Here's my rough shot at what your circuit might look like.
I use an op amp in the transimpedance mode to convert the tunnel diode noise current to voltage.
The op amp can be just about any low input bias current J-FET or MOSFET type.
The op amp should be powered by plus and minus supplies.
If you only have one supply, then you can bias the op amp plus input at 1/2 the supply volage using two 1kΩ resistors in series between the +V and ground. If you do that, then the op amp output needs to have a capacitor in series to block the DC voltage.
Also the polarity of C1 would have to be reversed.
You likely will need another amp at the output for further signal amplification, depending upon your requirements.
The resistor values are just a starting point and you may have to modify them when you see how the circuit operates.
R2 controls the circuit voltage gain.
V1 should be a variable 10V DC supply.