Zero eigenvalues of a photon blockade induced by a non-Hermitian Hamiltonian with a gain cavity

Under the weak driving limitation, we find that the strong photon blockade can be triggered when all the eigenvalues of the non-Hermitian Hamiltonian are equal to zero, so we name this the zero eigenvalues of a photon blockade induced by a non-Hermitian Hamiltonian. The possibility of realizing single-and two-photon blockades is investigated in the cavity QED system. A negative effective decay rate of the cavity is required, so the gain medium is needed to compensate the intrinsic loss rate of the cavity. The photon antibunching can be realized in both strong and weak nonlinear regimes, which is different from the conventional photon blockade and unconventional photon blockade. Our scheme has paved an avenue towards the study of photon blockades.