and QM ~10-1000 below 100mK -- and it should be possible to scale-up these systems, which is essential for the development of any useful quantum computer. Bottom-up approaches based on dilute ensembles of spins have achieved much larger values of tau2 (up to tens of ms) [7, 8], but these systems cannot be scaled up, although some proposals for qubits based on 2D nanostructures should be scalable [9-11]. Here we report that a new family of spin qubits based on rare-earth ions demonstrates values of Tau2 (~ 50microseconds) and QM (~1400) at 2.5 K, which suggests that rare-earth qubits may, in principle, be suitable for scalable quantum information processing at 4He temperatures

A group theoretical-study of planar methyl rotation

Most papers on methyl group tunnelling use a model in which the motion of a rigid rotator is hindered by a potential of threefold symmetry. There are a number of difficulties with such a description and, in this paper, the model is replaced by one which describes the motion of three protons, which have mutual interactions and which are hindered by an external potential. The analysis makes considerable use of symmetry ideas and arrives at conclusions which are substantially different from those of the previous model. A comparison of the two models shows that, in the absence of dipolar interactions, both will have an orbital singlet level with spin of 3/2, but that the level described as 2E in the rigid-rotator model will not occur in the present model and that there will be no corresponding level with fourfold degeneracy. Instead there will be two separated orbital singlets, each with spin 1/2. The inclusion of the dipolar interaction splits the quartet into two doublets, so that finally there are four separated low-lying energy levels, each being doubly degenerate