# Decoherence in a Penning trap

• I
Malamala

Twigg, gentzen and asd789

My gut feeling is that you can get the decoherence rate by taking the variance of this blackbody frequency shift (##\gamma = \sigma_\nu##, same idea as when you calculate the coherence time of a laser from bandwidth). Thus, the decoherence rate would bee $$\gamma = |\alpha_e - \alpha_g| \sqrt{\langle \| \vec{E}_{BBR} \|^4 \rangle - \langle \| \vec{E}_{BBR} \|^2 \rangle^2}$$ The quadratic term can be calculated from the blackbody partition function by looking at the expectation value of energy squared (just as you do when you calculate energy fluctuations in an ideal gas from the heat capacity).