Decoherence of motional states
Mon Jul 17 14:06:11 BST 2006
I am working on a paper at the moment describing the Schroedinger cat experiments that we performed with a single ion coupled to its motional state. In the referee comments there were a number of questions about the theoretical derivations. The majority I could answer as they related to the details of our particular experiment and analysis, however for the more fundamental ones I needed to ask one of my coauthors and he referred to the paper [Phys. Rev. A. 62 053807] by Turchette et al. This seems to be a useful for a lot of the theoretical results in the area of coupling between an ion and a bath of harmonic oscillators, as well as describing some very nice experiments.
Coupling of a charged harmonic oscillator with the surrounding electric field, E from the environment is of the form
V = -q x.E
where q is the charge on the particle and x is the position. The expectation value of E2 is always non-zero, so there is always coupling of noise from the environment to the particle.
- Two types of reservoir:
- amplitude damping: energy is transferred from the oscillator to the reservoir. The oscillator reaches thermal equilibrium with the reservoir ie decays to the thermal state density matrix at the mean temperature of the reservoir. This is achieved experimentally by amplitude noise in the trap field at the trapping frequency. Uniform field fluctuations.
- phase damping: no energy is transferred to the reservoir, but the phase of the oscillator decoheres. This is achieved experimentally by amplitude noise far from the trap frequency. Field gradients.
- Lots of equations...