In a double-slit experiment, the interference pattern observed is a result of the superposition of probability amplitudes associated with the different paths that a photon can take. This phenomenon is often described in terms of interference between different possibilities or paths of the same photon, rather than the photon interfering with itself.
However, when it comes to the interaction between different photons, interference can still occur under certain circumstances. This type of interference is known as "two-photon interference" or "quantum interference." It arises when two independent photons interact or overlap in such a way that their probability amplitudes combine, leading to observable interference effects.
Two-photon interference has been observed in various experiments, such as the Hong-Ou-Mandel effect, where two photons are simultaneously incident on a beam splitter and exhibit a characteristic bunching behavior. These interference phenomena involving multiple photons are important in the field of quantum optics and quantum information processing.
To address your second question, both types of interference, namely the interference between different possibilities of the same photon and the interference between different photons, can occur simultaneously. These phenomena are independent of each other and can be observed and studied separately or in combination, depending on the experimental setup and conditions.
It's important to note that the behavior of photons and other quantum particles is governed by the principles of quantum mechanics, which can be counterintuitive and differ from our everyday experiences with classical objects. Interference effects are one of the fascinating features of quantum mechanics, and they play a crucial role in understanding the wave-particle duality and the probabilistic nature of quantum systems.