论文标题
具有两体损失的弱相互作用的玻色气
Weakly interacting Bose gas with two-body losses
论文作者
论文摘要
我们研究了具有两粒子损失的弱相互作用的卵气体的多体动力学。我们表明，可以通过光学叶状巴赫共振来控制原子之间的非弹性散射过程，从而调节原子气体中的两体相互作用和原子气体的损失。有趣的是，散射幅度的低能行为受单个参数的控制，即复杂的$ s $ - 波散射长度$ a_c $。因此，多体动力学通过具有复杂散射长度的Lindblad主方程来描述。我们通过以类似于封闭的系统应用Bogoliubov近似来求解该方程。发现了各种特殊的动力学特性，其中一些被视为封闭的bose气体中著名结果的耗散性对应物。例如，我们表明，对平均场粒子衰减率的下一个校正是$ | n a_c^{3} |^{1/2} $的订单，这是Lee-huang-yang bose气体校正的类比。还发现，在二次Bogoliubov主方程中存在符号组SP $（4，\ Mathbb {C}）$的动态对称性，这是SU（1,1）相应封闭系统的SU（1,1）动态对称性的类比。我们进一步证实了Bogoliubov近似的有效性，通过将其结果与双孔玩具模型中的完整数值计算进行比较。最后，在最后一篇文章中还讨论了其他替代方法的概括，例如Gross-Pitaevskii方程和流体动力学理论的耗散版本。
We study the many-body dynamics of weakly interacting Bose gases with two-particle losses. We show that both the two-body interactions and losses in atomic gases may be tuned by controlling the inelastic scattering process between atoms by an optical Feshbach resonance. Interestingly, the low-energy behavior of the scattering amplitude is governed by a single parameter, i.e. the complex $s$-wave scattering length $a_c$. The many-body dynamics are thus described by a Lindblad master equation with complex scattering length. We solve this equation by applying the Bogoliubov approximation in analogy to the closed systems. Various peculiar dynamical properties are discovered, some of them may be regarded as the dissipative counterparts of the celebrated results in closed Bose gases. For example, we show that the next-order correction to the mean-field particle decay rate is to the order of $|n a_c^{3}|^{1/2}$, which is an analogy of the Lee-Huang-Yang correction of Bose gases. It is also found that there exists a dynamical symmetry of symplectic group Sp$(4,\mathbb{C})$ in the quadratic Bogoliubov master equation, which is an analogy of the SU(1,1) dynamical symmetry of the corresponding closed system. We further confirmed the validity of the Bogoliubov approximation by comparing its results with a full numerical calculation in a double-well toy model. Generalizations of other alternative approaches such as the dissipative version of the Gross-Pitaevskii equation and hydrodynamic theory are also discussed in the last.
