Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest whose dynamics evolve over a subset of the positive quadrant in the 2D plane. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Stability along the pass demands a bounded-input bounded-output property over the complete positive quadrant of the 2D plane and this is a very strong requirement, especially in terms of control law design. A more feasible alternative for some cases is strong practical stability, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality (LMI) based tests, which then extend to allow control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that extend to allow control law design in the presence of uncertainty in process model

Configurable unitary transformations and linear logic gates using quantum memories

We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favourable scaling with an increasing number of modes where N memories can be configured to implement an arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memories are used to implement a conditional CZ gate.Comment: 5 pages, 2 figure

Gauge Consistent Wilson Renormalization Group II: Non-Abelian Case

We give a wilsonian formulation of non-abelian gauge theories explicitly consistent with axial gauge Ward identitities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A wilsonian computation of the one-loop QCD beta function is performed.Comment: 34 pages, 1 eps figure, latex2e. Minor changes, version to appear in Int. J. Mod. Phy

Constructive algebraic renormalization of the abelian Higgs-Kibble model

We propose an algorithm, based on Algebraic Renormalization, that allows the restoration of Slavnov-Taylor invariance at every order of perturbation expansion for an anomaly-free BRS invariant gauge theory. The counterterms are explicitly constructed in terms of a set of one-particle-irreducible Feynman amplitudes evaluated at zero momentum (and derivatives of them). The approach is here discussed in the case of the abelian Higgs-Kibble model, where the zero momentum limit can be safely performed. The normalization conditions are imposed by means of the Slavnov-Taylor invariants and are chosen in order to simplify the calculation of the counterterms. In particular within this model all counterterms involving BRS external sources (anti-fields) can be put to zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page

Quantum study of information delay in electromagetically induced transparency

Using electromagnetically induced transparency (EIT), it is possible to delay and store light in atomic ensembles. Theoretical modelling and recent experiments have suggested that the EIT storage mechanism can be used as a memory for quantum information. We present experiments that quantify the noise performance of an EIT system for conjugate amplitude and phase quadratures. It is shown that our EIT system adds excess noise to the delayed light that has not hitherto been predicted by published theoretical modelling. In analogy with other continuous-variable quantum information systems, the performance of our EIT system is characterised in terms of conditional variance and signal transfer.Comment: 4 pages, 4 figure

Squeezing and entanglement delay using slow light

We examine the interaction of a weak probe with $N$ atoms in a lambda-level configuration under the conditions of electromagnetically induced transparency (EIT). In contrast to previous works on EIT, we calculate the output state of the resultant slowly propagating light field while taking into account the effects of ground state dephasing and atomic noise for a more realistic model. In particular, we propose two experiments using slow light with a nonclassical probe field and show that two properties of the probe, entanglement and squeezing, characterizing the quantum state of the probe field, can be well-preserved throughout the passage.Comment: 2 figures; v2: fixed some minor typographical errors in a couple of equations and corrected author spelling in one reference. v3: Added three authors; changed the entaglement definition to conform to a more accepted standard (Duan's entanglement measure); altered the abstract slightly. v4: fixed formatting of figure

Renormalization of the N=1 Abelian Super-Chern-Simons Theory Coupled to Parity-Preserving Matter

We analyse the renormalizability of an Abelian N=1 super-Chern-Simons model coupled to parity-preserving matter on the light of the regularization independent algebraic method. The model shows to be stable under radiative corrections and to be gauge anomaly free.Comment: Latex, 7 pages, no figure

Erratum : Squeezing and entanglement delay using slow light

An inconsistency was found in the equations used to calculate the variance of the quadrature fluctuations of a field propagating through a medium demonstrating electromagnetically induced transparency (EIT). The decoherence term used in our original paper introduces inconsistency under weak probe approximation. In this erratum we give the Bloch equations with the correct dephasing terms. The conclusions of the original paper remain the same. Both entanglement and squeezing can be delayed and preserved using EIT without adding noise when the decoherence rate is small.Comment: 1 page, no figur

Quantum Noise Locking

Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, can not rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and absence of coherent fields are shown, including a comparison with coherent locking techniques. Finally, we use NL to enable a stable readout of the squeezed vacuum state on a homodyne detector.Comment: Accepted for publication in Journal of Optics:B special issue on Quantum Contro

Renormalizability of Nonrenormalizable Field Theories

We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories which are actually physically equivalent to renormalizable ones. Our strategy is to show by means of the BRS formalism that the "nonrenormalizable" part of such fake nonrenormalizable theories, is a kind of gauge fixing, being confined in the cohomologically trivial sector of the theory.Comment: 3 pages, revtex, no figure