本文選題：玻色-愛因斯坦凝聚 + Feshbach共振��； 參考：《東南大學(xué)》2017年碩士論文

【摘要】：自從玻色-愛因斯坦凝聚實(shí)現(xiàn)以來,超冷原子物理成為了熱門的研究領(lǐng)域之一。超冷原子體系是凝聚態(tài)物理和原子物理中研究的一項(xiàng)重要課題,它將用于原子干涉儀、冷原子鐘、量子計(jì)算機(jī)的開發(fā)以及實(shí)現(xiàn)。繼在光晶格中預(yù)言并且觀測(cè)到超冷原子的超流-莫特絕緣體相變之后,人們對(duì)光晶格中超冷原子系統(tǒng)中潛在的量子相做了大量的研究。本文基于擴(kuò)展的玻色-哈伯德模型,對(duì)非均勻光晶格中超冷玻色原子體系的基態(tài)做了研究,其中光晶格的非均勻性主要體現(xiàn)在以下兩個(gè)方面:一是額外施加一個(gè)諧振勢(shì);二是認(rèn)為光晶格不同格點(diǎn)上原子之間存在不同的相互作用。依據(jù)平均場(chǎng)近似以及數(shù)值對(duì)角化方法,計(jì)算了表征體系基態(tài)性質(zhì)的一些參數(shù),即平均粒子數(shù)以及序參量,結(jié)果表明在合適的參數(shù)下非均勻的光晶格中同時(shí)存在莫特絕緣相和超流相。全文共分五章,具體如下:第一章首先介紹了玻色-愛因斯坦凝聚的概念以及發(fā)展,然后詳細(xì)回顧了原子冷卻與囚禁技術(shù)和Feshbach共振技術(shù),最后簡(jiǎn)要概述了玻色-愛因斯坦凝聚的理論基礎(chǔ),即平均場(chǎng)理論和Gross-Pitaevskii方程。第二章描述了光晶格,量子相變的概念以及用來研究光晶格中超冷原子發(fā)生相變的模型。第三章研究了在外加諧振勢(shì)的二維正方光晶格中超冷原子系統(tǒng)的量子相變,首先推導(dǎo)出此體系的哈密頓量,進(jìn)一步通過平均場(chǎng)理論分離出單個(gè)格點(diǎn)的哈密頓量,最后用數(shù)值對(duì)角化方法得到系統(tǒng)的基態(tài),并分析相圖以及平均粒子數(shù)三維圖得出結(jié)論:莫特絕緣相與超流相共存于非均勻的光晶格中。第四章研究了在二維正方光晶格中存在非均勻的排斥相互作用的超冷原子系統(tǒng)的量子相變,運(yùn)用與第三章類似的方法,采用平均場(chǎng)近似方法分離出單個(gè)格點(diǎn)的哈密頓量并用數(shù)值對(duì)角化方法得到系統(tǒng)的基態(tài),最后分析相圖以及平均粒子數(shù)三維圖得出結(jié)論:莫特絕緣相與超流相共存于光晶格中。第五章對(duì)全文進(jìn)行了總結(jié)和展望。
[Abstract]:Since the realization of Bose-Einstein condensation, ultracold atomic physics has become one of the hot research fields.Ultracold atomic system is an important subject in condensed matter physics and atomic physics. It will be used in the development and implementation of atomic interferometer, cold atomic clock and quantum computer.Following the prediction and observation of superfluid-Mott insulator phase transitions of ultra-cold atoms in optical lattices, a great deal of research has been done on the potential quantum phases in ultralow atomic systems in optical lattices.Based on the extended Bose-Hubbard model, the ground state of the supercooled boson atom system in the inhomogeneous optical lattice is studied in this paper. The inhomogeneity of the optical lattice is mainly reflected in the following two aspects: first, an extra resonant potential is applied;The second is that there are different interactions between atoms at different lattice points in the optical lattice.Based on the mean field approximation and the numerical diagonalization method, some parameters representing the properties of the ground state of the system, namely, the average number of particles and the order parameters, are calculated.The results show that both Mott insulating phase and supercurrent phase exist in the non-uniform optical lattice under suitable parameters.In chapter 1, the concept and development of Bose-Einstein condensation are introduced, and then atomic cooling and trapping techniques and Feshbach resonance techniques are reviewed in detail.Finally, the theoretical basis of Bose-Einstein condensation, namely, mean field theory and Gross-Pitaevskii equation, is briefly summarized.In chapter 2, the concepts of optical lattice, quantum phase transition and the model used to study the phase transition of supercooled atoms in optical lattice are described.In chapter 3, the quantum phase transition of ultracold atomic system in two-dimensional square optical lattice with external resonance potential is studied. Firstly, the Hamiltonian of the system is derived, and the Hamiltonian of a single lattice is further separated by the mean field theory.Finally, the ground state of the system is obtained by numerical diagonalization, and the phase diagram and the three dimensional average particle number diagram are analyzed. It is concluded that the Mott insulated phase and the supercurrent phase coexist in the non-uniform optical lattice.In chapter 4, the quantum phase transition of ultracold atomic system with inhomogeneous repulsive interaction in two-dimensional square optical lattice is studied.The Hamiltonian of a single lattice point is separated by the mean field approximation method and the ground state of the system is obtained by numerical diagonalization. Finally, the phase diagram and the three dimensional figure of the average particle number are analyzed. It is concluded that the Mott insulated phase and the supercurrent phase coexist in the optical lattice.The fifth chapter summarizes and prospects the full text.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O469

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 陸青青;侯凈敏;;Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice[J];Communications in Theoretical Physics;2010年05期

2 張 禮;費(fèi)米原子對(duì)的玻色-愛因斯坦凝聚[J];物理與工程;2005年01期

3 尹瀾;玻色-愛因斯坦凝聚領(lǐng)域Feshbach共振現(xiàn)象研究進(jìn)展[J];物理;2004年08期

4 王謹(jǐn),詹明生,高克林;原子的玻色-愛因斯坦凝聚[J];大學(xué)物理;1998年06期

相關(guān)重要報(bào)紙文章 前4條

1 桂運(yùn)安;楊保國(guó);;中科大首次成功操控約600對(duì)量子比特[N];安徽日?qǐng)?bào);2016年

2 佘惠敏;楊保國(guó);;超冷原子光晶格量子計(jì)算獲重大突破[N];經(jīng)濟(jì)日?qǐng)?bào);2016年

3 馮志文;;微型化領(lǐng)域正迎來第三次革命[N];科技日?qǐng)?bào);2015年

4 姜澎;;為冷原子研究打開新視角[N];文匯報(bào);2016年

相關(guān)博士學(xué)位論文 前1條

1 張東方;~(87)Rb原子玻色—愛因斯坦凝聚的實(shí)現(xiàn)以及~6Li和~(40)K原子的激光冷卻[D];中國(guó)科學(xué)院研究生院(武漢物理與數(shù)學(xué)研究所);2016年

，

本文編號(hào)：1733504