Perfect Transmission and Perfect Reflection of Bogoliubov Quasiparticles in a Dynamically Unstable Bose–Einstein Condensate

Abstract

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.