We added references to the Wolf and Tourrencin and A. Peters, K.Y. Chung and S. Chu articles. The latter of these articles does not address the quantum corrections 2.
The first example is the result announced in Equation (4), concerning the phase shift due to the gravity gradient gamma. This effect was first calculated by Wolf and Tourrencin Physics Letters A 251 (1999) pp 241–246 and discussed with more details in A. Peters, K.Y. Chung and S. Chu, Metrologia 2001, 38, 25–61.