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Acta Physica Sinica

DYNAMICS OF THE GENERALIZED JAYNES CUMMINGS MODEL FOR A TRAPPED ULTRACOLD ION

Ue L

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

Abstract The generalized Jaynes Cummings model describes the quantum interaction of the vibration of center of mass of a trapped ultracold ion and its inner degree of freedom with a quantized radiation field. By calculating the state vectors and corresponding mean values especially those evolving from the initial entangled ion states, we find that the system will present new phase sensitive and all quantized dynamical properties under red and blue sideband excitations.

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Journal of Modern Optics•Dec 3, 2014•9 citations
Abstract The generalized Jaynes Cummings model describes the quantum interaction of the vibration of center of mass of a trapped ultracold ion and its inner degree of freedom with a quantized radiation field. By calculating the state vectors and corresponding mean values especially those evolving from the initial entangled ion states, we find that the system will present new phase sensitive and all quantized dynamical properties under red and blue sideband excitations.
We showed that in Lamb-Dicke regime and under rotating wave approximation, the dynamical behavior of two trapped ions interacting with a laser beam resonant to the first red side-band of center-of-mass mode can be described by Jaynes-Cummings Model. An exact analytic solution for this kind of Jaynes-Cummings model is presented. The results showed that quantum collapses and revivals for the occupation of two atoms, and squeezing for vibratic motion of center-of-mass mode existed in both two different types of initial conditions. The maximum momentum squeezing for center-of-mass mode in these two types of conditions are found to be 42.4% and 43.8% respectively. The coherence, in the first type of initial conditions can keeps long times, and in the second type of initial conditions, a concrete form of coherent state is obtained, when the initial average number is very small.
Following the path of Bužek et al. in [Phys. Rev. A 56 2352 1997], we investigate the full intensity-dependent interaction between a motional two-level ion which is trapped in a f-deformed oscillator (so possessing vibrational modes too) with a single-mode nonlinear quantized field in the Lamb-Dicke limit. After finding the explicit form of the entire ion-field state vector in a general framework, we particularly restrict ourselves to an appropriate nonlinearity function (describing intensity-dependent interaction) corresponding to the center-of-mass motion of a trapped ion which explicitly depends on the Lamb-Dicke parameter as well as another well-known nonlinearity function in the form n. Then, we evaluate the effects of two different initial quantized field states as well as the considered nonlinearity function (via varying the Lamb-Dicke parameter) on a few physical properties of the system. For this purpose, we pay attention to the amount of entanglement, mean number of vibrational quanta (phonons), population inversion of the two-level ion and Q-distribution function. Finally, by comparing our results with the previously considered “linear” one which is pointed in the above Ref., we establish that, by tuning the Lamb-Dicke parameter, one can adjust the mentioned nonclassical properties of the system appropriately.