Artificial environments for trapped ions : protection of selected states

The fifth lesson (^8th chapter of the lecture) described the fabrication of artificial environments in experiments with trapped ions. This involves tailoring environments to ensure the survival of certain states. For example, for a two-level trapped ion, artificial environments can be created to protect arbitrarily selected vibrational states from decoherence. The ion needs to be illuminated with suitably directed lasers, resonantly exciting the carrier at the frequency of the ion's electronic transition or sidebands corresponding to the simultaneous excitation of the electronic state and vibrational quanta. The optical pumping of lasers returns part of the dissipation produced by spontaneous emission in the excited state to the fundamental electronic state of the vibrating ion. The resulting pilot equation assumes that the states to be protected are perfect "pointer states" (states insensitive to decoherence). The spontaneous emission rate must be small compared to the vibration frequency, and large compared to the laser-induced pumping rate. In addition, this pumping rate must be large compared with the natural decoherence rate due to stray fields in the trap. A practically important special case is that of radiative cooling, in which case the protected state is the vibrational ground state. The artificial environment has to be "tailor-made" for each state, which limits the general interest of the method in cases where non-classical superpositions of a priori unknown states are to be protected.