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

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

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

Quantum state engineering on an optical transition and decoherence in a Paul trap

A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.Comment: 4 pages, 5 figure

Quantum mechanical counterpart of nonlinear optics

Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent "displacement" of the motional quantum state may induce strong amplitude squeezing and quantum interferences.Comment: 6 pages, 4 figures, to be published in Phys. Rev. A 55 (June

Generation of mesoscopic superpositions of two squeezed states of motion for a trapped ion

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