原子—腔—场系统中量子纠缠信息交换、传递与保持的机理研究
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摘要
量子纠缠信息的交换、传递与保持问题,是当前量子光学与量子信息学领域的前沿重大课题之一,其成果在量子通信与量子光通信等高科技领域具有广阔的应用前景和重大的应用价值。本文利用全量子理论,对多种“原子-腔-场”相互作用系统中量子纠缠信息的交换、传递与保持问题进行了系统研究,由此获得了一系列既不同于现有报道又具有重要意义的新的结果和结论。本文的主要的研究结果如下:
1.采用数值计算的方法,研究了两个偶极-偶极相互作用的耦合双能级原子分别与单模奇相干态光场、单模偶相干态光场以及两态叠加单模Schr?dinger-cat态光场相互作用系统中原子与腔场之间的量子纠缠度的时间演化特征。结果表明,场-原子系统量子纠缠度的时间演化特性不仅与光场的初始平均光子数、场-原子之间的耦合强度、原子-原子之间的耦合强度以及频率失谐量等密切相关,而且还与原子的初始状态有关,并完全由这些因素共同决定。一般而言,纠缠度的时间演化普遍呈现出振荡性;并且在初始强场的条件下,场-原子之间的纠缠与退纠缠现象周期性的交替出现,且存在量子干涉现象;随着场-原子之间耦合强度的增大,量子纠缠不规则振荡的周期逐渐减小;当原子-原子之间耦合强度取某些定值时,量子纠缠度的时间演化会呈现出周期性的崩坍-回复现象,当原子-原子之间偶极-偶极相互作用较弱时,量子场熵演化规律与单光子J—C模型的情形相似,当偶极相互作用足够强时又与双光子J—C模型的特征相似。通过控制影响因素,尽可能使原子与光场较长时间处于较大程度的纠缠态,将有利于量子纠缠信息的传递。
2.建立了由多个相互独立的“原子-腔-场”相互作用系统的物理模型。利用全量子理论,分别研究了M个单原子分别与M个单(多)模光场依赖于强度耦合的单(多)光子相互作用过程、M个耦合双能级原子分别与M个单(多)模光场的单(多)光子相互作用过程,给出了不同情况下系统态矢的一般演化式,找到了利用原子-腔-场之间的相互作用过程来实现量子纠缠信息交换与传递的条件。结果发现:只要控制原子-腔场之间相互作用时间并使原子以特定速度穿过腔场,对于不同的模型有时还需要对出腔原子进行测量,并通过处于基态的原子与存储量子纠缠信息的腔场两者之间的相互作用最终使原子获得了量子纠缠信息。相反,纠缠原子中的量子纠缠信息也可传递给处于真空态的腔场。与此同时,作为“飞行的量子比特”的基态原子可将量子纠缠信息从一个腔场传递到另一个腔场。不仅如此,通过控制原子与腔场之间相互作用时间,也可使腔场或者原子初始量子纠缠信息被完全保持或部分保持。在不同的系统中,影响实现量子纠缠信息交换、传递与保持条件的因素各不相同。例如,通过对频率失谐量的控制,可使量子纠缠信息被完全交换、完全传递或完全保持,但原子之间的偶极相互作用会导致量子纠缠信息被非完全传递和非完全保持。由此可见:当处于基态的原子以特定速度通过处于量子纠缠态的腔场时,原子能够将光场的量子纠缠信息据为已有;反之,当纠缠原子以特定速度通过真空态腔场时,原子又能将自己携带的量子纠缠信息释放于腔场之中,这样便实现了原子-腔-场系统量子纠缠信息的交换与传递。研究还表明:利用原子能够捡起和释放量子纠缠信息的特点,可进一步实现腔-腔之间的异地量子纠缠信息的传递。
3.提出了由相干腔场与相干原子构成的综合物理模型,研究了相干原子束与单(多)模相干光场的单(多)光子的共振(非共振)相互作用过程,利用演化因子给出了相干原子束与相干腔场相互作用系统的演化规律。结果表明:腔场与原子相互作用过程中光场纠缠态与原子纠缠态可周期性地相互转换,这样便实现了量子纠缠信息的交换与传递。且其转换周期分别与原子-腔场之间相互作用的耦合强度g、相互作用时间t、原子(或光子湮灭)算符的复系数Aξ,k( Aη,k)、各模光场参与相互作用(或初始)的光子数N j, k( n j, k)以及光场所含的纵模数q等密切相关并完全由这些因素决定。研究还发现:在普遍情况下,量子纠缠信息交换与传递的条件分别与原子的跃迁频率ωa,k及其相对相位ξ、光场的频率ωf,k及其相对相位η、场-原子之间的耦合强度g以及场-原子相互作用时间t等均有关;但当原子与光场发生共振相互作用时,其条件仅与g、t有关。由此揭示出相干腔场与相干原子束相互作用过程中量子纠缠信息交换与传递的一般特征。另外,在适当条件下,原子纠缠态或光场纠缠态可以保持初态不变。在一定条件下,上述这些普遍性结果便过渡到了非相干原子与光场相互作用的特殊情形。
4.在考虑非线性效应的情况下,精确求解了由多个原子与多个腔场构成的联合系统态矢量随时间演化的一般表式,利用全量子理论并通过数值计算方法,详细研究了Kerr效应、Stark效应、以及虚光场效应对量子纠缠信息在原子与腔场之间周期性可逆交换与传递过程的影响。结果表明:①.Kerr介质对初始腔场为真空态或最低Fock态组成的纠缠态等一些特殊情形不产生任何影响,而对一般Fock态n k( n k≠0)都会改变其量子纠缠信息转换的相位和周期,且Kerr效应越强转换周期就越短,反之亦然,因此,通过选取不同Kerr介质并改变Kerr效应的强弱程度,可以控制量子纠缠信息交换与传递的快慢程度,还有,当考虑Kerr效应时,相位的改变也与腔场中光子数n k(k=1,2,3,…,M)的多少有关;②.Stark效应和初始场强对此过程也有着显著的影响:光场的量子纠缠程度会随着初始场强的增强而增大,在强场条件下,光场量子纠缠度可呈现出周期性的崩塌-回复现象,并且Stark移位参量越大,光场量子纠缠度振荡越剧烈,说明Stark效应破坏了光场量子纠缠度的时间稳定性;③.旋波近似对原子纠缠态与光场纠缠态两者之间的交换、传递与保持不产生任何影响;而在非旋波近似下,虚光场效应对纠缠态在腔场与原子之间相互转化的过程有着明显的影响:在光场纠缠信息传递给原子之后腔场并不能恢复到最初的真空态;伴随着纠缠态的转化和保持过程,相位有所改变并产生了多个干扰项。
