Optical High-order Coherence Effect Based On Superposition Of Multiple Indistinguishable Multi-photon Paths

Since the first report on second-order coherence of thermal light by Hanbury Brown and Twiss in1956, optical high-order coherence effects have attracted a lot of attentions, and prompted the foundation of quantum theory of optical coherence by Glauber in1963, which succesfully explains arbitrary-order coherence effects. Different from the first-order coherence such as Young’s double-slit interference representting the wave nature of light, optical high-order coherence relies on both the’ wave nature and the particle nature of light. At the same time, with the disappearance of first-order coherence, optical high-order coherence usually emerges, e.g., the high-order coherence effects between two independent light sources. With these properties, optical high-order coherence is exploited to study the quantum nature of light, including the classical light such as laser source and thermal source, and the quantum light such as the single-photon source and entangled biphoton source. On the other hand, by using specific light sources, a lot of optical setups are designed to demostrate some unique high-order coherence effects, which is quite useful in practice, such as testing the fundamental issues of quantum mechanics, quantum communication, quantum imaging. My research work mainly focuses on exploiting novel high-order coherence effects, and developing their applications.By analyzing the second-order coherence effects of thermal light, we realized that the key underlying physics is the superposition of two different but indistinguishable two-photon paths, which is also essential in explaining other second-order coherence effects between independent sources. Inspired by this fact, we immediately came to ask whether or not the superposition of multiple different but indistinguishable two-photon paths is possible, and could it enhance the second-order coherence effects? To answer the question, we designed an interferometer constructed by two first-order incoherent optical channels which can provide additional indistinguishable two-photon paths. By applying this interferometer to Hanbury Brown-Twiss interference of thermal light, we observed the enhancement of two-photon interference of thermal light, and a two-photon superbunching effect of thermal light was realized. The result shows that superposition of multiple indistinguishable two-photon paths can be realized in a linear system, offering an experimental cornerstone for studying the high-order coherence based on superposition of multiple indistinguishable multi-photon paths.Besides of the interferometer strategy, we also considered to introduce multiple different but indistinguishable two-photon paths by controlling the random-phase structure of the wavefront of light field. To achieve this goal, we designed a random-phase grating, which is constructed by a N-slit traditional grating with a specially encoded random phase on each slit. With such a random-phase grating, multiple indistinguishable two-photon paths are introduced, and the number of them increases with the increase of slit number N. In experiment, we used the random-phase grating to modulate the wavefront of a coherent light in a Hanbury Brown-Twiss setup. The results show that there is no first-order coherence fringes in the observation plane, but high visibility two-photon interference fringes emerges, and the visibility of the two-photon interference fringes increases with the increase of slit number N. These results again prove that superposition of multiple indistinguishable multi-photon paths can enhance the high-order coherence effect. Particularly, when N>2, the observed visibility exceeds the classical limitation of50%, which is the maximum visibility of the two-photon interference effects for classical light based on superposition of two indistinguishable two-photon paths. The developed strategy here by controlling the random phases also provides a promising method to exploit novel high-order coherence effect.Through the random-phase control, we designed a novel source which is obtained by encoding special random-phase modes on the wavefront of a single mode laser. With such a source, multiple indistinguishable quantum-like entangled two-photon paths, where a pair of photons come from the same position of the source plane, are introduced. By placing an object in front of the source, subwavelength interference can be observed via two-photon measurement in the far field plane due to the superposition of these quantum-like entangled two-photon paths. Such a subwavelength interference effect has been demonstrated in a proof-of-principle experiment, and the setup in our experiment can also be used to achieve super resolved optical lithography.By controlling the random phases of a continuous wave coherent light, we also obtained the interference effect between two temporally delayed two-photon paths with a time delay longer than the coherence time of single photon in a Franson interferometer. In the traditional Franson interferometer based on an entangled biphoton source, the signal photon and idler photon satisfies the conditions of energy conservation and emitted at the same time, which makes the coherence time of the two-photon amplitude of them much longer than the coherence time of any one of them. However, a coherent light does not have such a pair of correlated photons. To obtain such kind of two-photon path with much longer coherence time than that of single photon, we employed two correlated random-phase modes in the two arms of Franson interferometer, respectively. By carefully control the correlation between the random phases of the two modes, the interference effect between temporally delayed two-photon paths in Franson interferometer can be achieved through correlation measurement between the two modes of light fields. This result shows that random-phase control plays an important role in two-photon interference between temporally delayed two-photon paths.At last, we discussed high-order coherence effect between two light sources, and found that the high-order coherence effect depends on the way to erase the first-order coherence between the two sources. Optical high-order coherence effect can become quite different when the phase difference between the initial random phases of the two sources goes through different random walk processes, and the random walk process will leave fingerprint in the high-order coherence patterns. The result broadens our horizon of optical high-order coherence effects, offering new route to exploit novel high-order coherence effects and develop their applications.In summary, by using interferometer and random-phase control, we have successfully realized superposition of multiple indistinguishable multi-photon paths, which leads to the discovery of several novel high-order coherence effects. These results broaden our horizon of optical high-order coherence, and the developed methods in these works also provide alternative ways to exploit novel high-order coherence effects. At the same time, the reported high-order coherence effects have some potential applications in practice.