利用双模腔QED和中性里德伯原子系统进行量子信息处理
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摘要
在本论文中，我们主要研究基于腔QED系统和中性里德伯原子系统的量子信息处理方案。在量子光学中，非经典光场通常由Wigner函数或者Glauber-Sudarshan P函数定义。非经典光场的特性（如压缩、光子亚泊松分布等）通常由Mandel Q因子、二阶关联函数等物理量描述。利用这些物理量，在第二章第一部分中，我们讨论了双模场与Λ型三能级原子相互作用系统的压缩性质、光子统计和Cauchy-Schwarz不等式的违背等，此外，我们研究了双模场的关联函数。在第二部分中，我们提出直接测量双模场Wigner函数的方案。在这个方案中，正交偏振腔模与强驱动多能级原子的相互作用可以用时间平均有效哈密顿来描述，该有效哈密顿与光子数算符对易。原子基态的探测几率直接给出相平面空间上一点的Wigner函数的大小，我们把它推广至光场的非破坏性测量。
一个原子穿过多个光学腔的实验装置可用于纠缠量子化腔场。量子计算的逻辑0和1可以分别由单光子的左旋偏振态和右旋偏振态表示。利用这个装置，在第三章中，我们首先讨论通过绝热演化制备四模光子纠缠态的方案。该方案对原子位置的浮动和激光脉冲精确度的微小变化不敏感。接着，我们讨论在经典场驱动下，原子通过两个独立的拉曼跃迁过程与两个正交偏振模同时耦合制备多个腔模一维团簇态的方案。在大失谐条件下，原子自发辐射对态制备的影响可以减弱。
第四章主要讨论原子比特团簇态的制备和量子逻辑门的实现。原子的超精细能级用于存储量子信息。为了制备原子团簇态，我们使用包含光子探测器的腔QED实验系统。如果在态制备过程中没有光子泄漏，系统的耗散动力学可以由非厄密哈密顿描述。光子探测事件最终用于确认实验过程的成功与否。在第二部分，我们指出基于完整的纠缠通道，两个远程量子比特的量子逻辑门可以通过纠缠交换和纠缠纯化实现。这个方案可以在各种物理系统中实现。利用囚禁原子作为物质比特，光子作为飞行比特，我们给出了在双模腔QED系统中实现该方案的例子。
第五章主要研究中性里德伯原子系统中量子逻辑门的实现。中性原子通过里德伯阻塞实现远距离相互作用。结合与经典类似的偶极相互作用和F rster相互作用，我们讨论了实现多比特量子相位门、两比特交换门、两比特几何相位门等几个方案。在这些方案中，原子都不需要单独控制。我们详细讨论了不完美里德伯阻塞、范德瓦尔斯弱相互作用和原子自发辐射对量子逻辑门保真度的影响。最后，我们对基于中性里德伯原子系统量子计算的可扩展性做了简要讨论。
In this thesis, we theoretically study the implementation of quantum informationprocessing in the realm of two-mode cavity QED system and neutral Rydberg atomsystem.
In quantum optics, the definition of nonclassical light can be given by the Wignerfunction or more generally the Glauber-Sudarshan P function. The typical features ofa nonclassical light, such as squeezing, photon sub-poisson distribution, are describedby physical quantities like Mandel Q factor, second-order correlation function. Bymaking use of them, in the first part of chapter2, we discuss squeezing, photonstatistics, and violation of Cauchy-Schwarz inequality of a two-mode field afterinteracting with a Λ-typed three-level atom. Correlation between the two cavitymodes is also investigated. In the second part of chapter2, we propose a scheme fordirectly measuring the Wigner function of a two-mode field. In this scheme, the twoorthogonal polarized cavity modes dispersively coupling to a strongly drivenmultilevel atom is described by a time-averaged effective Hamiltonian that iscommuted with photon number operator. We show that the probability of detecting theatom in the ground state directly refers to the relevant value of Wigner function in thephase space. It is then generalized for quantum nondemolition measurements ofphotons.
A setup with an atom passing through multiple cavities can be used for entanglingquantized cavity fields. The quantum computational logic0and1can be encoded inthe left-circularly polarized state and right-circularly polarized state of a single photon,respectively. Using this kind of setup, in chapter3, we firstly present a scheme forpreparing four-mode entangled state through adiabatic passage. The nice feature ofour scheme is the insensitivity of the fluctuation of atomic position and theimprecision of laser pulses. Then, we propose that a one-dimensional cluster state formultiple cavity fields can be prepared in a way that an atom couples to bothorthogonal polarized cavity modes through two independent Raman transitionchannels assisted by an external driving laser. Decoherence due to atomic spontaneousemission can be reduced with the atom-cavity interaction being in the large-detuningregime.
Chapter4discusses the preparation of cluster state and implementation ofquantum logic gate for atoms in two-mode cavity QED system. Long-lived hyperfineground states of the atoms are used for storing quantum information. To prepareatomic cluster state, we use a cavity QED setup where photons leaking out of thecavity are collected by a photon detector. The dissipative dynamics in this system canbe described by a non-Hermitian Hamiltonian if there is not photon detected duringthe preparation process. The photon click incident can be finally used for confirmingthe successful events in the experiment. We show that the fidelity of prepared state isinsensitive to inefficiency of the photon detector. In the second part, based onwell-established entanglement channels, we show that a remote quantum phase gatecan be implemented between two distant qubits via entanglement swapping andentanglement purification. This protocol can be realized in different kinds of physicalsystems. To be specific, we give a brief example for its realization in two-mode cavityQED system, using trapped atoms as material qubits and photons as flying qubits.
