Detecting Friedel oscillations in ultracold Fermi gases

Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which a potential barrier provokes in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.Comment: 5 pages, 4 figure

Anticipating critical transitions in multi-dimensional systems driven by time- and state-dependent noise

The anticipation of bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. When approaching a co-dimension 1 bifurcation, the feedbacks that stabilise the initial state weaken and eventually vanish; a process referred to as critical slowing down (CSD). This motivates the use of variance and lag-1 autocorrelation as indicators of CSD. Both indicators rely on linearising the system's restoring rate. Additionally, the use of variance is limited to time- and state-independent driving noise, strongly constraining the generality of CSD. Here, we propose a data-driven approach based on deriving a Langevin equation to detect local stability changes and anticipate bifurcation-induced transitions in systems with generally time- and state-dependent noise. Our approach substantially generalizes the conditions underlying existing early warning indicators, which we showcase in different examples. Changes in deterministic dynamics can be clearly discriminated from changes in the driving noise. This reduces the risk of false and missed alarms of conventional CSD indicators significantly in settings with time-dependent or multiplicative noise. In multi-dimensional systems, our method can greatly advance the understanding of the coupling between system components and can avoid risks of missing CSD due to dimension reduction, which existing approaches suffer from

Comprehensive uncertainty estimation of the timing of Greenland warmings in the Greenland ice core records

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses, for example, for identification and dating of stadial– interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in different proxy archives, and for model-data comparisons in general. In this study we develop a statistical framework to quantify and propagate dating uncertainties in layer counted proxy archives using the example of the Greenland Ice Core Chronology 2005 (GICC05). We express the number of layers per depth interval as the sum of a structured component that represents both underlying physical processes and biases in layer counting, described by a regression model, and a noise component that represents the fluctuations of the underlying physical processes, as well as unbiased counting errors. The joint dating uncertainties for all depths can then be described by a multivariate Gaussian process from which the chronology (such as the GICC05) can be sampled. We show how the effect of a potential counting bias can be incorporated in our framework. Furthermore we present refined estimates of the occurrence times of Dansgaard–Oeschger events evidenced in Greenland ice cores together with a complete uncertainty quantification of these timings

Stable stadial and interstadial states of the last glacial's climate identified in a combined stable water isotope and dust record from Greenland

During the last glacial interval, the Northern Hemisphere climate was punctuated by a series of abrupt changes between two characteristic climate regimes. The existence of stadial (cold) and interstadial (milder) periods is typically attributed to a hypothesised bistability in the glacial North Atlantic climate system, allowing for rapid transitions from the stadial to the interstadial state – the so-called Dansgaard–Oeschger (DO) events – and more gradual yet still fairly abrupt reverse shifts. The physical mechanisms driving these regime transitions remain debated. DO events are characterised by substantial warming over Greenland and a reorganisation of the Northern Hemisphere atmospheric circulation, which are evident from concomitant shifts in the δ18O ratios and dust concentration records from Greenland ice cores. Treating the combined δ18O and dust record obtained by the North Greenland Ice Core Project (NGRIP) as a realisation of a two-dimensional, time-homogeneous, and Markovian stochastic process, we present a reconstruction of its underlying deterministic drift based on the leading-order terms of the Kramers–Moyal equation. The analysis reveals two basins of attraction in the two-dimensional state space that can be identified with the stadial and interstadial regimes. The drift term of the dust exhibits a double-fold bifurcation structure, while – in contrast to prevailing assumptions – the δ18O component of the drift is clearly mono-stable. This suggests that the last glacial's Greenland temperatures should not be regarded as an intrinsically bistable climate variable. Instead, the two-regime nature of the δ18O record is apparently inherited from a coupling to another bistable climate process. In contrast, the bistability evidenced in the dust drift points to the presence of two stable circulation regimes of the last glacial's Northern Hemisphere atmosphere.Stable stadial and interstadial states of the last glacial's climate identified in a combined stable water isotope and dust record from GreenlandpublishedVersio

Significance of uncertain phasing between the onsets of stadial–interstadial transitions in different Greenland ice core proxies

Different paleoclimate proxy records evidence repeated abrupt climate transitions during previous glacial intervals. These transitions are thought to comprise abrupt warming and increase in local precipitation over Greenland, sudden reorganization of the Northern Hemisphere atmospheric circulation, and retreat of sea ice in the North Atlantic. The physical mechanism underlying these so-called Dansgaard–Oeschger (DO) events remains debated. A recent analysis of Greenland ice core proxy records found that transitions in Na+ concentrations and δ18O values are delayed by about 1 decade with respect to corresponding transitions in Ca2+ concentrations and in the annual layer thickness during DO events. These delays are interpreted as a temporal lag of sea-ice retreat and Greenland warming with respect to a synoptic- and hemispheric-scale atmospheric reorganization at the onset of DO events and may thereby help constrain possible triggering mechanisms for the DO events. However, the explanatory power of these results is limited by the uncertainty of the transition onset detection in noisy proxy records. Here, we extend previous work by testing the significance of the reported lags with respect to the null hypothesis that the proposed transition order is in fact not systematically favored. If the detection uncertainties are averaged out, the temporal delays in the δ18O and Na+ transitions with respect to their counterparts in Ca2+ and the annual layer thickness are indeed pairwise statistically significant. In contrast, under rigorous propagation of uncertainty, three statistical tests cannot provide evidence against the null hypothesis. We thus confirm the previously reported tendency of delayed transitions in the δ18O and Na+ concentration records. Yet, given the uncertainties in the determination of the transition onsets, it cannot be decided whether these tendencies are truly the imprint of a prescribed transition order or whether they are due to chance. The analyzed set of DO transitions can therefore not serve as evidence for systematic lead–lag relationships between the transitions in the different proxies, which in turn limits the power of the observed tendencies to constrain possible physical causes of the DO events