In the present, the problems of exchange, transmission and maintain of quantum entangled information is always one of the foremost and important research topic in the regime of quantum optics and quantum informatics, its achievements is of broadening application prospects and great application values in the fields of Hi-technologies such as quantum optics and quantum informatics. In this thesis, the complete quantum theory is utilized to study the problems of exchange, transmission and maintain of quantum entangled information systematically within the various systems of atoms-cavities-fields interaction, and a series of new important research results is obtained that is rather different from the current scientific reports. The main research results are as follows:
1. By using numerical calculating method, the time evolution characteristic of quantum entanglement degree of different field-atom interaction systems are studied in detail, such as the two coupled two-level atoms with dipole-dipole interaction interacting with a single-mode odd coherent state light-field, interacting with a singled-mode even coherent state light-field, and interacting with two state superposition-a single-mode Schr?dinger-cat state light-field, respectively. It is showed that the time evolution properties of quantum entanglement degree of field-atom system are decided by such major factors as the initial mean photon-number of light-field, the coupled intensity between field-atom, the coupled intensity between atom-atom, the frequency detune, and the initial state of atom. In general, the time evolution of quantum entanglement degree can present the property of oscillation; under the condition of initial intensive-field, the phenomena of entanglement and disentanglement present periodically and alternatively, and the phenomenon of quantum interference follows in the same time; with the increasing of coupled intensity between field-atom, the anomalous oscillating period of quantum entanglement degree decreases gradually; if the coupled intensity between atom-atom is some certain and fixed value, the time evolution of quantum entanglement degree can display the phenomenon of periodical collapse-reversion, while the dipole-dipole interaction between atom-atom is weaker the time evolution characteristic of quantum field-entropy is similar to the situation of one-photon Jaynes-Cummings model, while it is strong enough that is very similar to the situation of two-photon Jaynes-Cummings model. From what had said above, we can see that it is possible to make atom and light-field staying in the maximum quantum entanglement state long time, which is benefited for the transmission of quantum entangled information.
