  Spontaneous symmetry breaking has revolutionized the understanding in
numerous fields of modern physics. Here, we theoretically demonstrate the
spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics
system in which an atomic ensemble interacts coherently with a single resonant
cavity mode. The interacting system can be effectively described by two coupled
oscillators with positive and negative mass when the two-level atoms are
prepared in their excited states. The occurrence of symmetry breaking is
controlled by the atomic detuning and the coupling to the cavity mode, which
naturally divides the parameter space into the symmetry broken and symmetry
unbroken phases. The two phases are separated by a spectral singularity, a
so-called exceptional point, where the eigenstates of the Hamiltonian coalesce.
When encircling the singularity in the parameter space, the quasi-adiabatic
dynamics shows chiral mode switching which enables topological manipulation of
quantum states.
