Dynamics of the collective modes of an inhomogeneous spin ensemble in a cavity

We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number pass without dispersion from negative to positive valued wave numbers without populating the zero wave number spin wave mode. The results are relevant for multi-mode collective quantum memories where qubits are encoded in different spin waves.Comment: Published version. Some small changes and correction

The field inside a random distribution of parallel dipoles

We determine the probability distribution for the field inside a random uniform distribution of electric or magnetic dipoles. For parallel dipoles, simulations and an analytical derivation show that although the average contribution from any spherical shell around the probe position vanishes, the Levy stable distribution of the field is symmetric around a non-vanishing field amplitude. In addition we show how omission of contributions from a small volume around the probe leads to a field distribution with a vanishing mean, which, in the limit of vanishing excluded volume, converges to the shifted distribution.Comment: RevTeX, 4 pages, 3 figures. Submitted to Phys. Rev. Let

Quantum simulation of the hexagonal Kitaev model with trapped ions

We present a detailed study of quantum simulations of coupled spin systems in surface-electrode ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics 321,2 (2006)]. The effective (pseudo)spin interactions making up such quantum simulators are found to be proportional to the dipole-dipole interaction between the trapped ions, and are mediated by motion which can be driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of a surface electrode and a cover electrode. These results are the starting point to derive an optimized surface-electrode geometry for trapping ions in the desired honeycomb lattice of Kitaev's model, where we design the dipole-dipole interactions in a way that allows for coupling all three bond types of the model simultaneously, without the need for time discretization. Finally we propose a simple wire structure that can be incorporated in a microfabricated chip to generate localized state-dependent forces which drive the couplings prescribed by this particular model; such a wire structure should be adaptable to many other situations.Comment: 24 pages, 7 figures. v2: simplified the derivation of (28) without changing conclusions; minor edits. v3: minor edit

Scalable designs for quantum computing with rare-earth-ion-doped crystals

Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopands in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions. In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly coupled registers in general scales poorly with register size. Although this is critical to previous proposals which rely on a high density of functional registers, we describe architectures and preparation strategies that will allow scalable quantum computers based on rare-earth-ion doped crystals.Comment: Submitted to Phys. Rev.