2. The physical model of interaction system composed of multi-independent atom-cavity-field is established. The complete quantum theory is used to study the processes of M two-level atoms interacting with M single-model (or M multi-model) light-field with intensity-dependent coupling through one-photon (or any multi-photon) interaction, and M pairs of coupled two-level atoms interacting with M single-model (or M multi-model) light-field through one-photon (or any multi-photon) interaction, respectively. The general expressions evolving with time of the combined state vector of the systems mentioned is given in different situations, and the conditions to realize exchange and transfer of quantum entangled information by using the interaction process among atom-cavity-field are found out. It is found that the quantum entangled information of light-field can transfer to atom, by controlling the interacting time of atom-cavity-field system and the flying velocity of atom through cavity, and by the interaction between the atom stayed in the ground state initial and the cavity-field to be stored the quantum entangled information initially, for the different model the atom flying out of the cavity sometimes need to be detected; contrary, the quantum entangled information of atom stayed in the entangled state initially can also transfer to the cavity-field which is initially stayed in the vacuum state. Meanwhile, the ground atom as flying qubit can also transfer the quantum entangled information from one cavity to another. Otherwise, the initial quantum entanglement information possessed by cavity-field or atom can be maintained completely or partially, by controlling the interaction time between atom and cavity-field. For the different atom-cavity-field interaction system, the factors of condition to affect realizing exchange, transmission and maintain of quantum entangled information are rather different. For example, the quantum entangled information can be exchanged, transferred and maintained completely by controlling the frequency detuning, but the dipole-dipole interaction between the two coupled two-level atoms can lead the quantum entangled information to transfer and maintain incompletely. It can be seen that when the atom stayed in the ground state initially and flying at a fixed velocity passes through the cavity-field, it can possess the quantum entangled information of light-field; contrary, when atom stayed in quantum entangled state initially and flying at a fixed velocity passes through the vacuum state cavity-field, it can release its quantum entangled information to the cavity-field, so one can realize the exchange and transmission of quantum entangled information of atom-cavity-field system. By utilizing the properties of atom picking up and giving off quantum entangled information, one can further realize the transmission of that from one cavity to another.
3. The synthesized physical model consisting of coherent cavity-fields and coherent atoms is proposed, the processes of coherent atom-beam interacting with a single-model (or multi-model) coherent state light-field through one-photon (or any multi-photon) resonant and nonresonant interaction is researched, and the characteristic of time evolution on the system of coherent atom-beam interacting with coherent cavity-field is given by using time evolution operator. The results show that the cavity-field entangled state and the atom entangled state can convert periodically each other in the process of cavity-field interacting with atom, and this can realize the exchange and transmission of quantum entangled information. It is pointed out that transform period mentioned above is closely related to the following factors, such as the coupled-interacting between atom and cavity-field, the interacting time t, the complex probability amplitude Aξ,kof atomic operator, he complex probability amplitude Aη,k of photon annihilation operator, the photon-number N j, k and n j, k of interaction of each model light-field at initial time, and the total longitudinal mode number q, and so forth. It is also found that in general case, the condition of exchange and transmission of quantum entangled information are related to the circular frequencyωa,k of atomic transition and its relative phaseξ, to the circular frequencyωf ,k of light-field and its relative phaseη, and to coupled-intensity g and interaction time t between the cavity-field and atom, especially when atom interacting with cavity-field resonantly, the conditions mentioned are related to the parameter g and t too. Therefore the general characteristic of transferring the quantum entangled information is revealed in the process of coherent atom-beam interacting with coherent cavity-field. Under the proper condition, the initial atomic entangled state and the cavity-field entangled state cab be also maintained. So the results of incoherent interaction are only the specific examples of these universal results under different conditions.
4. Considering nonlinear optical effects, the combined system state vector is solved exactly, which is made up of multi-atoms interacting with multi-cavity-field and evolving with time. By utilizing the complete quantum theory and numerical calculating method, that the Kerr effect, Stark effect and the imaginary light-field effect have important influences upon the periodical exchange and transfer of quantum entangled information between atom and cavity-field are further studied systematically. It is found that①. Kerr media have no any influence upon the entangled state which is made of initial vacuum state cavity-field or entangled superposition state of the lowest Fock state, for the general Fock state n k( n k≠0), Kerr effect can change the phase and period of transferring quantum entangled information, and the intensive Kerr effect is, the shorter converting period, vice versa. So one can control the converting rate of exchange and transfer of quantum entangled information by changing the intensity of Kerr effect. Besides, when considering Kerr effect, the phase change is also related to the photon-number n k(k=1,2,3,…,M) within cavity.②. Stark effect and initial intensity of light-field have direct influence on exchange and transmission of that, the quantum entanglement degree of light-field can increase with increasing of initial light-field intensity, the quantum entanglement degree of light-field can also present the phenomenon of collapses-revivals periodically under the condition of intensive field, the greater the Stark drift, the faster the oscillation of quantum entanglement degree of light-field. So, it is show that the time stability of quantum entanglement degree of light-field is broken.③.The Rotating-Wave Approximation(RWA) has no any influences upon the exchange, transmission and maintain between atomic entangled state and cavity-field entangled state, but the imaginary light-field effect have evident influences upon the process of entangled state converting between cavity-field and atom under the condition without RWA. After the entangled information of cavity-field transmits to atom, it can not be restored to the initial vacuum state, and its phase is changed and many disturbance items appear in the processes of transforming and maintaining entangled state.
1.采用数值计算的方法,研究了两个偶极-偶极相互作用的耦合双能级原子分别与单模奇相干态光场、单模偶相干态光场以及两态叠加单模Schr?dinger-cat态光场相互作用系统中原子与腔场之间的量子纠缠度的时间演化特征。结果表明,场-原子系统量子纠缠度的时间演化特性不仅与光场的初始平均光子数、场-原子之间的耦合强度、原子-原子之间的耦合强度以及频率失谐量等密切相关,而且还与原子的初始状态有关,并完全由这些因素共同决定。一般而言,纠缠度的时间演化普遍呈现出振荡性;并且在初始强场的条件下,场-原子之间的纠缠与退纠缠现象周期性的交替出现,且存在量子干涉现象;随着场-原子之间耦合强度的增大,量子纠缠不规则振荡的周期逐渐减小;当原子-原子之间耦合强度取某些定值时,量子纠缠度的时间演化会呈现出周期性的崩坍-回复现象,当原子-原子之间偶极-偶极相互作用较弱时,量子场熵演化规律与单光子J—C模型的情形相似,当偶极相互作用足够强时又与双光子J—C模型的特征相似。通过控制影响因素,尽可能使原子与光场较长时间处于较大程度的纠缠态,将有利于量子纠缠信息的传递。
2.建立了由多个相互独立的“原子-腔-场”相互作用系统的物理模型。利用全量子理论,分别研究了M个单原子分别与M个单(多)模光场依赖于强度耦合的单(多)光子相互作用过程、M个耦合双能级原子分别与M个单(多)模光场的单(多)光子相互作用过程,给出了不同情况下系统态矢的一般演化式,找到了利用原子-腔-场之间的相互作用过程来实现量子纠缠信息交换与传递的条件。结果发现:只要控制原子-腔场之间相互作用时间并使原子以特定速度穿过腔场,对于不同的模型有时还需要对出腔原子进行测量,并通过处于基态的原子与存储量子纠缠信息的腔场两者之间的相互作用最终使原子获得了量子纠缠信息。相反,纠缠原子中的量子纠缠信息也可传递给处于真空态的腔场。与此同时,作为“飞行的量子比特”的基态原子可将量子纠缠信息从一个腔场传递到另一个腔场。不仅如此,通过控制原子与腔场之间相互作用时间,也可使腔场或者原子初始量子纠缠信息被完全保持或部分保持。在不同的系统中,影响实现量子纠缠信息交换、传递与保持条件的因素各不相同。例如,通过对频率失谐量的控制,可使量子纠缠信息被完全交换、完全传递或完全保持,但原子之间的偶极相互作用会导致量子纠缠信息被非完全传递和非完全保持。由此可见:当处于基态的原子以特定速度通过处于量子纠缠态的腔场时,原子能够将光场的量子纠缠信息据为已有;反之,当纠缠原子以特定速度通过真空态腔场时,原子又能将自己携带的量子纠缠信息释放于腔场之中,这样便实现了原子-腔-场系统量子纠缠信息的交换与传递。研究还表明:利用原子能够捡起和释放量子纠缠信息的特点,可进一步实现腔-腔之间的异地量子纠缠信息的传递。
