C © Owned by the authors, published by EDP Sciences, 2013 Frequency metrology in quantum degenerate helium

Abstract. We have measured the absolute frequency of the 1557-nm doubly forbidden transition between the two metastable states of helium, 2 3S1 (lifetime 8000 s) and 2 1S0 (lifetime 20 ms), with 1 kHz precision. With an Einstein coefficient of 10−7 s−1 this is one of weakest optical transitions ever measured. The measurement was performed in a Bose-Einstein condensate of 4He * as well as in a Degenerate Fermi Gas of 3He*, trapped in a crossed dipole trap. From the isotope shift we deduced the nuclear charge radius difference between the -particle and the helion. Our value differs by 4 with a very recent result obtained on the 2 3S → 2 3P transition. 1