## 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 formV = -q

**x.E**where q is the charge on the particle and x is the position. The expectation value of

**E**^{2}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...

[permlink]