Electronic structure of superposition states in flux qubits

Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by $\sim 10^6$ -- $10^{10}$ electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions analogous to Schr\"odinger's cat. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and the large disparity between the values of superfluid and Fermi velocity in these systems.Comment: Minor cosmetic changes. Published version

Global carbon budget 2019

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFF) are based on energy statistics and cement production data, while emissions from land use change (ELUC), mainly deforestation, are based on land use and land use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) and terrestrial CO2 sink (SLAND) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2009–2018), EFF was 9.5±0.5 GtC yr−1, ELUC 1.5±0.7 GtC yr−1, GATM 4.9±0.02 GtC yr−1 (2.3±0.01 ppm yr−1), SOCEAN 2.5±0.6 GtC yr−1, and SLAND 3.2±0.6 GtC yr−1, with a budget imbalance BIM of 0.4 GtC yr−1 indicating overestimated emissions and/or underestimated sinks. For the year 2018 alone, the growth in EFF was about 2.1 % and fossil emissions increased to 10.0±0.5 GtC yr−1, reaching 10 GtC yr−1 for the first time in history, ELUC was 1.5±0.7 GtC yr−1, for total anthropogenic CO2 emissions of 11.5±0.9 GtC yr−1 (42.5±3.3 GtCO2). Also for 2018, GATM was 5.1±0.2 GtC yr−1 (2.4±0.1 ppm yr−1), SOCEAN was 2.6±0.6 GtC yr−1, and SLAND was 3.5±0.7 GtC yr−1, with a BIM of 0.3 GtC. The global atmospheric CO2 concentration reached 407.38±0.1 ppm averaged over 2018. For 2019, preliminary data for the first 6–10 months indicate a reduced growth in EFF of +0.6 % (range of −0.2 % to 1.5 %) based on national emissions projections for China, the USA, the EU, and India and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. Overall, the mean and trend in the five components of the global carbon budget are consistently estimated over the period 1959–2018, but discrepancies of up to 1 GtC yr−1 persist for the representation of semi-decadal variability in CO2 fluxes. A detailed comparison among individual estimates and the introduction of a broad range of observations shows (1) no consensus in the mean and trend in land use change emissions over the last decade, (2) a persistent low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) an apparent underestimation of the CO2 variability by ocean models outside the tropics. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set (Le Quéré et al., 2018a, b, 2016, 2015a, b, 2014, 2013). The data generated by this work are available at https://doi.org/10.18160/gcp-2019 (Friedlingstein et al., 2019)

Global Carbon Budget 2022

Accurate assessment of anthropogenic carbon dioxide (CO$_2$) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO$_2$ emissions (E$_{FOS}$) are based on energy statistics and cement production data, while emissions from land-use change (E$_{LUC}$), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO$_2$ concentration is measured directly, and its growth rate (G$_{ATM}$) is computed from the annual changes in concentration. The ocean CO$_2$ sink (S$_{OCEAN}$) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO$_2$ sink (S$_{LAND}$) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (B$_{IM}$), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the year 2021, E$_{FOS}$ increased by 5.1 % relative to 2020, with fossil emissions at 10.1 ± 0.5 GtC yr$^{−1}$ (9.9 ± 0.5 GtC yr$^{−1}$ when the cement carbonation sink is included), and E$_{LUC}$ was 1.1 ± 0.7 GtC yr$^{−1}$, for a total anthropogenic CO$_2$ emission (including the cement carbonation sink) of 10.9 ± 0.8 GtC yr$^{−1}$ (40.0 ± 2.9 GtCO$_2$). Also, for 2021, G$_{ATM}$ was 5.2 ± 0.2 GtC yr$^{−1}$ (2.5 ± 0.1 ppm yr$^{−1}$), S$_{OCEAN}$ was 2.9  ± 0.4 GtC yr$^{−1}$, and S$_{LAND}$ was 3.5 ± 0.9 GtC yr$^{−1}$, with a B$_{IM}$ of −0.6 GtC yr$^{−1}$ (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO$_2$ concentration averaged over 2021 reached 414.71 ± 0.1 ppm. Preliminary data for 2022 suggest an increase in E$_{FOS}$ relative to 2021 of +1.0 % (0.1 % to 1.9 %) globally and atmospheric CO$_2$ concentration reaching 417.2 ppm, more than 50 % above pre-industrial levels (around 278 ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2021, but discrepancies of up to 1 GtC yr$^{−1}$ persist for the representation of annual to semi-decadal variability in CO$_2$ fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO$_2$ flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at https://doi.org/10.18160/GCP-2022 (Friedlingstein et al., 2022b)

