On the stability of randomly sampled systems

Stability of randomly sampled linear systems studied by Liapunov function metho

Mixing 4D-Equipped and Unequipped Aircraft in the Terminal Area

On-board 4D guidance systems, which predict and control the touchdown time of an aircraft to an accuracy of a few seconds throughout the descent, were developed and demonstrated in several flight test programs. However, in addition to refinements of the on board system, two important issues still need to be considered. First, in order to make effective use of these on-board systems, it is necessary to understand and develop the interactions of the airborne and air traffic control (ATC) system in the proposed advanced environment. Unless the total system is understood, the advanced on-board system may prove unusable from an ATC standpoint. Second, in planning for a future system in which all aircraft are 4D equipped, it is necessary to confront the transition situation in which some percentage of traffic must still be handled by conventional means. In terms of 4D, this means that some traffic must still be given radar vectors and speed clearances (that is, be spaced by conventional distance separation techniques), while the 4D-equipped aircraft need to be issued time assignments. These apparent differences are reconciled and efficient ATC operation is developed

Feedback Control of Quantum Transport

The current through nanostructures like quantum dots can be stabilized by a feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles $n$. At large times, the feedback loop freezes the fluctuations of $n$ which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.Comment: 4 pages, 2 figure

Photonic chip based optical frequency comb using soliton induced Cherenkov radiation

By continuous wave pumping of a dispersion engineered, planar silicon nitride microresonator, continuously circulating, sub-30fs short temporal dissipative solitons are generated, that correspond to pulses of 6 optical cycles and constitute a coherent optical frequency comb in the spectral domain. Emission of soliton induced Cherenkov radiation caused by higher order dispersion broadens the spectral bandwidth to 2/3 of an octave, sufficient for self referencing, in excellent agreement with recent theoretical predictions and the broadest coherent microresonator frequency comb generated to date. In a further step, this frequency comb is fully phase stabilized. The ability to preserve coherence over a broad spectral bandwidth using soliton induced Cherenkov radiation marks a critical milestone in the development of planar optical frequency combs, enabling on one hand application in e.g. coherent communications, broadband dual comb spectroscopy and Raman spectral imaging, while on the other hand significantly relaxing dispersion requirements for broadband microresonator frequency combs and providing a path for their generation in the visible and UV. Our results underscore the utility and effectiveness of planar microresonator frequency comb technology, that offers the potential to make frequency metrology accessible beyond specialized laboratories.Comment: Changes: - Added data (new Fig.4) on the first full phase stabilization of a dissipative Kerr soliton (or dissipative cavity soliton) in a microresonator - Extended Fig. 8 in the SI - Introduced nomenclature of dissipative Kerr solitons - Minor other change

Coupling ideality of integrated planar high-Q microresonators

Chipscale microresonators with integrated planar optical waveguides are useful building blocks for linear, nonlinear and quantum optical devices. Loss reduction through improving fabrication processes has resulted in several integrated micro resonator platforms attaining quality (Q) factors of several millions. However only few studies have investigated design-dependent losses, especially with regard to the resonator coupling section. Here we investigate design-dependent parasitic losses, described by the coupling ideality, of the commonly employed microresonator design consisting of a microring resonator waveguide side-coupled to a straight bus waveguide. By systematic characterization of multi-mode high-Q silicon nitride microresonator devices, we show that this design can suffer from low coupling ideality. By performing full 3D simulations to numerically investigate the resonator to bus waveguide coupling, we identify the coupling to higher-order bus waveguide modes as the dominant origin of parasitic losses which lead to the low coupling ideality. Using suitably designed bus waveguides, parasitic losses are mitigated, and a nearly unity ideality and strong overcoupling (i.e. a ratio of external coupling to internal resonator loss rate > 9) are demonstrated. Moreover we find that different resonator modes can exchange power through the coupler, which therefore constitutes a mechanism that induces modal coupling, a phenomenon known to distort resonator dispersion properties. Our results demonstrate the potential for significant performance improvements of integrated planar microresonators, achievable by optimized coupler designs.Comment: 8 pages, 3 figures, 1 tabl

Simulation studies of time-control procedures for the advanced air traffic control system

The problem of mixing aircraft equipped with time-controlled guidance systems and unequipped aircraft in the terminal area has been investigated via a real-time air traffic control simulation. These four-dimensional (4D) guidance systems can predict and control the touchdown time of an aircraft to an accuracy of a few seconds throughout the descent. The objectives of this investigation were to (1) develop scheduling algorithms and operational procedures for various traffic mixes that ranged from 25% to 75% 4D-equipped aircraft; (2) examine the effect of time errors at 120 n. mi. from touchdown on touchdown time scheduling of the various mix conditions; and (3) develop efficient algorithms and procedures to null the initial time errors prior to reaching the final control sector, 30 n. mi. from touchdown. Results indicate substantial reduction in controller workload and an increase in orderliness when more than 25% of the aircraft are equipped with 4D guidance systems; initial random errors of up to + or - 2 min can be handled via a single speed advisory issued in the arrival control sector, thus avoiding disruption of the time schedule

Squashing Models for Optical Measurements in Quantum Communication

Measurements with photodetectors necessarily need to be described in the infinite dimensional Fock space of one or several modes. For some measurements a model has been postulated which describes the full mode measurement as a composition of a mapping (squashing) of the signal into a small dimensional Hilbert space followed by a specified target measurement. We present a formalism to investigate whether a given measurement pair of mode and target measurements can be connected by a squashing model. We show that the measurements used in the BB84 protocol do allow a squashing description, although the six-state protocol does not. As a result, security proofs for the BB84 protocol can be based on the assumption that the eavesdropper forwards at most one photon, while the same does not hold for the six-state protocol.Comment: 4 pages, 2 figures. Fixed a typographical error. Replaced the six-state protocol counter-example. Conclusions of the paper are unchange

On Predicting the Solar Cycle using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -- this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic mean-field models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap