Quantum echo in two-component Bose-Einstein condensates

The development of ultracold atom technology has enabled precise investigations on the quantum dynamics of quantum gases. Recently, inspired by experimental advancement, the SU(1 , 1) echo, akin to the well-known SU(2) spin echo, was proposed for the single -component Bose-Einstein condensate (BEC). In this paper, we investigate the possibility of quantum echo in the more intricate two -component BEC by fully exploiting its underlying symmetry, which is the Lie group Sp(4 , R ). We demonstrate that quantum echo can occur for the two -component BEC by applying a driving protocol consisting of two steps in each period. The first step can be any Bogoliubov Hamiltonian, while the second step is a Hamiltonian with interactions turned off, which plays a similar role as the pi pulse in spin echo. We confirm our theoretical results with numerical calculations for different examples of the two -component BEC. We further consider the effect of interactions between the excited boson modes on the quantum echo process and discuss the possible experimental implementation of this quantum echo.