费米气体在光晶格中的自俘获现象及其周期调制

研究了一维光晶格中费米气体从BCS区过渡到unitarity区研究相图及周期调制现象. 通过调节散射长度与耠合系数对相图的影响, 发现在unitarity 区, 从约瑟夫振荡到振荡自俘获及振荡自俘获到自俘获, 存在耦合系数的临界值, 同时得到了临界耦合系数与散射长度的关系. 关键词： 费米气体 自俘获 周期调制     

玻色-费米超流混合体系中的相互作用调制隧穿动力学

研究了玻色-费米超流混合体系中的相互作用调制隧穿动力学特性,其中玻色子位于对称双势阱中,费米子位于对称双势阱中心的简谐势阱中.采用双模近似方法得到描述双势阱玻色-爱因斯坦凝聚的动力学特性方程组,并将其与简谐势阱中分子玻色-爱因斯坦凝聚的Gross-Pitaevskii方程进行耦合.通过对不同参数下玻色-费米混合体系中的隧穿现象进行数值研究,发现简谐势阱中费米子与双势阱中玻色子的相互作用使双势阱玻色-爱因斯坦凝聚的隧穿动力学特性更加丰富.不但驱使双势阱中玻色-爱因斯坦凝聚从类约瑟夫森振荡转变为宏观量子自囚禁,而且宏观量子自囚禁表现为三种不同的形式:相位与时间呈负相关并随时间单调减小的自囚禁、相位随时间演化有界的自囚禁以及相位与时间呈正相关并随时间单调增大的自囚禁.     

双势阱玻色-爱因斯坦凝聚体系的自俘获现象及其周期调制效应

研究了双势阱玻色-爱因斯坦凝聚体系(BEC)的自俘获现象(self-trapping). 在平均场近似下通过相平面(phase space)分析的方法研究了两种自俘获的机理：1)势阱中的粒子数在平衡位置附近振动，而相对相位随时间单调变化(running-phase); 2) 势阱中的粒子数和相对相位都在平衡点附近振动. 研究了周期调制场对自俘获现象的影响，发现发生自俘获现象的相变参数能够被周期场非常有效的调制，从而在弱相互作用BEC体系中也可以观察到自俘获现象. 还研究了多体量子涨落对自俘获现象的影响，讨论了在现有的实验条件下对凝聚体自俘获现象进行观察和周期调制. 关键词： 玻色-爱因斯坦凝聚 自俘获 双势阱 周期调制     

含G对费米子动力学对称SP(10)模型的Dyson玻色子实现

将费米子动力学对称模型包含G费米子对能够构造出SP(10)或SO(12)动力学对称群.本文用GeneralizedDyson玻色子映射方法求出SP(10)对称群精确的玻色子映像,其子群SU(5)生成元的玻色子映像与sdg相互作用玻色子模型(IBM)SU(5)生成元相同,唯象sdgIBMSU(5)极限能谱公式可由费米子动力学对称模型的微观参数描述.     

相互作用玻色子模型的非厄米Dyson玻色子展开途径

通过Dyson玻色子展开及修正的Jancovici和Schiff代换,得到费米子集体S,D对态空间与相互作用玻色子模型s,d空间之间的一一对应.费米子算符的玻色子像被唯一确定,IBM哈密顿量具有非厄米形式.费米子矩阵元能够在玻色子空间内直接计算,并且,当需要清除伪态时,相应的投影计算也能在玻色子空间进行.     

Fermi超流气体在unitarity区域和Bose-Einstein 凝聚区域的自俘获现象研究

在平均场理论和两模近似下,通过观察布居数差随时间的演化, 以及布居数差的平均随非线性相互作用参数的变化, 研究了对称双势阱以及势阱间高频调制时Fermi超流气体在unitarity区域和Bose-Einstein凝聚区域的自俘获现象. 给出了出现自俘获现象的边界条件;发现高频调制在一定调制范围内使自俘获现象更容易实现. 最后研究了初值对自俘获的影响, 发现初值的绝对值|s(0)|的增加更有利于自俘获的实现.     

Dyson玻色子展开与原子核的相互作用玻色子模型

根据修正的Jancovici-Schiff (MJS)代换关于玻色子描述可以用作原子核的费米子描述的中间步骤的观点, 本文把相互作用玻色模型(IBM)看作在这种中间步骤引用的一种近似. 文中针对同类价核子的"多-j"组态以及包含两体有效相互作用的费米子哈密顿量, 按照通常的玻色子展开选择出结构上比较简单的玻色子哈密顿量; 借此通过一个么正变换建立了从微观途径确定s, d玻色子及IBM哈密顿量的方法; 根据MJS代换给出了把IBM态矢量变换为费米子态矢量的一般公式.     

两组分BECs在光晶格中的隧穿动力学及其周期调制效应

研究了两组分玻色-爱因斯坦凝聚体(BECs)在一维光晶格中的隧穿动力学及周期调制效应.在两模近似下,运用数值分析的方法,讨论了两组分间相互作用对体系的隧穿动力学行为的影响.进一步讨论了两组分间相互作用在周期调制下系统的动力学特性,分析了随着调制振幅和频率的变化,系统发生隧穿、不稳定和自俘获的区域分布,发现在中低频调制下,系统的隧穿动力学发生了明显的改变.     

Fermi超流气体在unitarity区域和Bose-Einstein凝聚区域的自俘获现象研究米

在平均场理论和两模近似下，通过观察布居数差随时间的演化，以及布居数差的平均随非线性相互作用参数的变化，研究了对称双势阱以及势阱问高频调制时Fermi超流气体在unitarity区域和Bose-Einstein凝聚区域的自俘获现象．给出了出现自俘获现象的边界条件；发现高频调制在一定调制范围内使自俘获现象更容易实现．最后研究了初值对自俘获的影响，发现初值的绝对值︳s（O）︳的增加更有利于自俘获的实现．     

轻子的束缚态波函数和反常磁矩

本文从Bethe-Salpeter方程出发讨论由费米子和标量玻色子组成的轻子束缚态波函数. 在组分粒子很重和内部运动为非相对论的假定下可以证明, 矢量相互作用能给出半径和反常磁矩都足够小的束缚态解, 但要求组分费米子质量远大于玻色子质量. 相反, 标量相互作用则只能给出半径和反常磁矩都很大的束缚态解.     

Landau-Zener tunneling of Bose-Fermi mixture in double-well

The nonlinear Landau-Zener tunneling of a Bose-Fermi mixture in a double-well potential is studied in the present paper. The effect of interaction parameters on bosonic and fermionic tunneling probability is studied for the mixture of ⁴⁰K-⁸⁷Rb. The tunneling phenomena of the system can be controled by adjusting sweeping rate, intraspecies interaction, interspecies interaction and the numbers of bosons and fermions. It is noted that there are three different regions in phase diagram: self-trapping (ST), complete tunneling (CT) and incomplete tunneling (ICT).     

Bose-fermi mixtures in a three-dimensional optical lattice

We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.     

Tunable Range Interactions and Multi-Roton Excitations for Bosons in a Bose-Fermi Mixture with Optical Lattices *

In this article, we discuss a method to control the long-range interactions between bosons in a three-dimensional Bose-Fermi mixture with the help of optical lattices on fermions. We find the range and the peaked momentum of the fermion-mediated interactions can be tuned by the optical lattice depth and the fermion density. If the fermion density is close to half-filling, roton excitations can be generated with weak Bose-Fermi interactions. Further, if the fermions are not exact at half-filling, multi-roton structure may emerge, implying competing density orders. Therefore, tuning the lattice depth and the fermion density in a Bose-Fermi mixture serves as an effective way to control the interaction range and resonant momentum between bosons.     

Topological properties of one-dimensional hardcore Bose-Fermi mixture

We study the topological properties of a one-dimensional （1D） hardcore Bose-Fermi mixture using the exact diagonalization method. We firstly add a hardcore boson to a fermionic system and by examining the edge states we find that the quasi-particle manifests the topological properties of the system. Then we study a mixture with 7 fermions and 1 boson. We find that the mixture also exhibits topological properties and its behaviors are similar to that of the corresponding fermionic system. We present a qualitative explanation to understand such behaviors using the mapping between a hardcore boson and a spinless fermion. These results show the existence of topological properties in a 1D hardcore Bose-Fermi mixture and may be realized using cold atoms trapped in optical lattices experimentally.     

Coherent interaction of a single fermion with a small bosonic field

We have experimentally studied few-body impurity systems consisting of a single fermionic atom and a small bosonic field on the sites of an optical lattice. Quantum phase revival spectroscopy has allowed us to accurately measure the absolute strength of Bose-Fermi interactions as a function of the interspecies scattering length. Furthermore, we observe the modification of Bose-Bose interactions that is induced by the interacting fermion. Because of an interference between Bose-Bose and Bose-Fermi phase dynamics, we can infer the mean fermionic filling of the mixture and quantify its increase (decrease) when the lattice is loaded with attractive (repulsive) interspecies interactions.     

Realization of a strongly interacting Bose-Fermi mixture from a two-component Fermi gas

We show the emergence of a strongly interacting Bose-Fermi mixture from a two-component Fermi mixture with population imbalance. By analyzing in situ density profiles of 6Li atoms in the BCS-BEC crossover regime, we identify a critical interaction strength, beyond which all minority atoms pair up with majority atoms and form a Bose condensate. This is the regime where the system can be effectively described as a boson-fermion mixture. We determine the dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field contributions. Our study realizes a gedanken experiment of bosons immersed in a Fermi sea of one of their constituents, revealing the composite nature of the bosons.     

Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

玻色-费米混合气体的非线性Landau-Zener隧穿

在有相互作用的非线性两模系统中, 通过对相互作用参数的调节, 研究了该系统中玻色-费米混合气体的Landau-Zener隧穿现象. 研究发现, 其中某一组分的自相互作用会影响另一组分粒子的隧穿, 使得隧穿出现临界现象. 关键词： 玻色-费米混合气体 Landau-Zener隧穿 量子绝热隧穿     

Degenerate Bose-Fermi mixture of metastable atoms

We report the observation of simultaneous quantum degeneracy in a dilute gaseous Bose-Fermi mixture of metastable atoms. Sympathetic cooling of helium-3 (fermion) by helium-4 (boson), both in the lowest triplet state, allows us to produce ensembles containing more than 10(6) atoms of each isotope at temperatures below 1 microK, and achieve a fermionic degeneracy parameter of T/TF = 0.45. Because of their high internal energy, the detection of individual metastable atoms with subnanosecond time resolution is possible, permitting the study of bosonic and fermionic quantum gases with unprecedented precision. This may lead to metastable helium becoming the mainstay of quantum atom optics.     

变分法研究一维Bose-Fermi系统的稳定性

利用能量泛函变分法研究了一维Bose-Fermi系统稳定基态的存在条件.根据Bose-Fermi系统的Lagrange量可以得到三维Bose-Fermi体系所满足的非线性动力学方程组.当外势阱的横向囚禁频率远大于轴向囚禁频率时,体系可以当作一维模型来处理.从描述三维体系的动力学方程可以得到描述一维体系的动力学方程,选取适当的无量纲参数,可以对一维动力学方程组进行无量纲处理,得到数值计算和理论分析中常用到的无量纲方程.选择高斯型试探解(简单孤立子解),利用能量泛函变分法得到一维Bose-Fermi体系稳定的高斯型孤立子存在条件.分析了两种特殊情况下孤立子能够稳定存在的区域以及原子数的临界条件,最后得出了一般情况下稳定基态存在时临界散射长度与原子数以及波包宽度之间的关系.