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

Sympathetic ground state cooling and coherent manipulation with two-ion-crystals

We have cooled a two-ion-crystal to the ground state of its collective modes of motion. Laser cooling, more specific resolved sideband cooling is performed sympathetically by illuminating only one of the two $^{40}$Ca$^+$ ions in the crystal. The heating rates of the motional modes of the crystal in our linear trap have been measured, and we found them considerably smaller than those previously reported by Q. Turchette {\em et. al.} Phys. Rev. A 61, 063418 (2000) in the case of trapped $^9$Be$^+$ ions. After the ground state is prepared, coherent quantum state manipulation of the atomic population can be performed. Within the coherence time, up to 12 Rabi oscillations are observed, showing that many coherent manipulations can be achieved. Coherent excitation of each ion individually and ground state cooling are important tools for the realization of quantum information processing in ion traps

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.

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

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 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

Integrating timescales with time-transfer functions: A practical approach for an INTIMATE database

© 2014 Elsevier Ltd.The purpose of the INTIMATE project is to integrate palaeo-climate information from terrestrial, ice and marine records so that the timing of environmental response to climate forcing can be compared in both space and time. One of the key difficulties in doing this is the range of different methods of dating that can be used across different disciplines. For this reason, one of the main outputs of INTIMATE has been to use an event-stratigraphic approach which enables researchers to co-register synchronous events (such as the deposition of tephra from major volcanic eruptions) in different archives (Blockley etal., 2012). However, this only partly solves the problem, because it gives information only at particular short intervals where such information is present. Between these points the ability to compare different records is necessarily less precise chronologically. What is needed therefore is a way to quantify the uncertainties in the correlations between different records, even if they are dated by different methods, and make maximum use of the information available that links different records. This paper outlines the design of a database that is intended to provide integration of timescales and associated environmental proxy information. The database allows for the fact that all timescales have their own limitations, which should be quantified in terms of the uncertainties quoted. It also makes use of the fact that each timescale has strengths in terms of describing the data directly associated with it. For this reason the approach taken allows users to look at data on any timescale that can in some way be related to the data of interest, rather than specifying a specific timescale or timescales which should always be used. The information going into the database is primarily: proxy information (principally from sediments and ice cores) against depth, age depth models against reference chronologies (typically IntCal or ice core), and time-transfer functions that relate different timescales to each other, through the use of event stratigraphies or global phenomena such as cosmogenic isotope production rate variations

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

Hydroclimatic changes in the British Isles through the Last-Glacial-Interglacial Transition:Multiproxy reconstructions from the Vale of Pickering, NE England

European paleoenvironmental records through the Last Glacial-Interglacial Transition (LGIT; ca 16-8 cal ka BP) record a series of climatic events occurring over decadal to multi-centennial timescales. Changes in components of the climatic system other than temperature (e.g. hydrology) through the LGIT are relatively poorly understood however, and further records of hydroclimatic changes are required in order to develop a more complete understanding on the phasing of environmental and anthropogenic responses in Europe to abrupt climate change. Here, we present a multiproxy palaeoenvironmental record (macroscale and microscale sedimentology, macrofossils, and carbonate stable isotopes) from a palaeolake sequence in the Vale of Pickering (VoP), NE England, which enables the reconstruction of hydroclimatic changes constrained by a radiocarbon-based chronology. Relative lake-level changes in the VoP occurred in close association (although not necessarily in phase) to threshold shifts across abrupt climate change transitions, most notably lowering during cooling intervals of the LGIT (∼GI-1d, ∼GI-1b, and ∼GS-1). This reflects more arid hydroclimates associated with these cooling episodes in the British Isles. Comparisons to hydrological records elsewhere in Europe show a latitudinal bifurcation, with Northern Europe (50–60°N) becoming more arid (humid), and Southern Europe (40–50°N) becoming more humid (arid) in response to these cooling (warming) intervals. We attribute these bifurcating signals to the relative positions of the Atlantic storm tracks, sea-ice margin, and North Atlantic Polar Front (NAPF) during the climatic events of the LGIT

Dark pair coherent states of the motion of a trapped ion

We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the X-Y plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly-correlated pair coherent state.Comment: 14 pages, 3 figure