3.提出了由相干腔场与相干原子构成的综合物理模型,研究了相干原子束与单(多)模相干光场的单(多)光子的共振(非共振)相互作用过程,利用演化因子给出了相干原子束与相干腔场相互作用系统的演化规律。结果表明:腔场与原子相互作用过程中光场纠缠态与原子纠缠态可周期性地相互转换,这样便实现了量子纠缠信息的交换与传递。且其转换周期分别与原子-腔场之间相互作用的耦合强度g、相互作用时间t、原子(或光子湮灭)算符的复系数Aξ,k( Aη,k)、各模光场参与相互作用(或初始)的光子数N j, k( n j, k)以及光场所含的纵模数q等密切相关并完全由这些因素决定。研究还发现:在普遍情况下,量子纠缠信息交换与传递的条件分别与原子的跃迁频率ωa,k及其相对相位ξ、光场的频率ωf,k及其相对相位η、场-原子之间的耦合强度g以及场-原子相互作用时间t等均有关;但当原子与光场发生共振相互作用时,其条件仅与g、t有关。由此揭示出相干腔场与相干原子束相互作用过程中量子纠缠信息交换与传递的一般特征。另外,在适当条件下,原子纠缠态或光场纠缠态可以保持初态不变。在一定条件下,上述这些普遍性结果便过渡到了非相干原子与光场相互作用的特殊情形。
4.在考虑非线性效应的情况下,精确求解了由多个原子与多个腔场构成的联合系统态矢量随时间演化的一般表式,利用全量子理论并通过数值计算方法,详细研究了Kerr效应、Stark效应、以及虚光场效应对量子纠缠信息在原子与腔场之间周期性可逆交换与传递过程的影响。结果表明:①.Kerr介质对初始腔场为真空态或最低Fock态组成的纠缠态等一些特殊情形不产生任何影响,而对一般Fock态n k( n k≠0)都会改变其量子纠缠信息转换的相位和周期,且Kerr效应越强转换周期就越短,反之亦然,因此,通过选取不同Kerr介质并改变Kerr效应的强弱程度,可以控制量子纠缠信息交换与传递的快慢程度,还有,当考虑Kerr效应时,相位的改变也与腔场中光子数n k(k=1,2,3,…,M)的多少有关;②.Stark效应和初始场强对此过程也有着显著的影响:光场的量子纠缠程度会随着初始场强的增强而增大,在强场条件下,光场量子纠缠度可呈现出周期性的崩塌-回复现象,并且Stark移位参量越大,光场量子纠缠度振荡越剧烈,说明Stark效应破坏了光场量子纠缠度的时间稳定性;③.旋波近似对原子纠缠态与光场纠缠态两者之间的交换、传递与保持不产生任何影响;而在非旋波近似下,虚光场效应对纠缠态在腔场与原子之间相互转化的过程有着明显的影响:在光场纠缠信息传递给原子之后腔场并不能恢复到最初的真空态;伴随着纠缠态的转化和保持过程,相位有所改变并产生了多个干扰项。
In the present, the problems of exchange, transmission and maintain of quantum entangled information is always one of the foremost and important research topic in the regime of quantum optics and quantum informatics, its achievements is of broadening application prospects and great application values in the fields of Hi-technologies such as quantum optics and quantum informatics. In this thesis, the complete quantum theory is utilized to study the problems of exchange, transmission and maintain of quantum entangled information systematically within the various systems of atoms-cavities-fields interaction, and a series of new important research results is obtained that is rather different from the current scientific reports. The main research results are as follows:
1. By using numerical calculating method, the time evolution characteristic of quantum entanglement degree of different field-atom interaction systems are studied in detail, such as the two coupled two-level atoms with dipole-dipole interaction interacting with a single-mode odd coherent state light-field, interacting with a singled-mode even coherent state light-field, and interacting with two state superposition-a single-mode Schr?dinger-cat state light-field, respectively. It is showed that the time evolution properties of quantum entanglement degree of field-atom system are decided by such major factors as the initial mean photon-number of light-field, the coupled intensity between field-atom, the coupled intensity between atom-atom, the frequency detune, and the initial state of atom. In general, the time evolution of quantum entanglement degree can present the property of oscillation; under the condition of initial intensive-field, the phenomena of entanglement and disentanglement present periodically and alternatively, and the phenomenon of quantum interference follows in the same time; with the increasing of coupled intensity between field-atom, the anomalous oscillating period of quantum entanglement degree decreases gradually; if the coupled intensity between atom-atom is some certain and fixed value, the time evolution of quantum entanglement degree can display the phenomenon of periodical collapse-reversion, while the dipole-dipole interaction between atom-atom is weaker the time evolution characteristic of quantum field-entropy is similar to the situation of one-photon Jaynes-Cummings model, while it is strong enough that is very similar to the situation of two-photon Jaynes-Cummings model. From what had said above, we can see that it is possible to make atom and light-field staying in the maximum quantum entanglement state long time, which is benefited for the transmission of quantum entangled information.
