Nonlinear vibrational analogue of coherent output coupler for Bose-Einstein condensed atoms

The analogies between coherent matter waves in Bose-Einstein condensates of atomic gases and coherent photons have been discussed in connection with possible realization of an “atom laser”. Theoretical discussions of the atom laser have considered the case in which atoms are fed into and coupled out of the condensate continuously. Here we discuss the analogy between the output coupler for the trapped coherent matter waves and collective nonlinear energy transfer in a system of three coupled pendulums with variable parameters. One pendulum in the system is weakly coupled through a spring with the pair of pendulums, which are tightly bound through a common string. We show that self-sustained oscillations of the energy distribution between the weakly coupled and tightly bound subsystems can occur. In our simulations, the coherent fraction of the total mechanical energy of the system, which is periodically transferred to the weakly linked subsystem, can be of the order of 1/4000 and even smaller. These periodic oscillations in the energy distribution are similar, and their time evolution is described by similar functions of time, to the quantum Rabi oscillations in the populations of the trapped and untrapped (out-coupled) states in the coherent output coupler in Bose-Einstein condensed atoms. The described effects can be used for the coherent control of the transfer of mechanical energy on the micro- and nano-scales.