In chapter5, we focus on implementation of quantum logic gates in neutralRydberg atom system. The long range interaction between distant neutral atoms isinduced by Rydberg blockade mechanism. Combining classical-like dipolarinteraction and F rster interaction we propose three schemes for implementing amulti-qubit quantum phase gate, a two-qubit quantum swap gate, and a two-qubitgeometric phase gate, respectively. Individual atom addressing are not involved in ourproposals. The effect of imperfect Rydberg blockade, perturbation of van der waalsinteraction and atomic spontaneous emission on gate fidelity are discussed in detailed.The scalability of quantum computation based on neutral Rydberg atom system is alsobriefly commented.
一个原子穿过多个光学腔的实验装置可用于纠缠量子化腔场。量子计算的逻辑0和1可以分别由单光子的左旋偏振态和右旋偏振态表示。利用这个装置，在第三章中，我们首先讨论通过绝热演化制备四模光子纠缠态的方案。该方案对原子位置的浮动和激光脉冲精确度的微小变化不敏感。接着，我们讨论在经典场驱动下，原子通过两个独立的拉曼跃迁过程与两个正交偏振模同时耦合制备多个腔模一维团簇态的方案。在大失谐条件下，原子自发辐射对态制备的影响可以减弱。
第四章主要讨论原子比特团簇态的制备和量子逻辑门的实现。原子的超精细能级用于存储量子信息。为了制备原子团簇态，我们使用包含光子探测器的腔QED实验系统。如果在态制备过程中没有光子泄漏，系统的耗散动力学可以由非厄密哈密顿描述。光子探测事件最终用于确认实验过程的成功与否。在第二部分，我们指出基于完整的纠缠通道，两个远程量子比特的量子逻辑门可以通过纠缠交换和纠缠纯化实现。这个方案可以在各种物理系统中实现。利用囚禁原子作为物质比特，光子作为飞行比特，我们给出了在双模腔QED系统中实现该方案的例子。
第五章主要研究中性里德伯原子系统中量子逻辑门的实现。中性原子通过里德伯阻塞实现远距离相互作用。结合与经典类似的偶极相互作用和F rster相互作用，我们讨论了实现多比特量子相位门、两比特交换门、两比特几何相位门等几个方案。在这些方案中，原子都不需要单独控制。我们详细讨论了不完美里德伯阻塞、范德瓦尔斯弱相互作用和原子自发辐射对量子逻辑门保真度的影响。最后，我们对基于中性里德伯原子系统量子计算的可扩展性做了简要讨论。
In this thesis, we theoretically study the implementation of quantum informationprocessing in the realm of two-mode cavity QED system and neutral Rydberg atomsystem.
In quantum optics, the definition of nonclassical light can be given by the Wignerfunction or more generally the Glauber-Sudarshan P function. The typical features ofa nonclassical light, such as squeezing, photon sub-poisson distribution, are describedby physical quantities like Mandel Q factor, second-order correlation function. Bymaking use of them, in the first part of chapter2, we discuss squeezing, photonstatistics, and violation of Cauchy-Schwarz inequality of a two-mode field afterinteracting with a Λ-typed three-level atom. Correlation between the two cavitymodes is also investigated. In the second part of chapter2, we propose a scheme fordirectly measuring the Wigner function of a two-mode field. In this scheme, the twoorthogonal polarized cavity modes dispersively coupling to a strongly drivenmultilevel atom is described by a time-averaged effective Hamiltonian that iscommuted with photon number operator. We show that the probability of detecting theatom in the ground state directly refers to the relevant value of Wigner function in thephase space. It is then generalized for quantum nondemolition measurements ofphotons.
A setup with an atom passing through multiple cavities can be used for entanglingquantized cavity fields. The quantum computational logic0and1can be encoded inthe left-circularly polarized state and right-circularly polarized state of a single photon,respectively. Using this kind of setup, in chapter3, we firstly present a scheme forpreparing four-mode entangled state through adiabatic passage. The nice feature ofour scheme is the insensitivity of the fluctuation of atomic position and theimprecision of laser pulses. Then, we propose that a one-dimensional cluster state formultiple cavity fields can be prepared in a way that an atom couples to bothorthogonal polarized cavity modes through two independent Raman transitionchannels assisted by an external driving laser. Decoherence due to atomic spontaneousemission can be reduced with the atom-cavity interaction being in the large-detuningregime.
Chapter4discusses the preparation of cluster state and implementation ofquantum logic gate for atoms in two-mode cavity QED system. Long-lived hyperfineground states of the atoms are used for storing quantum information. To prepareatomic cluster state, we use a cavity QED setup where photons leaking out of thecavity are collected by a photon detector. The dissipative dynamics in this system canbe described by a non-Hermitian Hamiltonian if there is not photon detected duringthe preparation process. The photon click incident can be finally used for confirmingthe successful events in the experiment. We show that the fidelity of prepared state isinsensitive to inefficiency of the photon detector. In the second part, based onwell-established entanglement channels, we show that a remote quantum phase gatecan be implemented between two distant qubits via entanglement swapping andentanglement purification. This protocol can be realized in different kinds of physicalsystems. To be specific, we give a brief example for its realization in two-mode cavityQED system, using trapped atoms as material qubits and photons as flying qubits.
In chapter5, we focus on implementation of quantum logic gates in neutralRydberg atom system. The long range interaction between distant neutral atoms isinduced by Rydberg blockade mechanism. Combining classical-like dipolarinteraction and F rster interaction we propose three schemes for implementing amulti-qubit quantum phase gate, a two-qubit quantum swap gate, and a two-qubitgeometric phase gate, respectively. Individual atom addressing are not involved in ourproposals. The effect of imperfect Rydberg blockade, perturbation of van der waalsinteraction and atomic spontaneous emission on gate fidelity are discussed in detailed.The scalability of quantum computation based on neutral Rydberg atom system is alsobriefly commented.
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