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

Analytical model of non-Markovian decoherence in donor-based charge quantum bits

We develop an analytical model for describing the dynamics of a donor-based charge quantum bit (qubit). As a result, the quantum decoherence of the qubit is analytically obtained and shown to reveal non-Markovian features: The decoherence rate varies with time and even attains negative values, generating a non-exponential decay of the electronic coherence and a later recoherence. The resulting coherence time is inversely proportional to the temperature, thus leading to low decoherence below a material dependent characteristic temperature.Comment: 19 pages, 3 figure

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

Schr\"{o}dinger cat state of trapped ions in harmonic and anharmonic oscillator traps

We examine the time evolution of a two level ion interacting with a light field in harmonic oscillator trap and in a trap with anharmonicities. The anharmonicities of the trap are quantified in terms of the deformation parameter $\tau$ characterizing the q-analog of the harmonic oscillator trap. Initially the ion is prepared in a Schr\"{o}dinger cat state. The entanglement of the center of mass motional states and the internal degrees of freedom of the ion results in characteristic collapse and revival pattern. We calculate numerically the population inversion I(t), quasi-probabilities $Q(t),$ and partial mutual quantum entropy S(P), for the system as a function of time. Interestingly, small deformations of the trap enhance the contrast between population inversion collapse and revival peaks as compared to the zero deformation case. For \beta =3 and $4,($ determines the average number of trap quanta linked to center of mass motion) the best collapse and revival sequence is obtained for \tau =0.0047 and \tau =0.004 respectively. For large values of \tau decoherence sets in accompanied by loss of amplitude of population inversion and for \tau \sim 0.1 the collapse and revival phenomenon disappear. Each collapse or revival of population inversion is characterized by a peak in S(P) versus t plot. During the transition from collapse to revival and vice-versa we have minimum mutual entropy value that is S(P)=0. Successive revival peaks show a lowering of the local maximum point indicating a dissipative irreversible change in the ionic state. Improved definition of collapse and revival pattern as the anharminicity of the trapping potential increases is also reflected in the Quasi- probability versus t plots.Comment: Revised version, 16 pages,6 figures. Revte

Quantum integrable multi atom matter-radiation models with and without rotating wave approximation

New integrable multi-atom matter-radiation models with and without rotating wave approximation (RWA) are constructed and exactly solved through algebraic Bethe ansatz. The models with RWA are generated through ancestor model approach in an unified way. The rational case yields the standard type of matter-radiaton models, while the trigonometric case corresponds to their q-deformations. The models without RWA are obtained from the elliptic case at the Gaudin and high spin limit.Comment: 9 pages, no figure, talk presented in int. conf. NEEDS04 (Gallipoli, Italy, July 2004

Центральная Азия в интересах Ирана, Китая, России и Турции: взгляд из США

Работа посвящена изучению реакции американских специалистов на внешнюю политику Ирана, Китая, России и Турции в Центральной Азии. В исследовании комплексно рассмотрена политика единственной сверхдержавы относительно отдельного региона в рамках общей стратегии США.Робота присвячена вивченню реакції американських фахівців на зовнішню політику Ірану, Китаю, Росії та Туреччини у Центральній Азії. У дослідженні комплексно розглянута політика єдиної наддержави щодо окремого регіону в рамках її загального стратегічного курсу.The thesis is focused on a study of the american specialists reactions toward foreign policy of China, Iran, Russia and Turkey in Central Asia. The research presents a complex investigation of the policy of the only superpower in the relation to a separate region in the frame of its general strategic course

Investigation of the neurovascular coupling in positive and negative BOLD responses in human brain at 7T