2. The physical model of interaction system composed of multi-independent atom-cavity-field is established. The complete quantum theory is used to study the processes of M two-level atoms interacting with M single-model (or M multi-model) light-field with intensity-dependent coupling through one-photon (or any multi-photon) interaction, and M pairs of coupled two-level atoms interacting with M single-model (or M multi-model) light-field through one-photon (or any multi-photon) interaction, respectively. The general expressions evolving with time of the combined state vector of the systems mentioned is given in different situations, and the conditions to realize exchange and transfer of quantum entangled information by using the interaction process among atom-cavity-field are found out. It is found that the quantum entangled information of light-field can transfer to atom, by controlling the interacting time of atom-cavity-field system and the flying velocity of atom through cavity, and by the interaction between the atom stayed in the ground state initial and the cavity-field to be stored the quantum entangled information initially, for the different model the atom flying out of the cavity sometimes need to be detected; contrary, the quantum entangled information of atom stayed in the entangled state initially can also transfer to the cavity-field which is initially stayed in the vacuum state. Meanwhile, the ground atom as flying qubit can also transfer the quantum entangled information from one cavity to another. Otherwise, the initial quantum entanglement information possessed by cavity-field or atom can be maintained completely or partially, by controlling the interaction time between atom and cavity-field. For the different atom-cavity-field interaction system, the factors of condition to affect realizing exchange, transmission and maintain of quantum entangled information are rather different. For example, the quantum entangled information can be exchanged, transferred and maintained completely by controlling the frequency detuning, but the dipole-dipole interaction between the two coupled two-level atoms can lead the quantum entangled information to transfer and maintain incompletely. It can be seen that when the atom stayed in the ground state initially and flying at a fixed velocity passes through the cavity-field, it can possess the quantum entangled information of light-field; contrary, when atom stayed in quantum entangled state initially and flying at a fixed velocity passes through the vacuum state cavity-field, it can release its quantum entangled information to the cavity-field, so one can realize the exchange and transmission of quantum entangled information of atom-cavity-field system. By utilizing the properties of atom picking up and giving off quantum entangled information, one can further realize the transmission of that from one cavity to another.
