Near field antenna for 0.3-100MHz
Yes it certainly sounds like a near-field transmission with the main energy being delivered as an alternating magnetic field and not a proper EM wave. The coil you describe sounds to me like it would have an inductance of about 2 uH and, to improve efficiency (at the low end) you could use parallel tuning. 

I estimate that about 140 nF of tuning from good ceramic capacitors would tune it at 300 kHz but this doesn't help much at the higher frequency (100 MHz) where a tuning capacitance of barely 1pF would be needed and of course this is not practical because the self capacitance of your 3 turn coil would exceed this.

So that's the first point I note - at the higher end of the scale your antenna is likely to be quite problematic at delivering energy to the Rubidium isotope.

I would therefore suggest a much smaller inductance and a single turn coil. With 1 turn I estimate the inductance to be about 200 nH or thereabouts and this would parallel tune at 100 MHz with a capacitance of about 13 pF.

But, at the lower frequencies you end up with problem because you would need to use a bank of RF relays to progressively switch-in a bunch of capacitors up to about 1.5 uF. It can be done but it needs special care AND to achieve frequency alignment with the tuning I would want to build the antenna around a circuit so that it self oscillates i.e. it is always running on tune.

This is the approach I would take but, I would also consider splitting the energy delivery into smaller chunks so that the electronics could be tailored for two or more frequency bands i.e. you have two or more antennas.

Of course, I have no idea how convenient this would be.