Physical realization of coupled Hilbert-space mirrors for quantum-state engineering

Manipulation of superpositions of discrete quantum states has a mathematical counterpart in the motion of a unit-length statevector in an N-dimensional Hilbert space. Any such statevector motion can be regarded as a succession of two-dimensional rotations. But the desired statevector change can also be treated as a succession of reflections, the generalization of Householder transformations. In multidimensional Hilbert space such reflection sequences offer more efficient procedures for statevector manipulation than do sequences of rotations. We here show how such reflections can be designed for a system with two degenerate levels - a generalization of the traditional two-state atom - that allows the construction of propagators for angular momentum states. We use the Morris-Shore transformation to express the propagator in terms of Morris-Shore basis states and Cayley-Klein parameters, which allows us to connect properties of laser pulses to Hilbert-space motion. Under suitable conditions on the couplings and the common detuning, the propagators within each set of degenerate states represent products of generalized Householder reflections, with orthogonal vectors. We propose physical realizations of this novel geometrical object with resonant, near-resonant and far-off-resonant laser pulses. We give several examples of implementations in real atoms or molecules.Comment: 15 pages, 6 figure

Quantum Gates and Memory using Microwave Dressed States

Trapped atomic ions have been successfully used for demonstrating basic elements of universal quantum information processing (QIP). Nevertheless, scaling up of these methods and techniques to achieve large scale universal QIP, or more specialized quantum simulations remains challenging. The use of easily controllable and stable microwave sources instead of complex laser systems on the other hand promises to remove obstacles to scalability. Important remaining drawbacks in this approach are the use of magnetic field sensitive states, which shorten coherence times considerably, and the requirement to create large stable magnetic field gradients. Here, we present theoretically a novel approach based on dressing magnetic field sensitive states with microwave fields which addresses both issues and permits fast quantum logic. We experimentally demonstrate basic building blocks of this scheme to show that these dressed states are long-lived and coherence times are increased by more than two orders of magnitude compared to bare magnetic field sensitive states. This changes decisively the prospect of microwave-driven ion trap QIP and offers a new route to extend coherence times for all systems that suffer from magnetic noise such as neutral atoms, NV-centres, quantum dots, or circuit-QED systems.Comment: 9 pages, 4 figure

Cavity Induced Interfacing of Atoms and Light

This chapter introduces cavity-based light-matter quantum interfaces, with a single atom or ion in strong coupling to a high-finesse optical cavity. We discuss the deterministic generation of indistinguishable single photons from these systems; the atom-photon entanglement intractably linked to this process; and the information encoding using spatio-temporal modes within these photons. Furthermore, we show how to establish a time-reversal of the aforementioned emission process to use a coupled atom-cavity system as a quantum memory. Along the line, we also discuss the performance and characterisation of cavity photons in elementary linear-optics arrangements with single beam splitters for quantum-homodyne measurements.Comment: to appear as a book chapter in a compilation "Engineering the Atom-Photon Interaction" published by Springer in 2015, edited by A. Predojevic and M. W. Mitchel