Exploring topological features of a dissipative qubit near an exceptional point

We study the behavior of a single dissipative qubit which is described by a non-Hermitian Hamiltonian that has effective space-time reflection (PT) symmetry. We use quantum state tomography to observe the PT-symmetry breaking transition as we cross the exceptional point by varying the coupling strength between the two quantum states. By changing the detuning of the coupling, we probe the topological features associated with encircling the exceptional point. In addition, we introduce a time-modulated coupling strength where the resulting Floquet Hamiltonian provides a richer phase diagram where the PT broken phase can occur for dissipations levels that are much smaller than the PT symmetry threshold in the static case. Here we observe multiple transitions breaking and restoring the PT-symmetric phase.