Is it possible to amplify near zero signals?
I've studied something called stochastic resonance as it applies to neurobiology, however it has applications in general signal processing. Basically, you apply a uniform noise generation to the signal you want to detect, and the idea is that the signal you want to generate will resonate with the noise and become more detectable. At a signal that low, I am unsure, but this is the only method I am aware of that helps with signal detection among very low signal to noise ratios.
For more information:

http://www.aps.org/publications/apsnews/199606/stochastic.cfm

http://en.wikipedia.org/wiki/Stochastic_resonance