Global carbon budget 2019

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFF) are based on energy statistics and cement production data, while emissions from land use change (ELUC), mainly deforestation, are based on land use and land use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) and terrestrial CO2 sink (SLAND) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2009–2018), EFF was 9.5±0.5 GtC yr−1, ELUC 1.5±0.7 GtC yr−1, GATM 4.9±0.02 GtC yr−1 (2.3±0.01 ppm yr−1), SOCEAN 2.5±0.6 GtC yr−1, and SLAND 3.2±0.6 GtC yr−1, with a budget imbalance BIM of 0.4 GtC yr−1 indicating overestimated emissions and/or underestimated sinks. For the year 2018 alone, the growth in EFF was about 2.1 % and fossil emissions increased to 10.0±0.5 GtC yr−1, reaching 10 GtC yr−1 for the first time in history, ELUC was 1.5±0.7 GtC yr−1, for total anthropogenic CO2 emissions of 11.5±0.9 GtC yr−1 (42.5±3.3 GtCO2). Also for 2018, GATM was 5.1±0.2 GtC yr−1 (2.4±0.1 ppm yr−1), SOCEAN was 2.6±0.6 GtC yr−1, and SLAND was 3.5±0.7 GtC yr−1, with a BIM of 0.3 GtC. The global atmospheric CO2 concentration reached 407.38±0.1 ppm averaged over 2018. For 2019, preliminary data for the first 6–10 months indicate a reduced growth in EFF of +0.6 % (range of −0.2 % to 1.5 %) based on national emissions projections for China, the USA, the EU, and India and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. Overall, the mean and trend in the five components of the global carbon budget are consistently estimated over the period 1959–2018, but discrepancies of up to 1 GtC yr−1 persist for the representation of semi-decadal variability in CO2 fluxes. A detailed comparison among individual estimates and the introduction of a broad range of observations shows (1) no consensus in the mean and trend in land use change emissions over the last decade, (2) a persistent low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) an apparent underestimation of the CO2 variability by ocean models outside the tropics. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set (Le Quéré et al., 2018a, b, 2016, 2015a, b, 2014, 2013). The data generated by this work are available at https://doi.org/10.18160/gcp-2019 (Friedlingstein et al., 2019)

