  The simplest $N=2$ supersymmetric quantum mechanical system is realized in
terms of the bosonic creation and annihilation operators obeying either
ordinary or deformed Heisenberg algebra involving Klein operator. The
construction comprises both the exact and spontaneously broken supersymmetry
cases with the scale of supersymmetry breaking being governed by the
deformation parameter. Proceeding from the broken supersymmetry case, we
realize the Bose-Fermi transformation and obtain spin-$1/2$ representation of
$SU(2)$ group in terms of one bosonic oscillator. We demonstrate that the
constructions can be generalized to the more complicated $N=2$ supersymmetric
systems, in particular, corresponding to the Witten supersymmetric quantum
mechanics.

High Energy Physics - Theory;Condensed Matter;High Energy Physics - Lattice;Nuclear Theory