Super and Sub-Poissonian photon statistics for single molecule spectroscopy

We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave laser field. The spectral diffusion is modeled based on a stochastic approach, in the spirit of the Anderson-Kubo line shape theory. Using a generating function formalism we solve the generalized optical Bloch equations, and obtain an exact analytical formula for the line shape and Mandel's Q parameter. The line shape exhibits well known behaviors, including motional narrowing when the stochastic modulation is fast, and power broadening. The Mandel parameter, describing the line shape fluctuations, exhibits a transition from a Quantum sub-Poissonian behavior in the fast modulation limit, to a classical super-Poissonian behavior found in the slow modulation limit. Our result is applicable for weak and strong laser field, namely for arbitrary Rabi frequency. We show how to choose the Rabi frequency in such a way that the Quantum sub-Poissonian nature of the emission process becomes strongest. A lower bound on $Q$ is found, and simple limiting behaviors are investigated. A non-trivial behavior is obtained in the intermediate modulation limit, when the time scales for spectral diffusion and the life time of the excited state, become similar. A comparison is made between our results, and previous ones derived based on the semi-classical generalized Wiener--Khintchine theorem.Comment: 14 Phys. Rev style pages, 10 figure

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.Comment: 7 pages, 2 figures. Shorter, significantly modified, updated versio

Sensitivity and back-action in charge qubit measurements by a strongly coupled single-electron transistor

We consider charge-qubit monitoring (continuous-in-time weak measurement) by a single-electron transistor (SET) operating in the sequential-tunneling regime. We show that commonly used master equations for this regime are not of the Lindblad form that is necessary and sufficient for guaranteeing valid physical states. In this paper we derive a Lindblad-form master equation and a corresponding quantum trajectory model for continuous measurement of the charge qubit by a SET. Our approach requires that the SET-qubit coupling be strong compared to the SET tunnelling rates. We present an analysis of the quality of the qubit measurement in this model (sensitivity versus back-action). Typically, the strong coupling when the SET island is occupied causes back-action on the qubit beyond the quantum back-action necessary for its sensitivity, and hence the conditioned qubit state is mixed. However, in one strongly coupled, asymmetric regime, the SET can approach the limit of an ideal detector with an almost pure conditioned state. We also quantify the quality of the SET using more traditional concepts such as the measurement time and decoherence time, which we have generalized so as to treat the strongly responding regime.Comment: About 11 pages, 6 figures. Changes in v2: we made general improvements to the manuscript including, but not limited to(!), the removal of one reference, and modification of the footnote

Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be extended to the quantum-diffusive limit when the average electron tunneling rate is very large compared to the extra change of the tunneling rate due to the presence of the electron in the dot closer to the PC. We find that in both quantum-jump and quantum-diffusive cases, the conditional dynamics of the CQD system can be described by the stochastic Schr\"{o}dinger equations for its conditioned state vector if and only if the information carried away from the CQD system by the PC reservoirs can be recovered by the perfect detection of the measurements.Comment: 14 pages, 1 figures, RevTex, onecolumn, to appear in Phys. Rev.

Beyond Crowd Judgments: Data-driven Estimation of Market Value in Association Football

Association football is a popular sport, but it is also a big business. From a managerial perspective, the most important decisions that team managers make concern player transfers, so issues related to player valuation, especially the determination of transfer fees and market values, are of major concern. Market values can be understood as estimates of transfer fees—that is, prices that could be paid for a player on the football market—so they play an important role in transfer negotiations. These values have traditionally been estimated by football experts, but crowdsourcing has emerged as an increasingly popular approach to estimating market value. While researchers have found high correlations between crowdsourced market values and actual transfer fees, the process behind crowd judgments is not transparent, crowd estimates are not replicable, and they are updated infrequently because they require the participation of many users. Data analytics may thus provide a sound alternative or a complementary approach to crowd-based estimations of market value. Based on a unique data set that is comprised of 4217 players from the top five European leagues and a period of six playing seasons, we estimate players’ market values using multilevel regression analysis. The regression results suggest that data-driven estimates of market value can overcome several of the crowd’s practical limitations while producing comparably accurate numbers. Our results have important implications for football managers and scouts, as data analytics facilitates precise, objective, and reliable estimates of market value that can be updated at any time

