  We present an optical quantum random number generator based on vacuum
fluctuation measurements that uses multi-mode coherent states generated by
electro-optical phase modulation of an intense optical carrier. In this
approach the weak coherent multi-mode state (or a vacuum state) interferes with
the carrier, which acts as a local oscillator, on each side mode independently.
The proposed setup can effectively compensate for deviations between the two
arms of a balanced detector by controlling the modulation index of the
electro-optical phase modulator. We perform a proof-of-principle experiment and
demonstrate random number generation with a possibility of real-time randomness
extraction at the rate of 400 Mbit/s.
