  We experimentally present a random phase feedback based on quantum noise to
generate a chaotic laser with Gaussian invariant distribution. The quantum
noise from vacuum fluctuations is acquired by balanced homodyne detection and
injected into a phase modulator to form a random phase feedback. An optical
switch using high-speed intensity modulator is employed to reset the chaotic
states repeatedly and the time evolutions of intensity statistical
distributions of the chaotic states stemming from the initial noise are
measured. By the quantum-noise random phase feedback, the transient intensity
distributions of the chaotic outputs are improved from asymmetric invariant
distributions to Gaussian invariant distributions, and the Gaussian invariant
distribution indicates a randomly perturbed dynamical transition from
microscopic initial noise to macroscopic stochastic fluctuation. The effects of
phase feedback bandwidth and modulation depth on the invariant distributions
are investigated experimentally. The chaotic time-delay signature and mean
permutation entropy are suppressed to 0.036 and enhanced to 0.999 using the
random phase feedback, respectively. The high-quality chaotic laser with
Gaussian invariant distribution can be a desired random source for ultrafast
random number generation and secure communication.
