Ion Vibration Induced Transparency And Three-body Interactions

The linear Paul trap provides us lots of physical models,such as Jaynes-Cummings(JC)and anti-JC models,and it has been used to generate various nonclassical states.Based on Paul trap,this thesis for master's degree mainly investigates the following problems:1.We study the ionic vibration induced transparency and Autler-Townes splitting.The ion in a linear Paul trap is supposed to be driven by two orthogonal laser beams,the one along the axial of the trap acts as the control light beam,the other as probe beam.When the frequency of the control laser is tuned to the first red sideband of the ionic transition,the coupling between the internal states of the ion and vibrational mode turns out to be a JC Hamiltonian,which together with the coupling between the probe beam and the two-level ion constructs a ?-type three-level structure.In this case the transparency window may appear in the absorption spectrum of the probe light,which is induced by the ionic vibration and is very similar to the cavity induced transparency.On the other hand,when the frequency of the control laser is tuned to the first blue side band of the ionic transition,the two-level ion and vibrational mode are governed by an anti-JC Hamiltonian,the total system including the probe beam forms a V-type three-level structure.And the Autler-Townes splitting in the absorption spectrum is found.2.We present a scheme for generating three-body interaction between ions via exchanging phonons.Considering the situation that there are many ions in a linear Paul trap,3N of them are driven by laser beams with two different frequencies,in which N ions are driven by the laser beams with the frequency ?R ??a-2?,where the detuning ? is close to,but not resonant with,the center-of-mass vibration frequency v,while the other 2N ions are driven by the laser beams with the frequency ?B =?a + ?.Such 3N ions can just exchange phonons via the center-of-mass vibration leaving the center-of-mass vibration unchanged.Meanwhile,three-ion interaction can be achieved in such a process.By adopting the generalized James' effective Hamiltonian method developed by us,we obtain the three-ion interaction's effective Hamiltonian.By selecting the ionic initial states,the two-ion interaction can be eliminated,the pure three-body interaction can be obtained,which does not depend on any vibration quantum number.3.We develop the generalized effective Hamiltonian method.James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems.This method is just corresponding to the second-order perturbation theory,and cannot be exploited to treat the problems which should be solved by using the third-or higher-order perturbation theory.By utilizing Markovian approximation and the rotating-wave approximation,we generalized James' effective Hamiltonian method to the third-order case.Using the method developed here,we reexamine two examples published recently[Physical Review Letters,2016,117(4):043601,Physical Review A,2015,92(2):023842],our results turn out to be the same as the original ones,and the resultant effective Hamiltonian is more general.