Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper box

Micromechanical resonators with fundamental vibrational mode frequencies in the range 10MHz–1GHz can now be fabricated [1, 2]. Applications include fast, ultrasensitive force and displacement detectors [3], electrometers [4, 5], and radio frequency signal processors [6]. However, the advances in the development of micromechanical devices also raise the fundamental question of whether mechanical systems containing macroscopic numbers of atoms will exhibit quantum behavior. Because of their size, quantum behavior in micromechanical systems will be strongly influenced by interactions with the environment and the existence of an experimentally accessible quantum regime will depend on the rate at which decoherence occurs [7].