  In this paper, we investigate theoretically the back-action evading
measurement of the collective mode of an interacting atomic Bose-Einstein
condensate (BEC) trapped in an optical cavity which is driven coherently by a
pump laser with a modulated amplitude. It is shown that for a specified kind of
amplitude modulation of the driving laser, one can measure a generalized
quadrature of the collective mode of the BEC indirectly through the output
cavity field with a negligible backaction noise in the good-cavity limit.
Nevertheless, the on-resonance added noise of measurement is suppressed below
the standard quantum limit (SQL) even in the bad cavity limit. Moreover, the
measurement precision can be controlled through the s-wave scattering frequency
of atomic collisions.
