Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at $ u=1/3$

Resonant inelastic light scattering experiments at $ u=1/3$ reveal a novel splitting of the long wavelength modes in the low energy spectrum of quasiparticle excitations in the charge degree of freedom. We find a single peak at small wavevectors that splits into two distinct modes at larger wavevectors. The evidence of well-defined dispersive behavior at small wavevectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long wavelength modes of the electron liquid.