Multilevel quantum systems lose coherence due to quantum jumps. One example is the spontaneous decay between the internal levels of an atom. In this work, we propose and implement a way to simulate experimentally a three-level system under a quantum jump using a three-mode photonic system. We simulated three different dynamics of spontaneous decay in a three-level atomic system: cascade decay, $\mathrm{\ensuremath{\Lambda}}$ decay, and
V decay. With an attenuated light coherent source at photon level, we have prepared photons in a three-path superposition state, which was encoded in parallel Gaussian modes. By programming a spatial light modulator (SLM) for producing periodical phase modulation, we were able to implement the corresponding dynamical maps for quantum jumps in terms of the Kraus operator decomposition. Our results have verified experimentally the variation of the population levels and the decoherence effects caused by quantum jumps in the three decay configurations of the three-level system.
We obtain photon statistics by using a quantum jump approach tailored to a system in which one or two qubits are coupled to a one-dimensional waveguide. Photons confined in the waveguide have strong interference effects, which are shown to play a vital role in quantum jumps and photon statistics. For a single qubit, for instance, the bunching of transmitted photons is heralded by a jump that increases the qubit population. We show that the distribution and correlations of waiting times offer a clearer and more precise characterization of photon bunching and antibunching. Further, the waiting times can be used to characterize complex correlations of photons which are hidden in ${g}^{(2)}(\ensuremath{\tau})$, such as a mixture of bunching and antibunching.