Asian emissions in 2006 for the NASA INTEX-B mission

A new inventory of air pollutant emissions in Asia in the year 2006 is developed to support the Intercontinental Chemical Transport Experiment-Phase B (INTEX-B) funded by the National Aeronautics and Space Administration (NASA). Emissions are estimated for all major anthropogenic sources, excluding biomass burning. We estimate total Asian anthropogenic emissions in the year 2006 as follows: 47.1 Tg SO2, 36.7 Tg NOx, 298.2 Tg CO, 54.6 Tg NMVOC, 29.2 Tg PM10, 22.2 Tg PM2.5, 2.97 Tg BC, and 6.57 Tg OC. We emphasize emissions from China because they dominate the Asia pollutant outflow to the Pacific and the increase of emissions from China since 2000 is of great concern. We have implemented a series of improved methodologies to gain a better understanding of emissions from China, including a detailed technology-based approach, a dynamic methodology representing rapid technology renewal, critical examination of energy statistics, and a new scheme of NMVOC speciation for model-ready emissions. We estimate China's anthropogenic emissions in the year 2006 to be as follows: 31.0 Tg SO2, 20.8 Tg NOx, 166.9 Tg CO, 23.2 Tg NMVOC, 18.2 Tg PM10, 13.3 Tg PM2.5, 1.8 Tg BC, and 3.2 Tg OC. We have also estimated 2001 emissions for China using the same methodology and found that all species show an increasing trend during 2001-2006: 36% increase for SO2, 55% for NOx, 18% for CO, 29% for VOC, 13% for PM10, and 14% for PM2.5, BC, and OC. Emissions are gridded at a resolution of 30 minW30 min and can be accessed at our web site (mic.greenresource.cn/intex-b2006)

Redox evolution of a degassing magma rising to the surface.

Volatiles carried by magmas, either dissolved or exsolved, have a fundamental effect on a variety of geological phenomena, such as magma dynamics1–5 and the composition of the Earth's atmosphere 6. In particular, the redox state of volcanic gases emanating at the Earth's surface is widely believed to mirror that of the magma source, and is thought to have exerted a first-order control on the secular evolution of atmospheric oxygen6,7. Oxygen fugacity (fO2 ) estimated from lava or related gas chemistry, however, may vary by as much as one log unit8–10, and the reason for such differences remains obscure. Here we use a coupled chemical–physical model of conduit flow to show that the redox state evolution of an ascending magma, and thus of its coexisting gas phase, is strongly dependent on both the composition and the amount of gas in the reservoir. Magmas with no sulphur show a systematic fO2 increase during ascent, by as much as 2 log units. Magmas with sulphur show also a change of redox state during ascent, but the direction of change depends on the initial fO2 in the reservoir. Our calculations closely reproduce the H2S/SO2 ratios of volcanic gases observed at convergent settings, yet the difference between fO2 in the reservoir and that at the exit of the volcanic conduit may be as much as 1.5 log units. Thus, the redox state of erupted magmas is not necessarily a good proxy of the redox state of the gases they emit. Our findings may require re-evaluation of models aimed at quantifying the role of magmatic volatiles in geological processes

Functional Connectivity of the Anterior Nucleus of the Thalamus in Pediatric Focal Epilepsy

OBJECTIVE: Whilst stimulation of the anterior nucleus of the thalamus has shown efficacy for reducing seizure frequency in adults, alterations in thalamic connectivity have not been explored in children. We tested the hypotheses that (a) the anterior thalamus has increased functional connectivity in children with focal epilepsy, and (b) this alteration in the connectome is a persistent effect of the disease rather than due to transient epileptiform activity. METHODS: Data from 35 children (7–18 years) with focal, drug-resistant epilepsy and 20 healthy children (7–17 years) were analyzed. All subjects underwent functional magnetic resonance imaging (fMRI) whilst resting and were simultaneously monitored with scalp electroencephalography (EEG). The fMRI timeseries were extracted for each Automated Anatomical Labeling brain region and thalamic subregion. Graph theory metrics [degree (DC) and eigenvector (EC) centrality] were used to summarize the connectivity profile of the ipsilateral thalamus, and its thalamic parcellations. The effect of interictal epileptiform discharges (IEDs) captured on EEG was used to determine their effect on DC and EC. RESULTS: DC was significantly higher in the anterior nucleus (p = 0.04) of the thalamus ipsilateral to the epileptogenic zone in children with epilepsy compared to controls. On exploratory analyses, we similarly found a higher DC in the lateral dorsal nucleus (p = 0.02), but not any other thalamic subregion. No differences in EC measures were found between patients and controls. We did not find any significant difference in DC or EC in any thalamic subregion when comparing the results of children with epilepsy before, and after the removal of the effects of IEDs. CONCLUSIONS: Our data suggest that the anterior and lateral dorsal nuclei of the thalamus are more highly functionally connected in children with poorly controlled focal epilepsy. We did not detect a convincing change in thalamic connectivity caused by transient epileptiform activity, suggesting that it represents a persistent alteration to network dynamics