Global carbon budget 2019

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFF) are based on energy statistics and cement production data, while emissions from land use change (ELUC), mainly deforestation, are based on land use and land use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) and terrestrial CO2 sink (SLAND) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2009–2018), EFF was 9.5±0.5 GtC yr−1, ELUC 1.5±0.7 GtC yr−1, GATM 4.9±0.02 GtC yr−1 (2.3±0.01 ppm yr−1), SOCEAN 2.5±0.6 GtC yr−1, and SLAND 3.2±0.6 GtC yr−1, with a budget imbalance BIM of 0.4 GtC yr−1 indicating overestimated emissions and/or underestimated sinks. For the year 2018 alone, the growth in EFF was about 2.1 % and fossil emissions increased to 10.0±0.5 GtC yr−1, reaching 10 GtC yr−1 for the first time in history, ELUC was 1.5±0.7 GtC yr−1, for total anthropogenic CO2 emissions of 11.5±0.9 GtC yr−1 (42.5±3.3 GtCO2). Also for 2018, GATM was 5.1±0.2 GtC yr−1 (2.4±0.1 ppm yr−1), SOCEAN was 2.6±0.6 GtC yr−1, and SLAND was 3.5±0.7 GtC yr−1, with a BIM of 0.3 GtC. The global atmospheric CO2 concentration reached 407.38±0.1 ppm averaged over 2018. For 2019, preliminary data for the first 6–10 months indicate a reduced growth in EFF of +0.6 % (range of −0.2 % to 1.5 %) based on national emissions projections for China, the USA, the EU, and India and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. Overall, the mean and trend in the five components of the global carbon budget are consistently estimated over the period 1959–2018, but discrepancies of up to 1 GtC yr−1 persist for the representation of semi-decadal variability in CO2 fluxes. A detailed comparison among individual estimates and the introduction of a broad range of observations shows (1) no consensus in the mean and trend in land use change emissions over the last decade, (2) a persistent low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) an apparent underestimation of the CO2 variability by ocean models outside the tropics. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set (Le Quéré et al., 2018a, b, 2016, 2015a, b, 2014, 2013). The data generated by this work are available at https://doi.org/10.18160/gcp-2019 (Friedlingstein et al., 2019)

Supplemental data of Global Carbon Project 2020

Supplement containing data related to the 2020 Global Carbon Budget from the Global Carbon Project. The original article is Friedlingstein et al: Global Carbon Budget 2020, Earth Syst. Sci. Data Discussions, 2020. https://doi.org/10.5194/essd-12-3269-2020. Further information is available on: http://www.globalcarbonproject.org/carbonbudget. File Global_Carbon_Budget_2020v1.0.xlsx includes the following: 1. Summary 2. Global Carbon Budget 3. Fossil fuel emissions by Fuel Type 4. Land-use change emissions 5. Ocean Sink 6. Terrestrial sink 7. Historical Budget. File National_Carbon_Emissions_2020v1.0.xlsx includes the following: 1. Summary 2. Territorial emissions 3. Consumption emissions 4. Emissions transfers 5. Country definitions 6. Disaggregation 7. Aggregatio

Global Carbon Budget 2020

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFOS) are based on energy statistics and cement production data, while emissions from land-use change (ELUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) and terrestrial CO2 sink (SLAND) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2010–2019), EFOS was 9.6 ± 0.5 GtC yr−1 excluding the cement carbonation sink (9.4 ± 0.5 GtC yr−1 when the cement carbonation sink is included), and ELUC was 1.6 ± 0.7 GtC yr−1. For the same decade, GATM was 5.1 ± 0.02 GtC yr−1 (2.4 ± 0.01 ppm yr−1), SOCEAN 2.5 ±  0.6 GtC yr−1, and SLAND 3.4 ± 0.9 GtC yr−1, with a budget imbalance BIM of −0.1 GtC yr−1 indicating a near balance between estimated sources and sinks over the last decade. For the year 2019 alone, the growth in EFOS was only about 0.1 % with fossil emissions increasing to 9.9 ± 0.5 GtC yr−1 excluding the cement carbonation sink (9.7 ± 0.5 GtC yr−1 when cement carbonation sink is included), and ELUC was 1.8 ± 0.7 GtC yr−1, for total anthropogenic CO2 emissions of 11.5 ± 0.9 GtC yr−1 (42.2 ± 3.3 GtCO2). Also for 2019, GATM was 5.4 ± 0.2 GtC yr−1 (2.5 ± 0.1 ppm yr−1), SOCEAN was 2.6 ± 0.6 GtC yr−1, and SLAND was 3.1 ± 1.2 GtC yr−1, with a BIM of 0.3 GtC. The global atmospheric CO2 concentration reached 409.85 ± 0.1 ppm averaged over 2019. Preliminary data for 2020, accounting for the COVID-19-induced changes in emissions, suggest a decrease in EFOS relative to 2019 of about −7 % (median estimate) based on individual estimates from four studies of −6 %, −7 %, −7 % (−3 % to −11 %), and −13 %. Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2019, but discrepancies of up to 1 GtC yr−1 persist for the representation of semi-decadal variability in CO2 fluxes. Comparison of estimates from diverse approaches and observations shows (1) no consensus in the mean and trend in land-use change emissions over the last decade, (2) a persistent low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) an apparent discrepancy between the different methods for the ocean sink outside the tropics, particularly in the Southern Ocean. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set (Friedlingstein et al., 2019; Le Quéré et al., 2018b, a, 2016, 2015b, a, 2014, 2013). The data presented in this work are available at https://doi.org/10.18160/gcp-2020 (Friedlingstein et al., 2020)

