光场量子态制备与光阱下的超冷原子量子态特性研究
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摘要
光子和冷原子及其相互作用体系已成为量子调控、量子计算和量子信息等新兴技术最有效的载体之一。光学系统在量子信息中具有独特的优势，光场量子态及纠缠态的制备掀起了人们极大的研究热情。另一方面，激光冷却和俘获技术使得人们可以对囚禁冷原子的量子态进行精密操控，以玻色－爱因斯坦凝聚体（BEC）为代表的冷原子的量子态具有特殊性质，激光作用下BEC量子态的研究成为一个备受关注的问题。本论文的工作以研究量子态的制备和特性为主线，分别研究了非经典光场量子态及纠缠态的制备、光阱下囚禁超冷原子量子态的特性等，主要内容如下：
1）附加单光子相干态(SPACS)的实现，使人们观察到了光场量子态从量子领域逐渐过渡到经典领域行为的奇妙现象，对于深入探讨量子和经典领域的边界问题有特殊的价值和意义。我们设计了一个简单的光学方案来产生非经典量子态：附加光子相干态(PACS)，与此同时，在出射信号光路得到SPACS的时候，闲置光将塌缩到N-qubit离散变量纠缠态，进而提出了一个使SPACS制备几率得到有效提高的光学方案，该方案同样可以用于杂化纠缠态的制备中。
2）利用Mach-Zehnder干涉装置，设计了产生SPACS纠缠态的可行光学方案，此方案产生的type II杂化纠缠态不同于其他类型的杂化纠缠态，实现了真正意义上的连续变量和离散变量量子态的纠缠。在type II杂化纠缠态中，无法指出哪个是自旋（或宇称）比特，如果把经典连续变量量子态和量子离散变量量子态分别视为死猫和活猫的话，type II杂化纠缠态可以视为纠缠的薛定谔猫态。
3）理论分析了双阱中由远共振红失谐激光形成的弱耦合BEC的约瑟夫森效应，通过对BEC密度分布和布居振荡的数值分析，发现当改变红失谐激光的强度来调制双阱BEC时，将呈现出三阱凝聚体的约瑟夫森振荡现象。本工作提供了一个新的实现BEC弱耦合的可行方案，有助于实验观察约瑟夫森效应。
4）对由光晶格和谐振子势组成的联合囚禁势中的超冷玻色气体，分析了当仅仅保留谐振子势而关掉光晶格时其密度－密度关联的时间演化。研究表明，由于谐振子势的调制作用，密度－密度关联呈现出周期性时间演化行为，我们给出了解析形式的解，该结果与数值分析结果相吻合，该解析表示对于用空间量子噪声干涉法测量谐振子的频率有潜在应用价值。
As it is well known photons, ultra-cold atoms and their interacting systems havebeen the most efficient carriers of the newly developed techniques of quantum manipulation, quantum computation and quantum information. The preparation ofquantum states of optical field has drawn great interests since the optical field has many special advantages in carrying quantum information. On the other hand, the techniques of laser cooling and trapping cold atoms provide an opportunity to manipulate cold atoms including Bose-Einstein condensates (BEC). The research on the properties of quantum states of BEC modulated by lasers is becoming the focused problem recently. Our present study focuses on the preparation and the properties of quantum states, including the optical preparation of some non-classical quantum states and entangled state and the properties of the quantum states of ultra-cold atoms. The main contents are as follows:
1) The experimental realization of single-photon-added coherent state (SPACS) provides a tool to take a closer look at the evolution of the quantum-to-classical transition and as a starting point for the investigation of the fuzzy border that separates the quantum and classical regimes of light behavior. We proposed a simple scheme to generate a special non-classical quantum state: photon-added coherent state (PACS). When SPACS is observed in the output signal channel, we can simultaneously obtain the generalized N-qubit discrete variable entangled state. Therefore, we give a simple optical scheme to further enhance the success probability of the SPACS generation, which can also be used in the preparation of the hybrid entangled state.
2) Based on the Mach-Zehnder interferometer, we proposed a feasible scheme to generate the entangled SPACS, and then lead to generation of the novel hybrid entangled state(type II hybrid entangled state). Type II hybrid entangled state is different from any other hybrid entangled state, it realizes the entanglement of continuous-variable and discrete-variable quantum state. This hybrid entangled state can not be interpreted as the spin or the parity qubit. We can view the new hybrid entangled state as the entangled schr?dinger’s cat state if we define the classical-world continuous variable and the quantum-world discrete variable as the living-cat and dead-cat states, respectively.
3) We theoretically considered the Josephson effect of BEC with a weak link created by superposing a far-off-resonant red-detuned laser beam on a double-well potential. Thenumerical simulations of the density distribution and the population oscillation show that there is clear Josephson effect for this sort of three-well system when the intensity of the laser beam is modulated. Our present work gives a feasible scheme to study a new type ofweak link which is crucial to investigate experimentally the Josephson effect.
