光场与三能级原子相互作用的熵动力学

【作者】 贾金平；

【导师】 朱开成；

【作者基本信息】 中南大学 ， 理论物理， 2005， 硕士

【摘要】 1989年,Phoenix和Knight等人将熵理论应用于量子光学领域,研究光场与原子相互作用时的信息关联与演化,显示出很大的优越性。由于熵函数自动包含了量子系统密度矩阵的全部统计矩,它不仅是一种十分灵敏的量子态纯度的操作测量,还被用于描述量子系统的纠缠程度,同时也是解释量子系统动力学特性的重要工具,在量子信息领域有着广泛的应用。另一方面,原子—光场纠缠特性的研究对原子、光场量子态的制备以及原子和光场的量子信息和量子计算领域有着广泛的应用。近十五年来,人们对于标准JCM以及各种推广形式的JCM中熵动力学作了大量的研究。但是,目前这些研究工作的一个共同特点是:（1）原子与场的耦合系数简单地看作常数处理;（2）仅限于考虑原子运动与模结构的二能级原子的讨论。本文将从这两方面作有意义的扩展工作。 本文首先运用全量子理论,（1）导出了考虑原子运动的∧-型三能级原子与单模场在共振情况下相互作用系统中的波函数;借助远离共振的条件Δ>>|ω₁-ω₂|（即Δ>>0）,也推导出了考虑原子运动与模结构的简并拉曼耦合J-C模型中的波函数;（2）导出了在共振情况且原子-场耦合系数随时间线形变化时∨-型三能级原子与单模场相互作用系统中的波函数,也推导出了变耦合系数的简并拉曼耦合J-C模型中的波函数。然后,利用P-K熵理论,借助已导出的波函数,具体讨论了不同的初始光场、原子运动与模结构以及耦合系数的变化对原子—场相互作用中场（原子）熵的影响。 研究表明:（1）原子运动导致场熵演化具有周期性,这种周期性并不依赖场的统计分布和强度而是依赖于原子运动和模结构参数εp;（2）不论是共振情况还是远离共振情况,在选取合适的参数εp（这种选取在实验上是可能的）时,都能得到较长时间的纯态光场;（3）通过∧-型三能级原子与单模场相互作用的演化过程并不能直接产生薛定谔猫态;（4）初始光场统计性质的不同对场熵产生较大的影响;（5）线形调制使场熵呈现的完美周期性振荡遭到破坏,当原子-场耦合系数变化缓慢时,原子进入统计混合态的速度被减缓;而当原子-场耦更多还原

【Abstract】 In 1989,the entropy theory has been applied to quantum optics by Phoenix and Knight, they have shown the entropy theory is a convenient and sensitive measure of the information concerning and evolution about interaction of the field with the atom. Entropy not only is a very useful operational measureof the purity of the quantum state,which automatically includes all moments of the density operator,but is applied to describe the degree of entanglement in quantum system,so has a intensive use in quantum information.On the other hand,the study on the properties of the entanglement between the field and the atom will have a entensive use in performing quantum state about the field and the atom and the field and atom of quantum information and computing.Much study has been done on entropic dynamics in the JCM and all kinds of generalized JCM,since 15 years recently.But,at present a trait of these study work in commom is: (i) the atom-field coupling coefficients is simply regarded to a constant;(ii) only limited to the effects of atomic motion and field mode structure on the two-level atom.In this paper,a significative generalized work will be done from the two aspects.In this paper,at first,we bring to bear the full quantum theory,(i) to educe the wave function of the system considering the interaction of a ∧-type three-level moving atom with field under on-resonance condition And the wave function in degenerate raman process JCM considering atomic motion and field mode structure by using the far-off- resonance condition;(ii) to educe the wave function of the system considering the interaction of a V -type three-level atom with field with a time-dependent atom-field coupling under on-resonance condition and the wave function in degenerate raman process JCM with a time-dependent atom-field coupling. Second,we utilize entropy theory,in virtue of the wave function,the effects of the different initial field, the atomic motion and field-mode structure and the time-dependent atom-field couplingcoefficient on the field entropy is discussed at length.The results show that: (1) the atomic motion leads to the periodic evolution of the field entropy,this periodicity does not depend on the statistical distribution and the intensity of the initial field mode,but depends on the atomic velocity v,the length of the cavity L and the field-mode structure parameters p .(2) both on-resonance condition and far-off-resonance condition,when making a suitable choice for parameter sp (this choice is experimentally possible),we can get pure field state for a long time.(3) there are no Schrodinger-cat states in the evolution processes of interaction of the field with the A-type three-level atom.(4) the difference of initial field will produce great effect in field entropy.(5) the perfect periodicity of field entropy has been destroyed due the linear modulation, When the atom-field coupling coefficient changes slowly,the speed of atom entering the statistical state;When the atom-field coupling coefficient changes rapidly,the oscillating frequency of the evolution of entropy is fastened.更多还原