  We present a theoretical study of the interaction between an atom
characterized by a degenerate ground state and a reciprocal environment, such
as a semiconductor nanoparticle, without the presence of external bias. Our
analysis reveals that the combined influence of the electron's intrinsic spin
magnetic moment on the environment and the chiral atomic dipolar transitions
may lead to either the spontaneous breaking of time-reversal symmetry or the
emergence of time-crystal-like states with remarkably long relaxation times.
The different behavior is ruled by the handedness of the precession motion of
the atom's spin vector, which is induced by virtual chiral-dipolar transitions.
Specifically, when the relative orientation of the precession angular velocity
and the electron spin vector is as in a spinning top, the system manifests
time-crystal-like states. Conversely, with the opposite relative orientation,
the system experiences spontaneous symmetry breaking of time-reversal symmetry.
Our findings introduce a novel mechanism for the spontaneous breaking of
time-reversal symmetry in atomic systems, and unveil an exciting opportunity to
engineer a nonreciprocal response at the nanoscale, exclusively driven by the
quantum vacuum fluctuations.
