Indistinguishable Chargeon-Fluxion Pairs in the Quantum Double of Finite Groups

We consider the category of finite dimensional representations of the quantum double of a finite group as a modular tensor category. We study auto-equivalences of this category whose induced permutations on the set of simple objects (particles) are of the special form of PJ, where J sends every particle to its charge conjugation and P is a transposition of a chargeon-fluxion pair. We prove that if the underlying group is the semidirect product of the additive and multiplicative groups of a finite field, then such an auto-equivalence exists. In particular, we show that for S_3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. Conversely, by considering such permutations as modular invariants, we show that a transposition of a chargeon-fluxion pair forms a modular invariant if and only if the corresponding group is isomorphic to the semidirect product of the additive and multiplicative groups of a finite near-field.Comment: 15 pages, arXiv:1006.5479 includes all results of this paper, v3: fixed a typo in eq (11

Feedback cooling of atomic motion in cavity QED

We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.Comment: 22 pages, 17 figure

Quantum feedback control of atomic motion in an optical cavity

We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies

Nonlinear Quantum Dynamics

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples.Comment: 13 pages, 3 figures, invited talk at the NATO Advanced Workshop, "Nonlinear Dynamics and Fundamental Interactions," (October, 2004, Tashkent

The Universe at Extreme Scale: Multi-Petaflop Sky Simulation on the BG/Q

Remarkable observational advances have established a compelling cross-validated model of the Universe. Yet, two key pillars of this model -- dark matter and dark energy -- remain mysterious. Sky surveys that map billions of galaxies to explore the `Dark Universe', demand a corresponding extreme-scale simulation capability; the HACC (Hybrid/Hardware Accelerated Cosmology Code) framework has been designed to deliver this level of performance now, and into the future. With its novel algorithmic structure, HACC allows flexible tuning across diverse architectures, including accelerated and multi-core systems. On the IBM BG/Q, HACC attains unprecedented scalable performance -- currently 13.94 PFlops at 69.2% of peak and 90% parallel efficiency on 1,572,864 cores with an equal number of MPI ranks, and a concurrency of 6.3 million. This level of performance was achieved at extreme problem sizes, including a benchmark run with more than 3.6 trillion particles, significantly larger than any cosmological simulation yet performed.Comment: 11 pages, 11 figures, final version of paper for talk presented at SC1