We investigate the sympathetic relaxation of a free-standing, vibrating carbon nano-tube that is mounted on an atom chip and is immersed in a cloud of ultra-cold atoms. Gas atoms colliding with the nano-tube excite phonons via a Casimir-Polder potent
ial. We use Fermis Golden Rule to estimate the relaxation rates for relevant experimental parameters and develop a fully dynamic theory of relaxation for the multi-mode phononic field embedded in a thermal atomic reservoir. Based on currently available experimental data, we identify the relaxation rates as a function of atom density and temperature that are required for sympathetic ground state cooling of carbon nano-tubes.
In current Bose-Einstein condensate experiments, the shot-to-shot variation of atom number fluctuates up to 10%. In here, we present a procedure to suppress such fluctuations by using a nonlinear p-pi-pbar matter wave interferometer for a Bose-Einste
in condensate with two internal states and a high beam-splitter asymmetry (p, pbar not-equal 0.5). We analyze the situation for an inhomogeneous trap within the Gross-Pitaevskii mean-field theory, as well as a quantum mechanical Josephson model, which addresses complementary aspects of the problem and agrees well otherwise.
