The Nambu–Goldstone (NG) mode in a Bose–Einstein condensate (BEC) transmits a potential barrier with probability 1 in the zero-energy limit, which is known as the anomalous tunneling. In this paper, we investigate the tunneling properties of quasiparticles in a dynamically unstable BEC. We prepare a multicomponent BEC (binary and spin-1 BECs) in a dynamically unstable state and solve the tunneling problem of the spin-wave excitation from the condensate. We find that the perfect transmission occurs even when the BEC is dynamically unstable if the spin-wave mode is the NG mode. Here, the mode that exhibits the perfect transmission is the dynamically unstable spin-wave, which is a pure-imaginary-eigenvalue solution of the Bogoliubov–de Gennes equation. Hence, we should take the zero-energy limit not along the real axis but along the imaginary axis. We also demonstrate the existence of the perfect reflection of a dynamically unstable mode at the point where the imaginary part of the eigenvalue takes its maximum. In this case, the incident and reflected waves destructively interfere, and the amplitude of the quasiparticle wave function is strongly suppressed. We numerically confirm that the perfect reflection is a generic nature of dynamically unstable modes and not related to the NG mode. A possible experimental scheme to observe the tunneling properties is discussed on the basis of real-time dynamics obtained by solving the time-dependent Gross–Pitaevskii equation.

中文翻译：

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动态不稳定玻色-爱因斯坦凝聚物中Bogoliubov准粒子的完美透射和完美反射

玻色-爱因斯坦凝析油（BEC）中的Nambu-Goldstone（NG）模式以零能量极限传输概率为1的势垒，这称为反常隧穿。在本文中，我们研究了在动态不稳定BEC中准粒子的隧穿特性。我们准备了处于动态不稳定状态的多组分BEC（二元和自旋1 BEC），并解决了冷凝水自旋波激发的隧穿问题。我们发现，即使自旋波模式为NG模式，即使BEC处于动态不稳定状态，也会发生完美的传输。在这里，表现出完美传输的模式是动态不稳定的自旋波，它是Bogoliubov-de Gennes方程的纯虚数特征值解决方案。因此，我们不应该沿着实轴而是沿着虚轴取零能量极限。我们还证明了在特征值的虚部达到最大值时动态不稳定模式的完美反射的存在。在这种情况下，入射波和反射波相消地干涉，并且准粒子波函数的振幅被强烈抑制。我们从数值上证实，完美反射是动态不稳定模式的一般性质，与NG模式无关。通过求解与时间有关的Gross–Pitaevskii方程获得的实时动力学，讨论了一种观察隧道性能的可能实验方案。入射波和反射波产生相消干涉，并大大抑制了准粒子波函数的振幅。我们从数值上证实，完美反射是动态不稳定模式的一般性质，与NG模式无关。通过求解与时间有关的Gross–Pitaevskii方程获得的实时动力学，讨论了一种观察隧道性能的可能实验方案。入射波和反射波产生相消干涉，并大大抑制了准粒子波函数的振幅。我们从数值上证实，完美反射是动态不稳定模式的一般性质，与NG模式无关。通过求解与时间有关的Gross–Pitaevskii方程获得的实时动力学，讨论了一种观察隧道性能的可能实验方案。