We study the ground-state properties of an atomic-molecular boson conversion model through an exact Bethe Ansatz solution. For a certain range of parameter choices, we prove that the ground-state Bethe roots lie on the positive real-axis. We then use a continuum limit approach to obtain a singular integral equation characterising the distribution of these Bethe roots. Solving this equation leads to an analytic expression for the ground-state energy. The form of the expression is consistent with the existence of a line of quantum phase transitions, which has been identified in earlier studies. This line demarcates a molecular phase from a mixed phase. Certain correlation functions, which characterise these phases, are then obtained through the Hellmann-Feynman theorem.
Stochastic and equilibrium pictures of the ultracold FFR molecular conversion rate
研究了超冷分子在Fano-费什巴赫共振绝热斜坡中的转化率，并在两种统计模型中进行了比较。一种模型，即所谓的随机相空间采样（SPSS）[E.Hodby等人，94 120402（2005）]通过根据相空间准则对原子对进行采样来评估相空间中两个原子分布的重叠。另一种模型，化学平衡理论（ChET）[S.Watabe和T.Nikuni，PRA.77 013616（2008）]考虑了化学和热平衡极限下的原子和分子分布。本研究应用SPSS和ChET的原型系统的K+ KK 2在所有的对称组合，即费米-费米，玻色-玻色，玻色-费米的情况下。为了检验SPSS的相空间准则的含义，使用四种不同的几何约束来分析分子转化的行为。我们的比较结果的SPSS与ChET表明，虽然他们似乎在大多数情况下相似，这两个模型引起相当不同的行为时，一个玻色-爱因斯坦凝聚体（BEC）的存在强烈影响分子的形成。
We analyze quantum phase transitions in a system of optical lattice bosons coupled to an array of atomic quantum dots, or pseudospins-1/2. The system parallels the Bose-Hubbard model with a single difference of the direct tunneling between the lattice sites being replaced by an assisted tunneling via coupling to the atomic quantum dots. We calculate the phase diagram of the combined system, numerically within the Gutzwiller ansatz and analytically using the mean-field decoupling approximation. The result of the assisted Bose-Hubbard model is that the Mott-superfluid transition still takes plac…
We study binary atomic boson-fermion mixtures confined in one dimensional box potentials by few-body theory with contact interactions and mean-field many-body theory with density-density interactions. A variety of correlations and structures arise as the inter- and intra- species interactions are tuned. Both few-body and many-body results show that miscible phase and three-chunk phase separation are directly observable in the density profiles. Meanwhile, two-chunk phase separation can be inferred from the few-body correlations and many-body density profiles. We present phase diagrams of select…
We predict the existence of high frequency modes in the interference pattern of two condensates made of fermionic-atom dimers. These modes, which result from fermion exchanges between condensates, constitute a striking signature of the dimer composite nature. From the 2-coboson spatial correlation function, that we derive analytically, and the Shiva diagrams that visualize many-body effects specific to composite bosons, we identify the physical origin of these high frequency modes and determine the conditions to see them experimentally by using bound fermionic-atom pairs trapped on optical lat…
Ultracold Bose atoms is the physical system, where the quantum and nonlinear phenomena play crucial role. Ultracold bosons are considered at the small finite temperatures. Bosons are considered as two different fluids: Bose-Einstein condensate and normal fluid (the thermal component). An extended hydrodynamic model is obtained for both fluids, where the pressure evolution equations and the pressure flux third rank tensor evolution equations are considered along with the continuity and Euler equations. It is found that the pressure evolution equation contains zero contribution of the short-rang…
Suppression and enhancement of bosonic stimulation by atomic interactions
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系电子研究实验室、MIT-哈佛超冷原子中心）
