  We study the dynamical interplay between ferroelectricity and magnetism in a
multiferroic with a helical magnetic order. We show that the dynamical
exchange-striction induces a biquadratic interaction between the spins and
transverse phonons resulting in quantum fluctuations of the spontaneous
ferroelectric polarization $\mathbf{P}$ in the ferroelectric phase. The
hybridization between the spin wave and the fluctuation of the electric
polarization leads to low-lying transverse phonon modes. Those are
perpendicular to $\mathbf{P}$ and to the helical spins at small wave vector but
then turn parallel to $\mathbf{P}$ at a wave vector close to the magnetic
modulation vector. For helical magnetic structure, the spin chirality which
determines the direction of $\mathbf{P}$, also possesses a long-range order.
Due to the dynamical Dzyaloshiskii-Moriya interaction, the spin-chirality is
strongly coupled to the spin fluctuation which implies an on-site inversion of
the spin-chirality in the ordered spin-1/2 system and results in a finite
scattering intensity of polarized neutrons from a cycloidal helimagnet.
