Reply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion ''

We show here that the model Hamiltonian used in our paper for ion vibrating in a q-analog harmonic oscillator trap and interacting with a classical single-mode light field is indeed obtained by replacing the usual bosonic creation and annihilation operators of the harmonic trap model by their q-deformed counterparts. The approximations made in our paper amount to using for the ion-laser interaction in a q-analog harmonic oscillator trap, the operator F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon A}, which is analogous to the corresponding operator for ion in a harmonic oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger }}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states |g,m> and |e,m> are not analytic vectors.Comment: Revtex, 4pages. To be Published in Physical Review A59, NO.4(April 99

Induced surface fluxes: A new framework for attributing Arctic sea ice volume balance biases to specific model errors

This is the final version. Available on open access from EGU via the DOI in this recordCode availability. The code used to create the fields of induced surface flux bias is written in Python and is provided as a Supplement (directory “ISF”). The code used to create Figs. 1–9, as well as Fig. B1, is also provided (directory “Figures”). In addition, the routines used to estimate errors in the ISF analysis are provided (directory “Analysis”). Finally, the code used to create Table 1 is provided (directory “Tables”). A set of auxiliary routines used by most of the above are also provided (directory “Library”). Most routines make use of the open-source Iris library, and several make use of the open-source Cartopy library.Data availability. Monthly mean ice thickness, ice fraction, snow thickness and surface radiation, as well as daily surface temperature and surface radiation, for the historical simulations of HadGEM2-ES, are available from the CMIP5 archive at https://cmip.llnl.gov/cmip5/data_portal.html (last access: February 2018). NSIDC ice concentration and melt onset data can be downloaded at http://nsidc.org/data/NSIDC-0051 (last access: May 2017; Cavalieri et al., 1996) and http://nsidc.org/data/NSIDC-0105 (last access: March 2016; Anderson et al., 2011) respectively. PIOMAS ice thickness data can be downloaded at http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/data/ (last access: March 2016; Zhang and Rothrock, 2003). ERAI surface radiation data can be downloaded at http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/ (last access: September 2016; Dee et al., 2011). ISCCP-FD surface radiation data are available at https://isccp.giss.nasa.gov/projects/browse_fc.html (last access: October 2015; Zhang et al., 2004). CERES surface radiation data are available at https://climatedataguide.ucar.edu/climate-data/ceres-ebaf. (last access: August 2014; Loeb et al., 2009)A new framework is presented for analysing the proximate causes of model Arctic sea ice biases, demonstrated with the CMIP5 model HadGEM2-ES (Hadley Centre Global Environment Model version 2 - Earth System). In this framework the Arctic sea ice volume is treated as a consequence of the integrated surface energy balance, via the volume balance. A simple model allows the local dependence of the surface flux on specific model variables to be described as a function of time and space. When these are combined with reference datasets, it is possible to estimate the surface flux bias induced by the model bias in each variable. The method allows the role of the surface albedo and ice thickness-growth feedbacks in sea ice volume balance biases to be quantified along with the roles of model bias in variables not directly related to the sea ice volume. It shows biases in the HadGEM2-ES sea ice volume simulation to be due to a bias in spring surface melt onset date, partly countered by a bias in winter downwelling longwave radiation. The framework is applicable in principle to any model and has the potential to greatly improve understanding of the reasons for ensemble spread in the modelled sea ice state. A secondary finding is that observational uncertainty is the largest cause of uncertainty in the induced surface flux bias calculation.Joint UK BEIS/Defra Met Office Hadley Centre Climate ProgrammeEuropean Union Horizon 2020Natural Environment Research Council (NERC

Investigating future changes in the volume budget of the Arctic sea ice in a coupled climate model

We present a method for analysing changes in the modelled volume budget of the Arctic sea ice as the ice declines during the 21st century. We apply the method to the CMIP5 global coupled model HadGEM2-ES to evaluate how the budget components evolve under a range of different forcing scenarios. As the climate warms and the ice cover declines, the sea ice processes that change the most in HadGEM2-ES are summer melting at the top surface of the ice due to increased net downward radiation and basal melting due to extra heat from the warming ocean. There is also extra basal ice formation due to the thinning ice. However, the impact of these changes on the volume budget is affected by the declining ice cover. For example, as the autumn ice cover declines the volume of ice formed by basal growth declines as there is a reduced area over which this ice growth can occur. As a result, the biggest contribution to Arctic ice decline in HadGEM2-ES is the reduction in the total amount of basal ice growth during the autumn and early winter.Changes in the volume budget during the 21st century have a distinctive seasonal cycle, with processes contributing to ice decline occurring in May–June and September to November. During July and August the total amount of sea ice melt decreases, again due to the reducing ice cover.The choice of forcing scenario affects the rate of ice decline and the timing and magnitude of changes in the volume budget components. For the HadGEM2-ES model and for the range of scenarios considered for CMIP5, the mean changes in the volume budget depend strongly on the evolving ice area and are independent of the speed at which the ice cover declines.</p

