發(fā)布時(shí)間：2018-07-08 10:49

  本文選題：Bose-Hubbard模型 + 分步絕熱合并��； 參考：《武漢大學(xué)》2017年碩士論文

【摘要】：玻色-愛(ài)因斯坦凝聚(Bose-Einstein condensate),簡(jiǎn)稱(chēng)BEC,是一種新奇的物質(zhì)形態(tài),此時(shí)凝聚態(tài)中的大部分粒子都處于相同的量子態(tài)。在BEC系統(tǒng)中,粒子之間的相互作用帶來(lái)許多有趣的現(xiàn)象,如粒子間自旋的交換,絕緣相和超流相之間的相變,渦旋現(xiàn)象等等。多體自旋單態(tài)是粒子總自旋為0,兩體糾纏度最大的量子態(tài)。多體自旋單態(tài)在量子模擬、量子計(jì)算、和高精密測(cè)量方向上有著非常寬廣的應(yīng)用。也可以利用它來(lái)解決一些沒(méi)有經(jīng)典解的問(wèn)題,如可以使用N粒子N能級(jí)的自旋單態(tài)來(lái)解決N陌生人問(wèn)題,秘密分享問(wèn)題和騙子檢測(cè)問(wèn)題。本文提出一種在光學(xué)超晶格中利用多個(gè)自旋為1,具有反鐵磁相互作用的粒子制備多體自旋單態(tài)的方法,并用通過(guò)數(shù)值模擬的方法給出結(jié)果。在第一章中,我們首先介紹了玻色-愛(ài)因斯坦凝聚現(xiàn)象的發(fā)展歷史和實(shí)驗(yàn)驗(yàn)證。其次介紹了光束縛和光阱的一些理論知識(shí)。最后介紹處理多體系統(tǒng)所用的理論方法,其中包括平均場(chǎng)理論方法和量子多體方法。在第二章中,我們首先介紹了我們所研究問(wèn)題的物理模型,即標(biāo)準(zhǔn)的Bose-Hubbard模型。其次細(xì)致介紹分步絕熱合并制備多體自旋單態(tài)的思想。第三章中我們對(duì)演化所需的條件進(jìn)行了討論。第四章中,我們首先給出數(shù)值模擬的結(jié)果,其次討論模擬條件在當(dāng)前實(shí)驗(yàn)中的可行性。由于光晶格勢(shì)阱在調(diào)節(jié)勢(shì)阱形狀、原子間相互作用形式等方面的優(yōu)良性質(zhì),我們選取雙勢(shì)阱的光晶格作為我們實(shí)驗(yàn)的單元。我們考慮多個(gè)自旋為1,具有反鐵磁相互作用的玻色子處于超光晶格中,數(shù)值模擬抬升勢(shì)阱,逐步絕熱合并的方法制備多粒子自旋單態(tài)。我們的模擬結(jié)果顯示,所制備的十六體自旋單態(tài)的保真度高達(dá)90%。同時(shí)我們給出了演化過(guò)程中廣義自旋壓縮參數(shù)隨時(shí)間變化的圖像,廣義自旋壓縮參數(shù)隨時(shí)間的奇偶性振蕩展示了它是一個(gè)很好的實(shí)驗(yàn)觀測(cè)量。廣義自旋壓縮參數(shù)對(duì)于確定實(shí)驗(yàn)中所制備的態(tài)是真正的自旋單態(tài)有著重要的標(biāo)識(shí)作用。最后,我們對(duì)模擬過(guò)程所選用的參數(shù)在實(shí)驗(yàn)上進(jìn)行了評(píng)估,所得結(jié)果展示了分步絕熱合并方法是一種可以在當(dāng)前實(shí)驗(yàn)條件下有效制備多體自旋單態(tài)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.
【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O469

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