基于耦合腔—玻色—爱因斯坦凝聚系统的量子效应及其操控
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摘要
腔量子电动力学(腔QED)描述了物质与谐振装置中的电磁场的相干作用,是量子信息处理的理想平台。实验上,利用高品质的谐振腔实现了原子和谐振腔的强耦合。在强耦合区域,腔场光子逃逸出腔外前,该光子已和腔内原子进行了多次的相干作用。这对于量子态工程和量子信息处理是非常重要的,实现原子气体和谐振腔强耦合很困难,原因在于原子气体具有很多自由度而难以控制。幸运地是,稀薄原子气体的玻色-爱因斯坦凝聚(BEC)的实现解决了这个困难。BEC中,所有的原子都处于一个相同的量子态,这大大地减少了原子气体的自由度。BEC的运动甚至能用一个单模的物质波场描述。瑞士的Brennecke等人于2007年首次实现了BEC和一个高品质的法布里-珀罗腔光学腔的强耦合并且测量出这个耦合腔-BEC系统的能谱。从此耦合腔-BEC系统的研究成为一个热点课题。最近文献[Nature464,1301(2010)]报道了利用耦合腔-BEC系统模拟出了狄克模型中预言的狄克量子相变。本论文我们主要研究基于该耦合腔-BEC系统下的量子效应及其操控。
第一章我们主要介绍耦合腔-BEC系统的国内外研究现状以及它的研究意义。
第二章我们对耦合腔-BEC系统做一个简单的介绍。重点介绍基于二维耦合腔-BEC系统的狄克模型以及狄克量子相变。然后介绍一个基于一维耦合腔-BEC系统的玻色-哈伯德模型。
第三章我们研究了一个掺杂的耦合腔-BEC系统。基于该系统,提出一个广义的狄克模型-掺杂狄克模型,进而引入一个新的相变参数-杂质比特的布居差。发现杂质比特能够诱导耦合腔-BEC系统发生狄克量子相变。通过调节杂质比特的布居差,可以有效地降低光学腔与BEC发生狄克量子相变的临界耦合强度,这为方便地观察狄克量子相变以及研究狄克量子相变相关的量子效应提供了一个技术方案。
第四章我们研究了一个两量子比特-耦合腔-BEC复合系统。发现对于同时射入腔中且只和腔场相互作用的两个量子比特来说,耦合腔-BEC系统等效于一个可控的退相位环境。退相位的衰减因子正比于腔场光子数在狄克哈密顿量基态下的涨落。该光子数的涨落可通过泵浦光来调控。我们继而研究了两个无耦合的量子比特间的量子关联在退相位环境中的动力学行为。发现对于初始态为X-型的量子态,两个量子比特之间的量子关联在特定条件下能够随着时间的演化而稳定的放大。因此利用耦合腔-BEC系统能放大射入腔中的两量子比特间的量子关联。最后我们给出了腔场光子数涨落在腔与BEC整个耦合区域的解析表达式,发现腔场光子数涨落在量子相变点附近急剧地增大。因而调控耦合腔-BEC系统的相变参数能敏感地放大两个量子比特之间的量子关联。
第五章我们研究了光学腔中两分量的BEC在双势阱间的隧穿动力学。发现光学腔能够诱导出一个有效的隧穿强度。当每个分量的BEC引起腔场本征频率的移动量不同时,每个分量BEC的有效隧穿强度存在差异,且这种差异可通过泵浦光来调控。我们继而研究了两分量BEC的空间分离度、混合度以及纠缠动力学。发现当两分量BEC的隧穿强度存在差异且可调控时,在隧穿动力学过程中会出现很多新奇的量子效应,如两分量BEC在双势阱中的空间分离,两原子场模间纠缠的完全转移等。控制两分量BEC在双势阱间的隧穿强度可制备任意混合度的两分量BEC。这表明如果把其中的一个分量BEC看成杂质,腔-双势阱-两分量BEC系统可看成一个量子掺杂装置。
第六章我们对本论文做一个总结和展望。
Cavity quantum electrodynamics (Cavity QED) describes the coherent in-teraction between matter and electromagnetic field confined within a resonator structure, and is considered as a useful platform for quantum information process-ing. A strong coupling regime can be reached experimentally by using high-quality resonators. In the regime, atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in, which is very important for quantum state engineering and quantum information processing. However, the tremendous degree of freedom of atomic gases is very difficult to control. Fortu-nately, the realization of a Bose-Einstein condensate (BEC) in a dilute atomic gas makes up for this deficiency. For a BEC, all atoms occupy the same motional quan-tum state which can substantially reduce the number of degree of freedom. The BEC are even described by a single mode of a matter-wave field. Brennecke et al firstly achieved the strong coupling of a BEC to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This opens a window to simulate a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions. Re-cently, using a coupled cavity-BEC system has realized the Dick quantum phase transtion(QPT)[Nature464,1301(2010)]. In this thesis, we mainly investigate the quantum effects and their manipulation in the coupled cavity-BEC systems.