4) For ultra-cold Bose gases in a combined potential of a harmonic trap and an optical lattice, we considered the evolution of the density-density correlation after switching off the optical lattice alone. Our studies show that the density-density correlation exhibits a periodic evolution behavior because of the modulation of the harmonic trap. A simple analytical expression for the motion of the interference peaks in the density-density correlation is given, which agrees well with our numerical results. This analytical expression gives potential application of the measurement of the harmonic frequency based on spatial quantum noise interferometry.
1）附加单光子相干态(SPACS)的实现，使人们观察到了光场量子态从量子领域逐渐过渡到经典领域行为的奇妙现象，对于深入探讨量子和经典领域的边界问题有特殊的价值和意义。我们设计了一个简单的光学方案来产生非经典量子态：附加光子相干态(PACS)，与此同时，在出射信号光路得到SPACS的时候，闲置光将塌缩到N-qubit离散变量纠缠态，进而提出了一个使SPACS制备几率得到有效提高的光学方案，该方案同样可以用于杂化纠缠态的制备中。
2）利用Mach-Zehnder干涉装置，设计了产生SPACS纠缠态的可行光学方案，此方案产生的type II杂化纠缠态不同于其他类型的杂化纠缠态，实现了真正意义上的连续变量和离散变量量子态的纠缠。在type II杂化纠缠态中，无法指出哪个是自旋（或宇称）比特，如果把经典连续变量量子态和量子离散变量量子态分别视为死猫和活猫的话，type II杂化纠缠态可以视为纠缠的薛定谔猫态。
3）理论分析了双阱中由远共振红失谐激光形成的弱耦合BEC的约瑟夫森效应，通过对BEC密度分布和布居振荡的数值分析，发现当改变红失谐激光的强度来调制双阱BEC时，将呈现出三阱凝聚体的约瑟夫森振荡现象。本工作提供了一个新的实现BEC弱耦合的可行方案，有助于实验观察约瑟夫森效应。
4）对由光晶格和谐振子势组成的联合囚禁势中的超冷玻色气体，分析了当仅仅保留谐振子势而关掉光晶格时其密度－密度关联的时间演化。研究表明，由于谐振子势的调制作用，密度－密度关联呈现出周期性时间演化行为，我们给出了解析形式的解，该结果与数值分析结果相吻合，该解析表示对于用空间量子噪声干涉法测量谐振子的频率有潜在应用价值。
As it is well known photons, ultra-cold atoms and their interacting systems havebeen the most efficient carriers of the newly developed techniques of quantum manipulation, quantum computation and quantum information. The preparation ofquantum states of optical field has drawn great interests since the optical field has many special advantages in carrying quantum information. On the other hand, the techniques of laser cooling and trapping cold atoms provide an opportunity to manipulate cold atoms including Bose-Einstein condensates (BEC). The research on the properties of quantum states of BEC modulated by lasers is becoming the focused problem recently. Our present study focuses on the preparation and the properties of quantum states, including the optical preparation of some non-classical quantum states and entangled state and the properties of the quantum states of ultra-cold atoms. The main contents are as follows:
1) The experimental realization of single-photon-added coherent state (SPACS) provides a tool to take a closer look at the evolution of the quantum-to-classical transition and as a starting point for the investigation of the fuzzy border that separates the quantum and classical regimes of light behavior. We proposed a simple scheme to generate a special non-classical quantum state: photon-added coherent state (PACS). When SPACS is observed in the output signal channel, we can simultaneously obtain the generalized N-qubit discrete variable entangled state. Therefore, we give a simple optical scheme to further enhance the success probability of the SPACS generation, which can also be used in the preparation of the hybrid entangled state.
2) Based on the Mach-Zehnder interferometer, we proposed a feasible scheme to generate the entangled SPACS, and then lead to generation of the novel hybrid entangled state(type II hybrid entangled state). Type II hybrid entangled state is different from any other hybrid entangled state, it realizes the entanglement of continuous-variable and discrete-variable quantum state. This hybrid entangled state can not be interpreted as the spin or the parity qubit. We can view the new hybrid entangled state as the entangled schr?dinger’s cat state if we define the classical-world continuous variable and the quantum-world discrete variable as the living-cat and dead-cat states, respectively.
3) We theoretically considered the Josephson effect of BEC with a weak link created by superposing a far-off-resonant red-detuned laser beam on a double-well potential. Thenumerical simulations of the density distribution and the population oscillation show that there is clear Josephson effect for this sort of three-well system when the intensity of the laser beam is modulated. Our present work gives a feasible scheme to study a new type ofweak link which is crucial to investigate experimentally the Josephson effect.
4) For ultra-cold Bose gases in a combined potential of a harmonic trap and an optical lattice, we considered the evolution of the density-density correlation after switching off the optical lattice alone. Our studies show that the density-density correlation exhibits a periodic evolution behavior because of the modulation of the harmonic trap. A simple analytical expression for the motion of the interference peaks in the density-density correlation is given, which agrees well with our numerical results. This analytical expression gives potential application of the measurement of the harmonic frequency based on spatial quantum noise interferometry.
引文
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