超冷原子氣體中的拓?fù)鋺B(tài)：非常規(guī)晶格與相互作用效應(yīng)
發(fā)布時(shí)間：2018-09-17 06:56
【摘要】：在這篇論文中,我們描述了對于超冷原子氣體體系中拓?fù)鋺B(tài)的三個(gè)研究工作.在前兩個(gè)工作中,我們分別提出了兩個(gè)在超冷原子體系中合成二維拓?fù)渚Ц竦膶?shí)驗(yàn)方案.在第三個(gè)工作中,我們描述了用極化偶極費(fèi)米氣體實(shí)現(xiàn)一維拓?fù)涑瑢?dǎo)體(Kitaev鏈)的方案,并著重研究了其中的相互作用效應(yīng).在第一個(gè)工作中,我們提出了一種基于相位刻印技術(shù),用磁場脈沖序列來合成拓?fù)浞瞧接沟拇啪Ц竦膶?shí)驗(yàn)方案.這個(gè)方案生成的等效哈密頓量,在絕熱極限下可以映射到Haldane的拓?fù)潢惤^緣體模型.通過調(diào)節(jié)磁場參數(shù),我們可以驅(qū)動哈密頓量的最低能帶發(fā)生一個(gè)由拓?fù)潢惤^緣體到拓?fù)淦接沟慕^緣體之間的拓?fù)湎嘧?在相變點(diǎn)附近可以實(shí)現(xiàn)拓?fù)淦綆?在第二個(gè)工作中,我們提出了用調(diào)幅的Raman激光以及射頻磁場來生成具有拓?fù)浞瞧接鼓軒ЫY(jié)構(gòu)的光通量晶格的實(shí)驗(yàn)方案.這個(gè)方案合成的不含時(shí)的等效哈密頓量的最低能帶的拓?fù)湫再|(zhì)依賴于Raman激光以及射頻磁場的強(qiáng)度.我們考察了不同的Raman激光以及射頻磁場強(qiáng)度下,等效哈密頓量的能帶以及相應(yīng)的陳數(shù),并由此得到了系統(tǒng)在單填充下的基態(tài)相圖.在相圖中包含三個(gè)不同的相:拓?fù)潢惤^緣體相,正常絕緣體相,以及半金屬相.這個(gè)方案同樣可以實(shí)現(xiàn)Haldane模型,拓?fù)湎嘧?以及拓?fù)淦綆?在第三個(gè)工作中,我們描述了用極化偶極費(fèi)米氣體實(shí)現(xiàn)一維相互作用拓?fù)涑瑢?dǎo)體的方案.我們用嚴(yán)格對角化的數(shù)值方法計(jì)算了相互作用下系統(tǒng)的能譜,并由此得到了以相互作用強(qiáng)度以及化學(xué)勢為參數(shù)的基態(tài)相圖.相圖中包含五個(gè)相:填充數(shù)為一的絕緣體相,填充數(shù)為零的真空相,填充數(shù)為1/2的Mott絕緣體相,拓?fù)涑瑢?dǎo)體相,以及Luttinger液體相.我們用基態(tài)能隙,保真度極化率,基態(tài)粒子數(shù)宇稱,以及基態(tài)的壓縮率等物理量描述了基態(tài)不同相的性質(zhì).我們計(jì)算了相互作用下的Majorana零模波函數(shù),描述了基態(tài)的糾纏性質(zhì)(糾纏譜,糾纏熵,中心荷),并且通過有限尺寸標(biāo)度的方法證實(shí)了Luttinger液體態(tài)元激發(fā)無能隙的特性.
