Could we make a supersonic electric airplane?

[Brage]

Hi guys, I've been reading a bit and watching a few youtube videos on electric aircraft, but have come across little to do with supersonic aircraft.
As far as I understand it an electric aircraft would use basically fans to push air behind it and as such generate thrust. The problem would be that once you go supersonic, in the rest frame of the aircraft, you would have to acclelerate the air you're pushing behind you to supersonic speeds, which I am not sure would be possible with such a propellor engine.
I study theoretical physics and not engineering so I am interested to see what responces you can give me and possible other ideas you guys come up with for a supersonic electric aircraft.
Thanks in advance to any responces.

 

[mfb]

Turbofans work at supersonic speeds and their main thrust comes from the fan, you can replace the inner turbine with an electric motor.