Probing Nuclear Sizes through Precision Spectroscopy of Ultracold Bosonic and Fermionic Helium

The helium atom, being a calculable system with narrow transitions that can be measured precisely, is an excellent candidate for testing state-of-the-art Quantum Electrodynamics calculations. This thesis presents a series of precise spectroscopic measurements on a narrow transition in ultracold trapped quantum gases of helium, using both the 3-He and 4-He isotopes, which exhibit distinctly different quantum-statistical behaviour in this ultracold regime. From the shift of this transition between the two isotopes, the difference in their nuclear charge radii is extracted, which is used as a benchmark quantity for comparison with other measurements and tests of Quantum Electrodynamics theory.