  We demonstrate detection of a vector light shift (VLS) using the quantum
lock-in method. The method offers precise and accurate VLS measurement without
being affected by real magnetic field fluctuations. We detect a VLS on a
Bose--Einstein condensate (BEC) of $^{87}$Rb atoms caused by an optical trap
beam with a resolution less than 1 Hz. We also demonstrate elimination of a VLS
by controlling the beam polarization to realize a long coherence time of a
transversally polarized $F$ = 2 BEC. Quantum lock-in VLS detection should find
wide application, including the study of spinor BECs, electric-dipole moment
searches, and precise magnetometry.

Quantum Gases