Optimal Reachability in Divergent Weighted Timed Games

Weighted timed games are played by two players on a timed automaton equipped with weights: one player wants to minimise the accumulated weight while reaching a target, while the other has an opposite objective. Used in a reactive synthesis perspective, this quantitative extension of timed games allows one to measure the quality of controllers. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. Decidability results exist for subclasses of one-clock games, and for a subclass with non-negative weights defined by a semantical restriction on the weights of cycles. In this work, we introduce the class of divergent weighted timed games as a generalisation of this semantical restriction to arbitrary weights. We show how to compute their optimal value, yielding the first decidable class of weighted timed games with negative weights and an arbitrary number of clocks. In addition, we prove that divergence can be decided in polynomial space. Last, we prove that for untimed games, this restriction yields a class of games for which the value can be computed in polynomial time

Density modulations in an elongated Bose-Einstein condensate released from a disordered potential

We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder, and not from initial phase fluctuations (thermal or quantum).Comment: Published version; 4+ pages; 4 figure

Efficient engineering of multi-atom entanglement through single-photon detections

We propose an efficient scheme to engineer multi-atom entanglement by detecting cavity decay through single-photon detectors. In the special case of two atoms, this scheme is much more efficient than previous probabilistic schemes, and insensitive to randomness in the atom's position. More generally, the scheme can be used to prepare arbitrary superpositions of multi-atom Dicke states without the requirements of high-efficiency detection and separate addressing of different atoms.Comment: 5 pages, 2 figure

The Complexity of Codiagnosability for Discrete Event and Timed Systems

In this paper we study the fault codiagnosis problem for discrete event systems given by finite automata (FA) and timed systems given by timed automata (TA). We provide a uniform characterization of codiagnosability for FA and TA which extends the necessary and sufficient condition that characterizes diagnosability. We also settle the complexity of the codiagnosability problems both for FA and TA and show that codiagnosability is PSPACE-complete in both cases. For FA this improves on the previously known bound (EXPTIME) and for TA it is a new result. Finally we address the codiagnosis problem for TA under bounded resources and show it is 2EXPTIME-complete.Comment: 24 pages

Anisotropic 2D diffusive expansion of ultra-cold atoms in a disordered potential

We study the horizontal expansion of vertically confined ultra-cold atoms in the presence of disorder. Vertical confinement allows us to realize a situation with a few coupled harmonic oscillator quantum states. The disordered potential is created by an optical speckle at an angle of 30{\deg} with respect to the horizontal plane, resulting in an effective anisotropy of the correlation lengths of a factor of 2 in that plane. We observe diffusion leading to non-Gaussian density profiles. Diffusion coefficients, extracted from the experimental results, show anisotropy and strong energy dependence, in agreement with numerical calculations

Localization of a matter wave packet in a disordered potential

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis

CONCUR Test-Of-Time Award 2020 Announcement

This short article announces the recipients of the CONCUR Test-of-Time Award 2020

Real-Time Synthesis is Hard!

We study the reactive synthesis problem (RS) for specifications given in Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very general setting, but on infinite words only; and only the very restrictive BRRS subcase is known to be decidable (see D'Souza et al. and Bouyer et al.). In this paper, we precise the decidability border of MITL synthesis. We show RS is undecidable on finite words too, and present a landscape of restrictions (both on the logic and on the possible controllers) that are still undecidable. On the positive side, we revisit BRRS and introduce an efficient on-the-fly algorithm to solve it

Phases and relativity in atomic gravimetry

The phase observable measured by an atomic gravimeter built up on stimulated Raman transitions is discussed in a fully relativistic context. It is written in terms of laser phases which are invariant under relativistic gauge transformations. The dephasing is the sum of light and atomic contributions which are connected to one another through their interplay with conservation laws at the interaction vertices. In the case of a closed geometry, a compact form of the dephasing is written in terms of a Legendre transform of the laser phases. These general expressions are illustrated by discussing two techniques used for compensating the Doppler shift, one corresponding to chirped frequencies and the other one to ramped variations.Comment: 7 pages, 1 figur