Significance of uncertain phasing between the onsets of stadial–interstadial transitions in different Greenland ice core proxies

Different paleoclimate proxy records evidence repeated abrupt climate transitions during previous glacial intervals. These transitions are thought to comprise abrupt warming and increase in local precipitation over Greenland, sudden reorganization of the Northern Hemisphere atmospheric circulation, and retreat of sea ice in the North Atlantic. The physical mechanism underlying these so-called Dansgaard–Oeschger (DO) events remains debated. A recent analysis of Greenland ice core proxy records found that transitions in Na+ concentrations and δ18O values are delayed by about 1 decade with respect to corresponding transitions in Ca2+ concentrations and in the annual layer thickness during DO events. These delays are interpreted as a temporal lag of sea-ice retreat and Greenland warming with respect to a synoptic- and hemispheric-scale atmospheric reorganization at the onset of DO events and may thereby help constrain possible triggering mechanisms for the DO events. However, the explanatory power of these results is limited by the uncertainty of the transition onset detection in noisy proxy records. Here, we extend previous work by testing the significance of the reported lags with respect to the null hypothesis that the proposed transition order is in fact not systematically favored. If the detection uncertainties are averaged out, the temporal delays in the δ18O and Na+ transitions with respect to their counterparts in Ca2+ and the annual layer thickness are indeed pairwise statistically significant. In contrast, under rigorous propagation of uncertainty, three statistical tests cannot provide evidence against the null hypothesis. We thus confirm the previously reported tendency of delayed transitions in the δ18O and Na+ concentration records. Yet, given the uncertainties in the determination of the transition onsets, it cannot be decided whether these tendencies are truly the imprint of a prescribed transition order or whether they are due to chance. The analyzed set of DO transitions can therefore not serve as evidence for systematic lead–lag relationships between the transitions in the different proxies, which in turn limits the power of the observed tendencies to constrain possible physical causes of the DO events

Orbital insolation variations, intrinsic climate variability, and Quaternary glaciations

The relative role of external forcing and of intrinsic variability is a key question of climate variability in general and of our planet's paleoclimatic past in particular. Over the last 100 years since Milankovic's contributions, the importance of orbital forcing has been established for the period covering the last 2.6 Myr and the Quaternary glaciation cycles that took place during that time. A convincing case has also been made for the role of several internal mechanisms that are active on timescales both shorter and longer than the orbital ones. Such mechanisms clearly have a causal role in Dansgaard–Oeschger and Heinrich events, as well as in the mid-Pleistocene transition. We introduce herein a unified framework for the understanding of the orbital forcing's effects on the climate system's internal variability on timescales from thousands to millions of years. This framework relies on the fairly recent theory of non-autonomous and random dynamical systems, and it has so far been successfully applied in the climate sciences for problems like the El Niño–Southern Oscillation, the oceans' wind-driven circulation, and other problems on interannual to interdecadal timescales. Finally, we provide further examples of climate applications and present preliminary results of interest for the Quaternary glaciation cycles in general and the mid-Pleistocene transition in particular

Orbital insolation variations, intrinsic climate variability, and Quaternary glaciations

International audienceThe relative role of external forcing and of intrinsic variability is a key question of climate variability in general and of our planet's paleoclimatic past in particular. Over the last 100 years since Milankovic's contributions, the importance of orbital forcing has been established for the period covering the last 2.6 Myr and the Quaternary glaciation cycles that took place during that time. A convincing case has also been made for the role of several internal mechanisms that are active on timescales both shorter and longer than the orbital ones. Such mechanisms clearly have a causal role in Dansgaard-Oeschger and Heinrich events, as well as in the mid-Pleistocene transition. We introduce herein a unified framework for the understanding of the orbital forcing's effects on the climate system's internal variability on timescales from thousands to millions of years. This framework relies on the fairly recent theory of non-autonomous and random dynamical systems, and it has so far been successfully applied in the climate sciences for problems like the El Niño-Southern Oscillation, the oceans' wind-driven circulation, and other problems on interannual to interdecadal timescales. Finally, we provide further examples of climate applications and present preliminary results of interest for the Quaternary glaciation cycles in general and the mid-Pleistocene transition in particular

The Temporal Phasing of Rapid Dansgaard–Oeschger Warming Events Cannot Be Reliably Determined [in review, Climate of the Past]

Dansgaard–Oeschger (DO) warming events occurred throughout the last glacial period. Greenland ice cores show a rapid warming during each stadial to interstadial transition, alongside abrupt loss of sea ice and major reorganisation of the atmospheric circulation. Other records also indicate simultaneous abrupt changes to the oceanic circulation. Recently, an advanced Bayesian ramp fitting method has been developed and used to investigate time lags between transitions in these different climate elements, with a view to determining the relative order of these changes. Here, we subject this method to a critical review. Using ice core data, climate model output, and carefully synthesised data representing DO warming events, we demonstrate that the method suffers from noise-induced bias of up to 15 years. This bias means that the method will tend to yield transition onsets that are too early, and we find that the estimated timings of noisier transitions are more strongly biased. Further investigation of DO warming event records in climate models and ice core data reveals that the bias is on the same order of magnitude as potential timing differences between the abrupt transitions of different climate elements. Additionally, we find that higher-resolution records would not reduce this bias. We conclude that time lags of less than 20 years cannot be reliably detected, as we cannot exclude the possibility that they result solely from the bias. This prevents the unambiguous determination of the temporal phasing of DO warming events