3. The synthesized physical model consisting of coherent cavity-fields and coherent atoms is proposed, the processes of coherent atom-beam interacting with a single-model (or multi-model) coherent state light-field through one-photon (or any multi-photon) resonant and nonresonant interaction is researched, and the characteristic of time evolution on the system of coherent atom-beam interacting with coherent cavity-field is given by using time evolution operator. The results show that the cavity-field entangled state and the atom entangled state can convert periodically each other in the process of cavity-field interacting with atom, and this can realize the exchange and transmission of quantum entangled information. It is pointed out that transform period mentioned above is closely related to the following factors, such as the coupled-interacting between atom and cavity-field, the interacting time t, the complex probability amplitude Aξ,kof atomic operator, he complex probability amplitude Aη,k of photon annihilation operator, the photon-number N j, k and n j, k of interaction of each model light-field at initial time, and the total longitudinal mode number q, and so forth. It is also found that in general case, the condition of exchange and transmission of quantum entangled information are related to the circular frequencyωa,k of atomic transition and its relative phaseξ, to the circular frequencyωf ,k of light-field and its relative phaseη, and to coupled-intensity g and interaction time t between the cavity-field and atom, especially when atom interacting with cavity-field resonantly, the conditions mentioned are related to the parameter g and t too. Therefore the general characteristic of transferring the quantum entangled information is revealed in the process of coherent atom-beam interacting with coherent cavity-field. Under the proper condition, the initial atomic entangled state and the cavity-field entangled state cab be also maintained. So the results of incoherent interaction are only the specific examples of these universal results under different conditions.
4. Considering nonlinear optical effects, the combined system state vector is solved exactly, which is made up of multi-atoms interacting with multi-cavity-field and evolving with time. By utilizing the complete quantum theory and numerical calculating method, that the Kerr effect, Stark effect and the imaginary light-field effect have important influences upon the periodical exchange and transfer of quantum entangled information between atom and cavity-field are further studied systematically. It is found that①. Kerr media have no any influence upon the entangled state which is made of initial vacuum state cavity-field or entangled superposition state of the lowest Fock state, for the general Fock state n k( n k≠0), Kerr effect can change the phase and period of transferring quantum entangled information, and the intensive Kerr effect is, the shorter converting period, vice versa. So one can control the converting rate of exchange and transfer of quantum entangled information by changing the intensity of Kerr effect. Besides, when considering Kerr effect, the phase change is also related to the photon-number n k(k=1,2,3,…,M) within cavity.②. Stark effect and initial intensity of light-field have direct influence on exchange and transmission of that, the quantum entanglement degree of light-field can increase with increasing of initial light-field intensity, the quantum entanglement degree of light-field can also present the phenomenon of collapses-revivals periodically under the condition of intensive field, the greater the Stark drift, the faster the oscillation of quantum entanglement degree of light-field. So, it is show that the time stability of quantum entanglement degree of light-field is broken.③.The Rotating-Wave Approximation(RWA) has no any influences upon the exchange, transmission and maintain between atomic entangled state and cavity-field entangled state, but the imaginary light-field effect have evident influences upon the process of entangled state converting between cavity-field and atom under the condition without RWA. After the entangled information of cavity-field transmits to atom, it can not be restored to the initial vacuum state, and its phase is changed and many disturbance items appear in the processes of transforming and maintaining entangled state.
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