Atom-molecule conversion system subject to phase noises

The dynamics of atom-molecule conversion system subject to dephasing noises is studied in this paper. With the dephasing master equation and the mean-field theory, we drive a Bloch equation for the system, this equation is compared with the Bloch equation derived by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy truncation approach. Fixed points of the system are calculated by solving both the Bloch equations and the master equation, comparison between these two calculations suggests that while in a short time the mean-field theory is a good approximation for the atom-molecule conversion system, a high order hierarchy truncation approach is necessary for the system in a long time scale. Although the MFT can not predict correctly the fixed points, its prediction on the stability of the fixed points are consistent with the BBGKY theory for a wide range of parameters.