Decreases in stimulus-dependent blood oxygenation level dependent (BOLD) signal and their underlying neurovascular origins have recently gained considerable interest. In this study a multi-echo, BOLD-corrected vascular space occupancy (VASO) functional magnetic resonance imaging (fMRI) technique was used to investigate neurovascular responses during stimuli that elicit positive and negative BOLD responses in human brain at 7 T. Stimulus-induced BOLD, cerebral blood volume (CBV), and cerebral blood flow (CBF) changes were measured and analyzed in ‘arterial’ and ‘venous’ blood compartments in macro- and microvasculature. We found that the overall interplay of mean CBV, CBF and BOLD responses is similar for tasks inducing positive and negative BOLD responses. Some aspects of the neurovascular coupling however, such as the temporal response, cortical depth dependence, and the weighting between ‘arterial’ and ‘venous’ contributions, are significantly different for the different task conditions. Namely, while for excitatory tasks the BOLD response peaks at the cortical surface, and the CBV change is similar in cortex and pial vasculature, inhibitory tasks are associated with a maximum negative BOLD response in deeper layers, with CBV showing strong constriction of surface arteries and a faster return to baseline. The different interplays of CBV, CBF and BOLD during excitatory and inhibitory responses suggests different underlying hemodynamic mechanisms

Squeezing arbitrary cavity-field states through their interaction with a single driven atom

We propose an implementation of the parametric amplification of an arbitrary radiation-field state previously prepared in a high-Q cavity. This nonlinear process is accomplished through the dispersive interactions of a single three-level atom (fundamental |g>, intermediate |i>, and excited |e> levels) simultaneously with i) a classical driving field and ii) a previously prepared cavity mode whose state we wish to squeeze. We show that, in the adiabatic approximantion, the preparation of the initial atomic state in the intermediate level |i> becomes crucial for obtaing the degenerated parametric amplification process.Comment: Final published versio

Measurements of neutrons produced by high-energy muons at the Boulby Underground Laboratory

We present the first measurements of the muon-induced neutron flux at the Boulby Underground Laboratory. The experiment was carried out with an 0.73 tonne liquid scintillator that also served as an anticoincidence system for the ZEPLIN-II direct dark matter search. The experimental method exploited the delayed coincidences between high-energy muon signals and gamma-rays from radiative neutron capture on hydrogen or other elements. The muon-induced neutron rate, defined as the average number of detected neutrons per detected muon, was measured as 0.079±0.003 (stat.) neutrons/muon using neutron-capture signals above 0.55 MeV in a time window of 40-190 [mu]s after the muon trigger. Accurate Monte Carlo simulations of the neutron production, transport and detection in a precisely modeled laboratory and experimental setup using the GEANT4 toolkit gave a result 1.8 times higher than the measured value. The difference greatly exceeds all statistical and systematic uncertainties. As the vast majority of neutrons detected in the current setup were produced in lead we evaluated from our measurements the neutron yield in lead as (1.31±0.06)×10-3 neutrons/muon/(g/cm2) for a mean muon energy of about 260 GeV.http://www.sciencedirect.com/science/article/B6TJ1-4SP3SN4-1/1/d863f0e951f0d571b41082e3cc9b081

The evolution of Palaeolake Flixton and the environmental context of Star Carr:An oxygen and carbon isotopic record of environmental change for the early Holocene

This paper presents δ18O and δ13C values from three early Holocene lacustrine carbonate sequences from Palaeolake Flixton in northeastern England. The δ13C values are typical of carbonates precipitating in an open lake system with the exception of samples from the very uppermost parts of these sequences which have values more typical of palustrine or tufaceous carbonates and, therefore, indicate the progressive contraction and shrinkage of the lake system overtime. The δ18O values record an initial increase to an early peak at the onset of the Holocene but a subsequent decline in values of such a magnitude that by ca 8000 yrs B.P. the δ18O value of the precipitated carbonate is consistent with carbonates that precipitated at the end of the Loch Lomond Stadial. The early increase and peak in δ18O values is suggested to reflect the climatic amelioration at the onset of the Holocene, as temperatures progressively rose. The decline cannot be explained by any known temperature shifts, however, this “depletion trend” is seen in several other early Holocene lacustrine records from across the British Isles. This decline is suggested to reflect a shift in the seasonality of precipitation from a more seasonal precipitation regime typical of a “continental” climate, with strong seasonal contrasts in rainfall, to a more “maritime” climate which was characterised by consistent levels of rainfall occurring across the year. The relative timing of human activity at Star Carr suggests human occupation occurred after this isotopic decline under “maritime” rather than “continental” climates