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Acta Physica Sinica

Interaction between a trapped ion with a single-mode quantized radiation field

Qu Zhao-Jun, Liu Sheng-dian, Chuan‐Lu Yang, 烟台师范学院物理系，烟台 264000

Published Jan 1, 2005• 3 citations
Publisher

Abstract

The statistical properties of the system consisting of a trapped ion and a single_mode quantized radiation field are investigated under the conditions of carrier excitation (ωL=ω0), red excitation ［ωL=ω０-jν(j=1,2,3)］ and blue excitation ［ωL=ω０+jν(j=1,2,3)］.The time_evolution of the state of the system,the photon_and phonon_state exchange conditions and the corresponding populations of the ion are discussed.The corresponding averages and variances for photon and phonon numbers,as well as the second_order correlation function for the photon and phonon fields etc,have been obtained.

DOI
10.7498/aps.54.1156

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The statistical properties of the system consisting of a trapped ion and a single_mode quantized radiation field are investigated under the conditions of carrier excitation (ωL=ω0), red excitation ［ωL=ω０-jν(j=1,2,3)］ and blue excitation ［ωL=ω０+jν(j=1,2,3)］.The time_evolution of the state of the system,the photon_and phonon_state exchange conditions and the corresponding populations of the ion are discussed.The corresponding averages and variances for photon and phonon numbers,as well as the second_order correlation function for the photon and phonon fields etc,have been obtained.
In this paper we study the full quantum approach to the interaction of NNN trapped two-level ions with NNN quantized fields in such a way that each of the trapped ions separately interacts with one of the quantized fields. A semiclassical model of this type of interaction has been already studied, using classical laser fields instead of quantized fields, by Cirac and Zoller [Phys. Rev. Lett. 74, 4091 (1995)]. During each interaction, the excitation of a trapped ion occurs due to the occurrence of resonance between the trapped ion and one of the modes of multimode quantized field. In this way, we are able to find the quantized radiation field, which propagates from each excited trapped ion after its deexcitation. It is demonstrated that such a propagated field is a function of the position of ion within the trap, ion number, trapping and ionic transition frequencies, spontaneous emission rate, and time evolution of trapped ionic operators. In the continuation, to achieve the explicit form of such a field we propose a method to evaluate the temporal evolution of operators of the system by utilizing the Heisenberg operator approach. Via the propagated field of each trapped ion, the spectral properties such as intensities as well as power spectra of their radiations are evaluated. Furthermore, the quantum statistics of field and in particular, its photon antibunching and sub-Poissonian statistical properties are investigated. Finally, resonance spectroscopy of the trapped ions is obtained by which one can allocate a characteristic spectrum to each of them.
In this paper, the dynamical properties of a trapped three-level ion which interacts with a two-mode quantized field in the presence of a Kerr medium are studied. The ion-field coupling is also considered to be intensity-dependent (nonlinear interaction). In this respect, the Λ, V and ladder-type three-level ions are considered. Via solving the time-dependent Schörodinger equation, the state vectors of the corresponding ion-field systems are analytically obtained after choosing special initial conditions. In the continuation, the mean phonon number as a criterion of trapping energy, the population inversion as a criterion of exchanging energy (between the ion and the field) and the linear entropy as a criterion of entanglement between the trapped ion and the field are studied. To get more general insight about the interaction conditions, the effect of intensity-dependent ion-field coupling (nonlinearity regime) on the dynamics of system is investigated. Finally, by comparing the obtained results for the three configurations of trapped three-level ions with the previously considered two-level one, we conclude that the degree of entanglement for three-level ions is more than the two-level ion. Also, among the considered trapped ions, the ladder-type ion possesses the most amount of entanglement with the quantized field, whereas the Λ-type possesses the least. We also conclude that, the general temporal behaviour of the other considered quantities (mean phonon number and population inversion) are the same for all three types of trapped three-level ions.
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.