Discrepancies between decoherence and the Loschmidt echo

The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the loss of coherence produced by an environment coupled to the system. For classically chaotic systems both quantities display a number of -- supposedly universal -- regimes that can lead on to think of them as equivalent quantities. We study the decay of the Loschmidt echo and the purity for systems with finite dimensional Hilbert space and present numerical evidence of some fundamental differences between them.Comment: 6 pages, 3 figures. Changed title. Added 1 figure. Published version

Integrated fiber-mirror ion trap for strong ion-cavity coupling

We present and characterize fiber mirrors and a miniaturized ion-trap design developed to integrate a fiber-based Fabry-Perot cavity (FFPC) with a linear Paul trap for use in cavity-QED experiments with trapped ions. Our fiber-mirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trapped-ion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Optical profilometry allows us to determine the radii of curvature and ellipticities of the fiber mirrors. From finesse measurements, we infer a single-atom cooperativity of up to 12 for FFPCs longer than 200 μm in length; comparison to cavities constructed with reference substrate mirrors produced in the same coating run indicates that our FFPCs have similar scattering losses. We characterize the birefringence of our fiber mirrors, finding that careful fiber-mirror selection enables us to construct FFPCs with degenerate polarization modes. As FFPCs are novel devices, we describe procedures developed for handling, aligning, and cleaning them. We discuss experiments to anneal fiber mirrors and explore the influence of the atmosphere under which annealing occurs on coating losses, finding that annealing under vacuum increases the losses for our reference substrate mirrors. X-ray photoelectron spectroscopy measurements indicate that these losses may be attributable to oxygen depletion in the mirror coating. Special design considerations enable us to introduce a FFPC into a trapped ion setup. Our unique linear Paul trap design provides clearance for such a cavity and is miniaturized to shield trapped ions from the dielectric fiber mirrors. We numerically calculate the trap potential in the absence of fibers. In the experiment additional electrodes can be used to compensate distortions of the potential due to the fibers. Home-built fiber feedthroughs connect the FFPC to external optics, and an integrated nanopositioning system affords the possibility of retracting or realigning the cavity without breaking vacuum

Semiclassical approach to fidelity amplitude

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio

Topological Qubits with Majorana Fermions in Trapped Ions

We propose a method of encoding a topologically-protected qubit using Majorana fermions in a trapped-ion chain. This qubit is protected against major sources of decoherence, while local operations and measurements can be realized. Furthermore, we show that an efficient quantum interface and memory for arbitrary multiqubit photonic states can be built, encoding them into a set of entangled Majorana-fermion qubits inside cavities.Comment: 9 pages, 2 figure