[Abstract]:In this paper, we describe three studies of topological states in supercooled atomic gas systems. In the first two works, we have proposed two experimental schemes for the synthesis of two-dimensional topological lattices in ultra-cold atomic systems. In the third work, we describe the scheme of using polarized dipole Fermi gas to realize one-dimensional topological superconductors (Kitaev chains), and focus on the study of the interaction effect. In the first work, we propose an experimental scheme for the synthesis of topological nonmediocre magnetic lattices using magnetic pulse sequences based on phase lithography. The equivalent Hamiltonian generated by this scheme can be mapped to Haldane's topological old insulator model under adiabatic limit. By adjusting the magnetic field parameters, we can drive the lowest energy band of Hamiltonian to take place a topological phase transition between the topological Chen insulator and the topological mediocre insulator. The topological flat band can be realized near the phase transition point. In the second work, we propose an experimental scheme for the generation of luminous flux lattices with topologically nonmediocre band structures using amplitude modulated Raman lasers and RF magnetic fields. The topological properties of the minimum energy band of the time-free equivalent Hamiltonian synthesized by this scheme depend on the intensity of Raman laser and RF magnetic field. We investigate the energy bands of equivalent Hamiltonian and the corresponding aging numbers at different Raman laser and RF magnetic field intensities, and obtain the ground state phase diagram of the system under single filling. There are three different phases in the phase diagram: topological old insulator phase, normal insulator phase, and semi-metallic phase. This scheme can also achieve Haldane model, topological phase transition, and topological flat band. In the third work, we describe the scheme of one-dimensional interacting topological superconductors using polarized dipole Fermi gas. The energy spectrum of the system under interaction is calculated by strictly diagonalized numerical method, and the ground state diagram with the interaction intensity and chemical potential as parameters is obtained. There are five phases in the phase diagram: the insulator phase with one filling number, the vacuum phase with zero filling number, the Mott insulator phase with 1 / 2 filling number, the topological superconductor phase and the Luttinger liquid phase. The properties of different phases in the ground state are described by means of the ground state energy gap, the fidelity polarizability, the parity of the ground state population and the squeezing ratio of the ground state. We calculate the Majorana zero-mode wave function under the interaction, describe the entanglement properties of the ground state (entanglement spectrum, entanglement entropy, central charge), and prove the characteristics of the Luttinger liquid state element excited without energy gap by the finite scale method.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O469
[Abstract]:In this paper, we describe three studies of topological states in supercooled atomic gas systems. In the first two works, we have proposed two experimental schemes for the synthesis of two-dimensional topological lattices in ultra-cold atomic systems. In the third work, we describe the scheme of using polarized dipole Fermi gas to realize one-dimensional topological superconductors (Kitaev chains), and focus on the study of the interaction effect. In the first work, we propose an experimental scheme for the synthesis of topological nonmediocre magnetic lattices using magnetic pulse sequences based on phase lithography. The equivalent Hamiltonian generated by this scheme can be mapped to Haldane's topological old insulator model under adiabatic limit. By adjusting the magnetic field parameters, we can drive the lowest energy band of Hamiltonian to take place a topological phase transition between the topological Chen insulator and the topological mediocre insulator. The topological flat band can be realized near the phase transition point. In the second work, we propose an experimental scheme for the generation of luminous flux lattices with topologically nonmediocre band structures using amplitude modulated Raman lasers and RF magnetic fields. The topological properties of the minimum energy band of the time-free equivalent Hamiltonian synthesized by this scheme depend on the intensity of Raman laser and RF magnetic field. We investigate the energy bands of equivalent Hamiltonian and the corresponding aging numbers at different Raman laser and RF magnetic field intensities, and obtain the ground state phase diagram of the system under single filling. There are three different phases in the phase diagram: topological old insulator phase, normal insulator phase, and semi-metallic phase. This scheme can also achieve Haldane model, topological phase transition, and topological flat band. In the third work, we describe the scheme of one-dimensional interacting topological superconductors using polarized dipole Fermi gas. The energy spectrum of the system under interaction is calculated by strictly diagonalized numerical method, and the ground state diagram with the interaction intensity and chemical potential as parameters is obtained. There are five phases in the phase diagram: the insulator phase with one filling number, the vacuum phase with zero filling number, the Mott insulator phase with 1 / 2 filling number, the topological superconductor phase and the Luttinger liquid phase. The properties of different phases in the ground state are described by means of the ground state energy gap, the fidelity polarizability, the parity of the ground state population and the squeezing ratio of the ground state. We calculate the Majorana zero-mode wave function under the interaction, describe the entanglement properties of the ground state (entanglement spectrum, entanglement entropy, central charge), and prove the characteristics of the Luttinger liquid state element excited without energy gap by the finite scale method.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O469
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