Multiphoton resonances for all-optical quantum logic with multiple cavities

We develop a theory for the interaction of multilevel atoms with multimode cavities yielding cavity-enhanced multiphoton resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realized when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the Fredkin gate and iSWAP operation; the system seems promising for scalability

On open quantum systems, effective Hamiltonians and device characterization

High fidelity models, which support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model for open systems describes the dynamics with a master equation in Lindblad form. The Linblad operators are rarely derived from first principles, resulting in dynamical models which miss those additional terms that must generally be added to bring the master equation into Lindblad form, together with concomitant other terms that must be assimilated into an effective Hamiltonian. In first principles derivations such additional terms are often cancelled (countered), frequently in an ad hoc manner. In the case of a Superconducting Quantum Interference Device (SQUID) coupled to an Ohmic bath, the resulting master equation implies the environment has a significant impact on the system's energy. We discuss the prospect of keeping or cancelling this impact; and note that, for the SQUID, measuring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux, results in experimentally measurable differences between models. If this is not done correctly, device characterization will be prone to systemic errors.Comment: 5 pages, 3 figure

Recovery of classical chaotic-like behaviour in a quantum three body problem

Recovering trajectories of quantum systems whose classical counterparts display chaotic behaviour has been a subject that has received a lot of interest over the last decade. However, these studies have focused on driven dissipative systems. The relevance and impact of chaotic-like phenomena to quantum systems has been highlighted in recent studies which have shown that quantum chaos is significant in some aspects of quantum computation and information processing. In this paper we study a three body system comprising of identical particles arranged so that the system's classical trajectories exhibit Hamiltonian chaos. Here we show that it is possible to recover very nearly classical-like chaotic trajectories from such a system through an unravelling of the master equation

Clustering U.S. 2016 presidential candidates through linguistic appraisals

Producción CientíficaThe main purpose of this paper is to cluster the United States (U.S.) 2016 presidential candidates taking the linguistic appraisals made by a random representative sample of adults living in the U.S. as our starting point. To do this, we have used the concept of ordinal proximity measure (see García-Lapresta and Pérez-Román), which allows to determine the degree of consensus in a group of agents when a set of alternatives is evaluated through non-necessarily qualitative scales.Ministerio de Economía, Industria y Competitividad (project ECO2016-77900-P

On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole

For any real limit-$n$ $2n$th-order selfadjoint linear differential expression on $[0,\infty)$, Titchmarsh- Weyl matrices $M(\lambda)$ can be defined. Two matrices of particu lar interest are the matrices $M_D(\lambda)$ and $M_N(\lambda)$ assoc iated respectively with Dirichlet and Neumann boundary conditions at $x=0$. These satisfy $M_D(\lambda) = -M_{N}(\lambda)^{-1}$. It is known that when these matrices have poles (which can only lie on the real axis) the existence of valid HELP inequalities depends on their behaviour in the neighbourhood of these poles. We prove a conjecture of Bennewitz and use it, together with a new algorithm for computing the Laurent expansion of a Titchmarsh-Weyl matrix in the neighbourhood of a pole, to investigate the existence of HELP inequalities for a number of differential equations which have so far proved awkward to analys

Signatures of the collapse and revival of a spin Schr\"{o}dinger cat state in a continuously monitored field mode

We study the effects of continuous measurement of the field mode during the collapse and revival of spin Schr\"{o}dinger cat states in the Tavis-Cummings model of N qubits (two-level quantum systems) coupled to a field mode. We show that a compromise between relatively weak and relatively strong continuous measurement will not completely destroy the collapse and revival dynamics while still providing enough signal-to-noise resolution to identify the signatures of the process in the measurement record. This type of measurement would in principle allow the verification of the occurrence of the collapse and revival of a spin Schr\"{o}dinger cat state.Comment: 5 pages, 2 figure