在光学超晶格中高效制备多体自旋单态

发布时间：2018-07-08 10:49

本文选题：Bose-Hubbard模型 + 分步绝热合并　；参考：《武汉大学》2017年硕士论文

【摘要】：玻色-爱因斯坦凝聚(Bose-Einstein condensate),简称BEC,是一种新奇的物质形态,此时凝聚态中的大部分粒子都处于相同的量子态。在BEC系统中,粒子之间的相互作用带来许多有趣的现象,如粒子间自旋的交换,绝缘相和超流相之间的相变,涡旋现象等等。多体自旋单态是粒子总自旋为0,两体纠缠度最大的量子态。多体自旋单态在量子模拟、量子计算、和高精密测量方向上有着非常宽广的应用。也可以利用它来解决一些没有经典解的问题,如可以使用N粒子N能级的自旋单态来解决N陌生人问题,秘密分享问题和骗子检测问题。本文提出一种在光学超晶格中利用多个自旋为1,具有反铁磁相互作用的粒子制备多体自旋单态的方法,并用通过数值模拟的方法给出结果。在第一章中,我们首先介绍了玻色-爱因斯坦凝聚现象的发展历史和实验验证。其次介绍了光束缚和光阱的一些理论知识。最后介绍处理多体系统所用的理论方法,其中包括平均场理论方法和量子多体方法。在第二章中,我们首先介绍了我们所研究问题的物理模型,即标准的Bose-Hubbard模型。其次细致介绍分步绝热合并制备多体自旋单态的思想。第三章中我们对演化所需的条件进行了讨论。第四章中,我们首先给出数值模拟的结果,其次讨论模拟条件在当前实验中的可行性。由于光晶格势阱在调节势阱形状、原子间相互作用形式等方面的优良性质,我们选取双势阱的光晶格作为我们实验的单元。我们考虑多个自旋为1,具有反铁磁相互作用的玻色子处于超光晶格中,数值模拟抬升势阱,逐步绝热合并的方法制备多粒子自旋单态。我们的模拟结果显示,所制备的十六体自旋单态的保真度高达90%。同时我们给出了演化过程中广义自旋压缩参数随时间变化的图像,广义自旋压缩参数随时间的奇偶性振荡展示了它是一个很好的实验观测量。广义自旋压缩参数对于确定实验中所制备的态是真正的自旋单态有着重要的标识作用。最后,我们对模拟过程所选用的参数在实验上进行了评估,所得结果展示了分步绝热合并方法是一种可以在当前实验条件下有效制备多体自旋单态的方法。
[Abstract]:Bose-Einstein condensate), is a novel material form in which most particles in condensed matter are in the same quantum state. In bec system, the interaction between particles leads to many interesting phenomena, such as the spin exchange between particles, the phase transition between insulating phase and supercurrent phase, the vortex phenomenon and so on. The multibody spin single state is a quantum state in which the total spin of particles is 0 and the entanglement of two bodies is the greatest. Multibody spin single states are widely used in quantum simulation, quantum computation, and high precision measurement. It can also be used to solve some problems without classical solutions, such as the problem of N strangers, secret sharing and fraud detection by using the spin state of N level of N particle. In this paper, we present a method of preparing multibody spin single states in optical superlattices by using a number of particles with antiferromagnetic interaction. The results are obtained by numerical simulation. In the first chapter, we first introduce the development history and experimental verification of Bose-Einstein condensation. Secondly, some theoretical knowledge of optical binding and optical trap are introduced. Finally, the theoretical methods used to deal with multibody systems, including mean field theory and quantum multibody method, are introduced. In the second chapter, we first introduce the physical model of the problem we study, that is, the standard Bose-Hubbard model. Secondly, the idea of preparing multi-body spin single states by step adiabatic combination is introduced in detail. In the third chapter, we discuss the necessary conditions for evolution. In chapter 4, we first give the results of numerical simulation, and then discuss the feasibility of simulation conditions in current experiments. Due to the excellent properties of the optical lattice potential well in regulating the shape of the potential well and the form of interaction between atoms, we select the optical lattice of the double potential well as our experimental unit. We consider that several bosons with antiferromagnetic interaction are in superoptical lattices. We numerically simulate the lifting of potential wells and fabricate multi-particle spin single states by means of gradual adiabatic combination. Our simulation results show that the fidelity of the hexadecimal spin single states is as high as 90%. At the same time, we give the image of the variation of generalized spin compression parameters with time during the evolution process. The odd-even oscillation of generalized spin compression parameters with time shows that it is a good experimental observation. The generalized spin squeezing parameters play an important role in determining that the state prepared in the experiment is a true spin single state. Finally, the parameters selected for the simulation process are evaluated experimentally. The results show that the step adiabatic combination method is an effective method for the preparation of multibody spin single states under the current experimental conditions.
【学位授予单位】：武汉大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469

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