Amplification of fluctuations in a spinor Bose-Einstein condensate

Dynamical instabilities in a ⁸⁷Rb $F=1$ spinor Bose-Einstein condensate are used as a parametric amplifier of quantum spin fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in quantitative agreement with theory. We quantify the microscopic spin fluctuations of the initially paramagnetic condensate by applying this amplifier and measuring the resulting macroscopic magnetization. The variance of these fluctuations agrees with predictions of a beyond-mean-field theory. This spin amplifier is thus shown to be nearly quantum limited at a gain as high as 30 dB.