Field strength dependence of grey matter R2* on venous oxygenation

The relationship between venous blood oxygenation and change in transverse relaxation rate (ΔR2 *) plays a key role in calibrated BOLD fMRI. This relationship, defined by the parameter β, has previously been determined using theoretical simulations and experimental measures. However, these earlier studies have been confounded by the change in venous cerebral blood volume (CBV) in response to functional tasks. This study used a double-echo gradient echo EPI scheme in conjunction with a graded isocapnic hyperoxic sequence to assess quantitatively the relationship between the fractional venous blood oxygenation (1-Yv) and transverse relaxation rate of grey matter (ΔR2 * GM), without inducing a change in vCBV. The results demonstrate that the relationship between ΔR2 * and fractional venous oxygenation at all magnet field strengths studied was adequately described by a linear relationship. The gradient of this relationship did not increase monotonically with field strength, which may be attributed to the relative contributions of intravascular and extravascular signals which will vary with both field strength and blood oxygenation

Model-based Bayesian inference of brain oxygenation using quantitative BOLD

© 2019 The Authors Streamlined Quantitative BOLD (sqBOLD) is an MR technique that can non-invasively measure physiological parameters including Oxygen Extraction Fraction (OEF) and deoxygenated blood volume (DBV) in the brain. Current sqBOLD methodology rely on fitting a linear model to log-transformed data acquired using an Asymmetric Spin Echo (ASE) pulse sequence. In this paper, a non-linear model implemented in a Bayesian framework was used to fit physiological parameters to ASE data. This model makes use of the full range of available ASE data, and incorporates the signal contribution from venous blood, which was ignored in previous analyses. Simulated data are used to demonstrate the intrinsic difficulty in estimating OEF and DBV simultaneously, and the benefits of the proposed non-linear model are shown. In vivo data are used to show that this model improves parameter estimation when compared with literature values. The model and analysis framework can be extended in a number of ways, and can incorporate prior information from external sources, so it has the potential to further improve OEF estimation using sqBOLD

Two-photon interaction between trapped ions and cavity fields

In this paper, we generalize the ordinary two-photon Jaynes-Cummings model (TPJCM) by considering the atom (or ion) to be trapped in a simple harmonic well. A typical setup would be an optical cavity containing a single ion in a Paul trap. Due to the inclusion of atomic vibrational motion, the atom-field coupling becomes highly nonlinear what brings out quite different behaviors for the system dynamics when compared to the ordinary TPJCM. In particular, we derive an effective two-photon Hamiltonian with dependence on the number operator of the ion's center-of-mass motion. This dependence occurs both in the cavity induced Stark-shifs and in the ion-field coupling, and its role in the dynamics is illustrated by showing the time evolution of the probability of occupation of the electronic levels for simple initial preparations of the state of the system.Comment: 9 pages, 10 figure

The Late Quaternary tephrostratigraphy of annually laminated sediments from Meerfelder Maar, Germany

© 2015 Elsevier Ltd.The record of Late Quaternary environmental change within the sediments of Meerfelder Maar in the Eifel region of Germany is renowned for its high precision chronology, which is annually laminated throughout the Last Glacial to Interglacial transition (LGIT) and most of the Holocene. Two visible tephra layers are prominent within the floating varve chronology of Meerfelder Maar. An Early Holocene tephra layer, the Ulmener Maar Tephra (~11,000 varve years BP), provides a tie-line of the Meerfelder Maar record to the varved Holocene record of nearby Lake Holzmaar. The Laacher See Tephra provides another prominent time marker for the late Allerød, ~200 varve years before the transition into the Younger Dryas at 12,680 varve years BP. Further investigation has now shown that there are also 15 cryptotephra layers within the Meerfelder Maar LGIT-Holocene stratigraphy and these layers hold the potential to make direct comparisons between the Meerfelder Maar record and other palaeoenvironmental archives from across Europe and the North Atlantic. Most notable is the presence of the Vedde Ash, the most widespread Icelandic eruption known from the Late Quaternary, which occurred midway through the Younger Dryas. The Vedde Ash has also been found in the Greenland ice cores and can be used as an isochron around which the GICC05 and Meerfelder Maar annual chronologies can be compared. Near the base of the annual laminations in Meerfelder Maar a cryptotephra is found that correlates to the Neapolitan Yellow Tuff, erupted from Campi Flegrei in southern Italy, 1200km away. This is the furthest north that the Neapolitan Yellow Tuff has been found, highlighting its importance in the construction of a European-wide tephrostratigraphic framework. The co-location of cryptotephra layers from Italian, Icelandic and Eifel volcanic sources, within such a precise chronological record, makes Meerfelder Maar one of the most important tephrostratotype records for continental Europe during the Last Glacial to Interglacial transition

Implementation of quantum gates and preparation of entangled states in cavity QED with cold trapped ions

We propose a scheme to perform basic gates of quantum computing and prepare entangled states in a system with cold trapped ions located in a single mode optical cavity. General quantum computing can be made with both motional state of the trapped ion and cavity state being qubits. We can also generate different kinds of entangled states in such a system without state reduction, and can transfer quantum states from the ion in one trap to the ion in another trap. Experimental requirement for achieving our scheme is discussed.Comment: To appear in J. Opt.

Quantum integrability and Bethe ansatz solution for interacting matter-radiation systems

A unified integrable system, generating a new series of interacting matter-radiation models with interatomic coupling and different atomic frequencies, is constructed and exactly solved through algebraic Bethe ansatz. Novel features in Rabi oscillation and vacuum Rabi splitting are shown on the example of an integrable two-atom Buck-Sukumar model with resolution of some important controversies in the Bethe ansatz solution including its possible degeneracy for such models.Comment: Latex, 7 pages, 1 figure. Final version to be published in J Phys A (as Letter