Jiannis Pachos

Quantum computation with trapped ions in an optical cavity

Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup and commonly addressed by laser fields. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the quantum Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.

Quantum Computation with a One-Dimensional Optical Lattice

We present an economical dynamical control scheme to perform quantum computation on a one-dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the lattice. They can be activated by external laser beams resulting in a two-qubit phase gate or in an exchange interaction. A realization of the Toffoli gate is presented, which requires only a single laser pulse and no individual atom addressing.

Decoherence-free dynamical and geometrical entangling phase gates

It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903 (2002)] and employing entangling Raman- or STIRAP-like transitions that restrict the time evolution of the system onto stable ground states.

Universal quantum computation by holonomic and nonlocal gates with imperfections

We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic gates, is investigated. Additionally, the influence of quantum decoherence on holonomic teleportation used as a computational primitive is studied. Advantages of the holonomic implementation with respect to control errors and dissipation are presented.

Geometric phases of mesoscopic spin in Bose-Einstein condensates

We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfinestates of the BEC. We find that the presence of intrinsic interatomic collisions creates degeneracy in energy that allows implementation of the non-Abelian geometric phases as well. The evolutions produced can be used to produce interference between different atomic species with high numbers of atoms or to fine control the difference in atoms between the two species. Finally, we show that errors in the standard Berry phase due to elastic collisions may be corrected by controlling inelastic collisions between atoms.

Topological features in ion-trap holonomic computation

Topological features in quantum computing provide controllability and noise error avoidance in the performance of logical gates. While such resilience is favored in the manipulation of quantum systems, it is very hard to identify topological features in nature. This paper proposes a scheme where holonomic quantum gates have intrinsic topological features. An ion trap is employed where the vibrational modes of the ions are coherently manipulated with lasers in an adiabatic cyclic way producing geometrical holonomic gates. A crucial ingredient of the manipulation procedures is squeezing of the vibrational modes, which effectively suppresses exponentially any undesired fluctuations of the squeezing parameter, thus making the gates resilient to control errors.

Spontaneous emission of an atom in front of a mirror

Motivated by a recent experiment [J. Eschner et al., Nature (London) 413, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and a lens imposes boundary conditions on the electric field in a plane close to the atom, we derive the intensities of the emitted light as a function of an effective atom-mirror distance. The results obtained are in good agreement with the experimental findings.

Geometrical phases for the G(4,2) Grassmannian manifold

We generalize the usual Abelian Berry phase generated for example in a system with two nondegenerate states to the case of a system with two doubly degenerate energy eigenspaces. The parametric manifold describing the space of states of the first case is formally given by the G(2,1) Grassmannian manifold, while for the generalized system it is given by the G(4,2) one. For the latter manifold which exhibits a much richer structure than its Abelian counterpart we calculate the connection components, the field strength and the associated geometrical phases that evolve nontrivially both of the degenerate eigenspaces. A simple atomic model is proposed for their physical implementation.

Topological quantum gates with quantum dots

We present an idealized model involving interacting quantum dots that can support both the dynamical and geometrical forms of quantum computation. We show that by employing a structure similar to the one used in the Aharonov–Bohm effect we can construct a topological two-qubit phase-gate that is to a large degree independent of the exact values of the control parameters and therefore resilient to control errors. The main components of the set-up are realizable with present technology.