  We present the first measurements of the electric and magnetic form factors
of the neutron in the time-like (positive $q^2$) region as function of
four-momentum transfer. We explored the differential cross sections of the
reaction $e^+e^- \rightarrow \bar{n}n$ with data collected with the BESIII
detector at the BEPCII accelerator, corresponding to an integrated luminosity
of 354.6 pb$^{-1}$ in total at twelve center-of-mass energies between $\sqrt{s}
= 2.0 - 2.95$ GeV. A relative uncertainty of 18% and 12% for the electric and
magnetic form factors, respectively, is achieved at $\sqrt{s} = 2.3935$ GeV.
Our results are comparable in accuracy to those from electron scattering in the
comparable space-like (negative $q^2$) region of four-momentum transfer. The
electromagnetic form factor ratio $R_{\rm em}\equiv |G_E|/|G_M|$ is within the
uncertainties close to unity. We compare our result on $|G_E|$ and $|G_M|$ to
recent model predictions, and the measurements in the space-like region to test
the analyticity of electromagnetic form factors.