In chapter1, we introduce background materials about present subject under our consideration as well as the significance of the cavity-BEC systems.
In chapter2, we give a brief introduction about cavity-BEC systems. We put emphasis on introducing a Dicke model and its corresponding Dicke QPT, which based on a two-dimensional cavity-BEC systems. Then we have introduced a self- consistent Bose-Habbard model, which described a one-dimensional cavity-BEC systems.
In chapter3, we have investigated an impurity-doped cavity-BEC system. We have presented a new generalized Dicke model, an impurity-doped Dicke model to describe the system. It is shown that the impurity atom can induce Dicke QPT from the normalphase to superradiant phase at a critic value of the impurity population. It is revealed that the impurity-induced Dicke QPT can happen in an arbitrary coupling regime of the cavity field and atoms while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens the door to observing the Dicke QPT and studying new physics related to the Dicke QPT in new parameter regimes of the field-atom coupling.
In chapter4, we investigate a two qubits-coupled cavity-BEC system. For the two qubits that enter the cavity at the same time and only interact with the cavity filed, the coupled cavity-BEC system is equivalent to a controlled dephasing environment. The dephasing factor is proportional to the photon number fluctu-ation under the ground state of Dick Hamiltonian, which can be adjusted by the pump field. Then we have studied analytically the dynamic behaviors of quantum correlation measured by quantum discord between two uncoupled qubits, which are immersed in the dephasing environment. We show that the quantum discord of the two honinteracting qubits can be greatly amplified for certain initially pre-pared X-type states in the time evolution. Therefore, the coupled cavity-BEC can amplify the the quantum correlation of the two qubits. Finally, we obtain the an-alytical expression of the cavity photon number fluctuation in the full cavity-BEC coupling area. It is found that the cavity photon number fluctuation near the QPT point increases dramatically, which is the physical mechanism of the sensitive QD amplification.
In chapter5, we study tunneling dynamics of a two-component BEC coupled with an optical cavity, which are trapped in a dowble-well. We found the optical cavity can induce an effective tunneling strength. When the cavity frequency shifts induced by each component BEC are different, The difference of the effective tunneling strengths between the two-component BEC can be adjusted by the pump field. Then we studied the dynamics of the space separating degree, mixing degree and entanglement about the two-component BEC. It is found the difference of the effective tunneling strengths can induce a lot of novel quantum effects in the tunneling dynamics process, Such as space separation of the two-component BEC, completely transfer of the entanglement between the atomic field modes, etc. Arbitrary mixing degree of two component BEC can be prepared in the tunneling dynamics. This suggests that if one component BEC are considered as impurities, the cavity-double well-two-component BEC system can be used as a quantum impurity-doped device.
In chapter6, we present a summary and outlook.
第一章我们主要介绍耦合腔-BEC系统的国内外研究现状以及它的研究意义。
第二章我们对耦合腔-BEC系统做一个简单的介绍。重点介绍基于二维耦合腔-BEC系统的狄克模型以及狄克量子相变。然后介绍一个基于一维耦合腔-BEC系统的玻色-哈伯德模型。
第三章我们研究了一个掺杂的耦合腔-BEC系统。基于该系统,提出一个广义的狄克模型-掺杂狄克模型,进而引入一个新的相变参数-杂质比特的布居差。发现杂质比特能够诱导耦合腔-BEC系统发生狄克量子相变。通过调节杂质比特的布居差,可以有效地降低光学腔与BEC发生狄克量子相变的临界耦合强度,这为方便地观察狄克量子相变以及研究狄克量子相变相关的量子效应提供了一个技术方案。
第四章我们研究了一个两量子比特-耦合腔-BEC复合系统。发现对于同时射入腔中且只和腔场相互作用的两个量子比特来说,耦合腔-BEC系统等效于一个可控的退相位环境。退相位的衰减因子正比于腔场光子数在狄克哈密顿量基态下的涨落。该光子数的涨落可通过泵浦光来调控。我们继而研究了两个无耦合的量子比特间的量子关联在退相位环境中的动力学行为。发现对于初始态为X-型的量子态,两个量子比特之间的量子关联在特定条件下能够随着时间的演化而稳定的放大。因此利用耦合腔-BEC系统能放大射入腔中的两量子比特间的量子关联。最后我们给出了腔场光子数涨落在腔与BEC整个耦合区域的解析表达式,发现腔场光子数涨落在量子相变点附近急剧地增大。因而调控耦合腔-BEC系统的相变参数能敏感地放大两个量子比特之间的量子关联。
第五章我们研究了光学腔中两分量的BEC在双势阱间的隧穿动力学。发现光学腔能够诱导出一个有效的隧穿强度。当每个分量的BEC引起腔场本征频率的移动量不同时,每个分量BEC的有效隧穿强度存在差异,且这种差异可通过泵浦光来调控。我们继而研究了两分量BEC的空间分离度、混合度以及纠缠动力学。发现当两分量BEC的隧穿强度存在差异且可调控时,在隧穿动力学过程中会出现很多新奇的量子效应,如两分量BEC在双势阱中的空间分离,两原子场模间纠缠的完全转移等。控制两分量BEC在双势阱间的隧穿强度可制备任意混合度的两分量BEC。这表明如果把其中的一个分量BEC看成杂质,腔-双势阱-两分量BEC系统可看成一个量子掺杂装置。
第六章我们对本论文做一个总结和展望。
Cavity quantum electrodynamics (Cavity QED) describes the coherent in-teraction between matter and electromagnetic field confined within a resonator structure, and is considered as a useful platform for quantum information process-ing. A strong coupling regime can be reached experimentally by using high-quality resonators. In the regime, atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in, which is very important for quantum state engineering and quantum information processing. However, the tremendous degree of freedom of atomic gases is very difficult to control. Fortu-nately, the realization of a Bose-Einstein condensate (BEC) in a dilute atomic gas makes up for this deficiency. For a BEC, all atoms occupy the same motional quan-tum state which can substantially reduce the number of degree of freedom. The BEC are even described by a single mode of a matter-wave field. Brennecke et al firstly achieved the strong coupling of a BEC to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This opens a window to simulate a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions. Re-cently, using a coupled cavity-BEC system has realized the Dick quantum phase transtion(QPT)[Nature464,1301(2010)]. In this thesis, we mainly investigate the quantum effects and their manipulation in the coupled cavity-BEC systems.
In chapter1, we introduce background materials about present subject under our consideration as well as the significance of the cavity-BEC systems.
In chapter2, we give a brief introduction about cavity-BEC systems. We put emphasis on introducing a Dicke model and its corresponding Dicke QPT, which based on a two-dimensional cavity-BEC systems. Then we have introduced a self- consistent Bose-Habbard model, which described a one-dimensional cavity-BEC systems.
In chapter3, we have investigated an impurity-doped cavity-BEC system. We have presented a new generalized Dicke model, an impurity-doped Dicke model to describe the system. It is shown that the impurity atom can induce Dicke QPT from the normalphase to superradiant phase at a critic value of the impurity population. It is revealed that the impurity-induced Dicke QPT can happen in an arbitrary coupling regime of the cavity field and atoms while the Dicke QPT in the standard Dicke model occurs only in the strong coupling regime of the cavity field and atoms. This opens the door to observing the Dicke QPT and studying new physics related to the Dicke QPT in new parameter regimes of the field-atom coupling.
In chapter4, we investigate a two qubits-coupled cavity-BEC system. For the two qubits that enter the cavity at the same time and only interact with the cavity filed, the coupled cavity-BEC system is equivalent to a controlled dephasing environment. The dephasing factor is proportional to the photon number fluctu-ation under the ground state of Dick Hamiltonian, which can be adjusted by the pump field. Then we have studied analytically the dynamic behaviors of quantum correlation measured by quantum discord between two uncoupled qubits, which are immersed in the dephasing environment. We show that the quantum discord of the two honinteracting qubits can be greatly amplified for certain initially pre-pared X-type states in the time evolution. Therefore, the coupled cavity-BEC can amplify the the quantum correlation of the two qubits. Finally, we obtain the an-alytical expression of the cavity photon number fluctuation in the full cavity-BEC coupling area. It is found that the cavity photon number fluctuation near the QPT point increases dramatically, which is the physical mechanism of the sensitive QD amplification.
In chapter5, we study tunneling dynamics of a two-component BEC coupled with an optical cavity, which are trapped in a dowble-well. We found the optical cavity can induce an effective tunneling strength. When the cavity frequency shifts induced by each component BEC are different, The difference of the effective tunneling strengths between the two-component BEC can be adjusted by the pump field. Then we studied the dynamics of the space separating degree, mixing degree and entanglement about the two-component BEC. It is found the difference of the effective tunneling strengths can induce a lot of novel quantum effects in the tunneling dynamics process, Such as space separation of the two-component BEC, completely transfer of the entanglement between the atomic field modes, etc. Arbitrary mixing degree of two component BEC can be prepared in the tunneling dynamics. This suggests that if one component BEC are considered as impurities, the cavity-double well-two-component BEC system can be used as a quantum impurity-doped device.
In chapter6, we present a summary and outlook.
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