Low Energy Excitations in Quantum Condensates

Z.-Ch. Wang, Hongbing Yang, Shuting Yin

William Hoston, Li You

瞬 内野

Daisuke Takahashi, Yusuke Kato

We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.

S. Stringari

Shohei Watabe, Yusuke S. Kato

We investigate transmission and reflection of Bose-Einstein condensate excitations in the low-energy limit across a potential barrier separating two condensates with different densities. Bogoliubov excitation in the low-energy limit has an incident angle where perfect transmission occurs. This condition corresponds to the Brewster's law for the electromagnetic wave. There also exists the total internal reflection of the Bogoliubov excitation in the low-energy limit. In the case of the normal incidence, our result in the low-energy limit is consistent with a result for weakly interacting one-dimensional Bose gases treated as Tomonaga-Luttinger liquids.