Policy Uncertainty, Symbiosis, and the Optimal Fiscal and Monetary Conservativeness

This paper extends the stabilization game between monetary and fiscal authorities to the case of multiplicative (model) uncertainty. In this context, the “symbiosis assumption”, i.e. fiscal and monetary policy share the same ideal targets, no longer guarantees the achievement of ideal output and inflation, unless the ideal output is equal to its natural level. A time consistency problem arises.Monetary-fiscal policy interactions, uncertainty, symbiosis.

Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up

This paper presents a first mathematical convergence analysis of a Fock states feedback stabilization scheme via single-photon corrections. This measurement-based feedback has been developed and experimentally tested in 2012 by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel Raimond. Here, we consider the infinite-dimensional Markov model corresponding to the ideal set-up where detection errors and feedback delays have been disregarded. In this ideal context, we show that any goal Fock state can be stabilized by a Lyapunov-based feedback for any initial quantum state belonging to the dense subset of finite rank density operators with support in a finite photon-number sub-space. Closed-loop simulations illustrate the performance of the feedback law.Comment: 2 figures, extended version of the IEEE CDC2015 conference pape

Dynamics of bad-cavity enhanced interaction with cold Sr atoms for laser stabilization

Hybrid systems of cold atoms and optical cavities are promising systems for increasing the stability of laser oscillators used in quantum metrology and atomic clocks. In this paper we map out the atom-cavity dynamics in such a system and demonstrate limitations as well as robustness of the approach. We investigate the phase response of an ensemble of cold strontium-88 atoms inside an optical cavity for use as an error signal in laser frequency stabilization. With this system we realize a regime where the high atomic phase-shift limits the dynamical locking range. The limitation is caused by the cavity transfer function relating input field to output field. However, the cavity dynamics is shown to have only little influence on the prospects for laser stabilization making the system robust towards cavity fluctuations and ideal for the improvement of future narrow linewidth lasers.Comment: 10 pages, 7 figure

Generalized cover ideals and the persistence property

Let $I$ be a square-free monomial ideal in $R = k[x_1,\ldots,x_n]$, and consider the sets of associated primes ${\rm Ass}(I^s)$ for all integers $s \geq 1$. Although it is known that the sets of associated primes of powers of $I$ eventually stabilize, there are few results about the power at which this stabilization occurs (known as the index of stability). We introduce a family of square-free monomial ideals that can be associated to a finite simple graph $G$ that generalizes the cover ideal construction. When $G$ is a tree, we explicitly determine ${\rm Ass}(I^s)$ for all $s \geq 1$. As consequences, not only can we compute the index of stability, we can also show that this family of ideals has the persistence property.Comment: 15 pages; revised version has a new introduction; references updated; to appear in J. Pure. Appl. Algebr