Global Carbon Budget 2022

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFOS) are based on energy statistics and cement production data, while emissions from land-use change (ELUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly, and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO2 sink (SLAND) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ.For the year 2021, EFOS increased by 5.1 % relative to 2020, with fossil emissions at 10.1 ± 0.5 GtC yr−1 (9.9 ± 0.5 GtC yr−1 when the cement carbonation sink is included), and ELUC was 1.1 ± 0.7 GtC yr−1, for a total anthropogenic CO2 emission (including the cement carbonation sink) of 10.9 ± 0.8 GtC yr−1 (40.0 ± 2.9 GtCO2). Also, for 2021, GATM was 5.2 ± 0.2 GtC yr−1 (2.5 ± 0.1 ppm yr−1), SOCEAN was 2.9 ± 0.4 GtC yr−1, and SLAND was 3.5 ± 0.9 GtC yr−1, with a BIM of −0.6 GtC yr−1 (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO2 concentration averaged over 2021 reached 414.71 ± 0.1 ppm. Preliminary data for 2022 suggest an increase in EFOS relative to 2021 of +1.0 % (0.1 % to 1.9 %) globally and atmospheric CO2 concentration reaching 417.2 ppm, more than 50 % above pre-industrial levels (around 278 ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2021, but discrepancies of up to 1 GtC yr−1 persist for the representation of annual to semi-decadal variability in CO2 fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO2 flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at https://doi.org/10.18160/GCP-2022 (Friedlingstein et al., 2022b)

Global Carbon Budget 2022

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (E-FOS) are based on energy statistics and cement production data, while emissions from land-use change (E-LUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly, and its growth rate (G(ATM)) is computed from the annual changes in concentration. The ocean CO2 sink (S-OCEAN) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO2 sink (S-LAND) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (B-IM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as +/- 1 sigma. For the year 2021, EFOS increased by 5.1% relative to 2020, with fossil emissions at 10.1 +/- 0.5 GtC yr(-1) (9.9 +/- 0.5 GtC yr(-1) when the cement carbonation sink is included), and ELUC was 1.1 +/- 0.7 GtC yr(-1),for a total anthropogenic CO2 emission (including the cement carbonation sink) of 10.9 +/- 0.8 GtC yr 1 (40.0 +/- 2.9 GtCO(2)). Also, for 2021, G(ATM) was 5.2 +/- 0.2 GtC yr(-1) (2.5 +/- 0.1 ppm yr(-1)), S-OCEAN was 2.9 +/- 0.4 GtC yr(-1), and SLAND was 3.5 +/- 0.9 GtC yr(-1), with a B-IM of 0.6 GtC yr(-1) (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO2 concentration averaged over 2021 reached 414.71 +/- 0.1 ppm. Preliminary data for 2022 suggest an increase in E-FOS relative to 2021 of +1.0% (0.1% to 1.9 %) globally and atmospheric CO2 concentration reaching 417.2 ppm, more than 50% above pre-industrial levels (around 278 ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959-2021, but discrepancies of up to 1 GtC yr(-1) persist for the representation of annual to semi-decadal variability in CO2 fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO2 flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at https://doi.org/10.18160/GCP-2022 (Friedlingstein et al., 2022b)