Optical Pumping (Zeeman Effect)

I am a bit confused about optical pumping-style experiments, and why increasing the strength of the magnetic field increases the amount of optical pumping --> increases the transmission of light through rubidium

So basically we have Rubidium with energy levels like this:
http://t3.gstatic.com/images?q=tbn:ANd9GcRPcNj_MWyOh1pOkvsfohSY6o9HRxO25v031mNC2xG7nFfnoWtj2Q

My understanding is, an external magnetic field will cause the final splittings on the right (into m_F levels), and as we increase the magnetic field from 0 the gap between the m_F levels gets broader [until we pass the weak field limit and get the quadratic Zeeman effect instead].

Can someone help me understand why increasing this gap increases the amount of pumping/rubidium polarization we get? Based on the theory of how/why it work, it just seems like, 'as long as there is a gap, we will get optical pumping'. Why does an applied field cause so much more light transmission than just the Earth's magnetic field?
 

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