Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequencyComment: 6 figures, 13 page

Maximum likelihood frequency estimation in smart grid applications

International audienceThis paper focuses on the estimation of the fundamental frequency in balanced three-phase power systems. Specifically, we propose a Maximum Likelihood Estimator (MLE) that exploits the multidimensional nature of electrical signals. For perfectly sinusoidal signals, we show that the MLE can be expressed according to the periodogram of the instantaneous positive component. For harmonic signals, we demonstrate that the MLE can be approximated by a cumulated periodogram of the zero, positive and negative sequence components. As compared to single-phase estimators, statistical analysis and simulation results prove that the proposed estimator decreases the Mean Square Error by a factor of three, whatever the Signal to Noise Ratio (SNR) or data length. Furthermore, simulations with experimental data show that the proposed technique outperforms classical spectral estimators such as MUSIC

Searching for vector dark matter with an optomechanical accelerometer

We consider using optomechanical accelerometers as resonant detectors for ultralight dark matter. As a concrete example, we describe a detector based on a silicon nitride membrane fixed to a beryllium mirror, forming an optical cavity. The use of different materials gives access to forces proportional to baryon (B) and lepton (L) charge, which are believed to be coupling channels for vector dark matter particles ("dark photons"). The cavity meanwhile provides access to quantum-limited displacement measurements. For a centimeter-scale membrane pre-cooled to 10 mK, we argue that sensitivity to vector B-L dark matter can exceed that of the E\"{o}t-Wash experiment in integration times of minutes, over a fractional bandwidth of $\sim 0.1\%$ near 10 kHz (corresponding to a particle mass of $10^{-10}$eV/c$^2$). Our analysis can be translated to alternative systems such as levitated particles, and suggests the possibility of a new generation of table-top experiments

Direct discovery of the inner exoplanet in the HD 206893 system : Evidence for deuterium burning in a planetary-mass companion

Aims. HD 206893 is a nearby debris disk star that hosts a previously identified brown dwarf companion with an orbital separation of ∼10 au. Long-term precise radial velocity (RV) monitoring, as well as anomalies in the system proper motion, has suggested the presence of an additional, inner companion in the system. Methods. Using information from ongoing precision RV measurements with the HARPS spectrograph, as well as Gaia host star astrometry, we have undertaken a multi-epoch search for the purported additional planet using the VLTI/GRAVITY instrument. Results. We report a high-significance detection over three epochs of the companion HD 206893c, which shows clear evidence for Keplerian orbital motion. Our astrometry with ∼50−100 μarcsec precision afforded by GRAVITY allows us to derive a dynamical mass of 12.7MJup and an orbital separation of 3.53 au for HD 206893c. Our fits to the orbits of both companions in the system use both Gaia astrometry and RVs to also provide a precise dynamical estimate of the previously uncertain mass of the B component, and therefore allow us to derive an age of 155 ± 15 Myr for the system. We find that theoretical atmospheric and evolutionary models that incorporate deuterium burning for HD 206893c, parameterized by cloudy atmosphere models as well as a “hybrid sequence” (encompassing a transition from cloudy to cloud-free), provide a good simultaneous fit to the luminosity of both HD 206893B and c. Thus, accounting for both deuterium burning and clouds is crucial to understanding the luminosity evolution of HD 206893c. Conclusions. In addition to using long-term RV information, this effort is an early example of a direct imaging discovery of a bona fide exoplanet that was guided in part by Gaia astrometry. Utilizing Gaia astrometry is expected to be one of the primary techniques going forward for identifying and characterizing additional directly imaged planets. In addition, HD 206893c is an example of an object narrowly straddling the deuterium-burning limit but unambiguously undergoing deuterium burning. Additional discoveries like this may therefore help clarify the discrimination between a brown dwarf and an extrasolar planet. Lastly, this discovery is another example of the power of optical interferometry to directly detect and characterize extrasolar planets where they form, at ice-line orbital separations of 2−4 au

Direct Discovery of the Inner Exoplanet in the Hd 206893 System: Evidence for Deuterium Burning in a Planetary-Mass Companion

Aims. HD 206893 is a nearby debris disk star that hosts a previously identified brown dwarf companion with an orbital separation of ~ 10 au. Long-Term precise radial velocity (RV) monitoring, as well as anomalies in the system proper motion, has suggested the presence of an additional, inner companion in the system. Methods. Using information from ongoing precision RV measurements with the HARPS spectrograph, as well as Gaia host star astrometry, we have undertaken a multi-epoch search for the purported additional planet using the VLTI/GRAVITY instrument. Results. We report a high-significance detection over three epochs of the companion HD 206893c, which shows clear evidence for Keplerian orbital motion. Our astrometry with ~ 50-100 µarcsec precision afforded by GRAVITY allows us to derive a dynamical mass of 12.7${+1.2}_{-1.0}$MJup and an orbital separation of 3.53${+0.08}_{-0.06}$ au for HD 206893c. Our fits to the orbits of both companions in the system use both Gaia astrometry and RVs to also provide a precise dynamical estimate of the previously uncertain mass of the B component, and therefore allow us to derive an age of 155 ± 15 Myr for the system. We find that theoretical atmospheric and evolutionary models that incorporate deuterium burning for HD 206893c, parameterized by cloudy atmosphere models as well as a hybrid sequence (encompassing a transition from cloudy to cloud-free), provide a good simultaneous fit to the luminosity of both HD 206893B and c. Thus, accounting for both deuterium burning and clouds is crucial to understanding the luminosity evolution of HD 206893c. Conclusions. In addition to using long-Term RV information, this effort is an early example of a direct imaging discovery of a bona fide exoplanet that was guided in part by Gaia astrometry. Utilizing Gaia astrometry is expected to be one of the primary techniques going forward for identifying and characterizing additional directly imaged planets. In addition, HD 206893c is an example of an object narrowly straddling the deuterium-burning limit but unambiguously undergoing deuterium burning. Additional discoveries like this may therefore help clarify the discrimination between a brown dwarf and an extrasolar planet. Lastly, this discovery is another example of the power of optical interferometry to directly detect and characterize extrasolar planets where they form, at ice-line orbital separations of 2-4 au

Estimation methods for elementary chirp model parameters

In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one-component elementary chirp model. It is proved that the proposed estimators are strongly consistent and follow the normal distribution asymptotically. We also suggest how to obtain proper initial values for these methods. The problem of finding initial values is a difficult problem when the number of components in the model is large, or when the signal-to-noise ratio is low, or when two frequency rates are close to each other. We propose sequential procedures to estimate the multiple-component elementary chirp model parameters. We prove that the theoretical properties of sequential least squares estimators and sequential approximate least squares estimators coincide with those of least squares estimators and approximate least squares estimators, respectively. To evaluate the performance of the proposed estimators, numerical experiments are performed. It is observed that the proposed sequential estimators perform well even in situations where least squares estimators do not perform well. We illustrate the performance of the proposed sequential algorithm on a bat data