Interference And Distinguishability Of Multi-photon States

Optics has been widely applied in different scientific research. Especially, after the invention of laser, more and more researches and discoveries are based on this excellent light source. Moreover, light is putting the development of modern physics. For example, the research on the emission induced the birth of quantum mechanics, which made human enter the quantum world. Since 1980's, there appeared a new method to deal with the information based on quantum mechanics —quantum information. In quantum information, the superposition and collapse measurement of quantum states ensure the security of the quantum key distribution. Also, the superposition and evolution of the quantum state can support the parallel work for a quantum computer. So its computation efficiency is much better than an electronic computer.In experiment, researchers are trying many physical system to realize quantum information and quantum computation. Among all the systems, the optical system is more feasible than others. The information can be transmit easily with photons. Almost all the quantum key distribution use photons as the transmitter. Moreover, it is easy to generate different photons states with nonlinear optical process. The mature manipulation and detection of photonic state make photons apply to many quantum information protocols. So, the first experiments of quantum key distribution, verification of quantum nonlocality, and quantum state teleportation are realized with photon system.However, the manipulation of photon state in quantum protocols is the result of photon interference. For example, the optical part of single photon quantum distribution is a single photon interferometer. The multi-photon interference has been the heart of quantum computation with linear optics. We need research different photon interferennce, which will offer much more methods for quantum information science. Conversely, we can use the language of quantum computation to describe and analyze the photonic interference. All the manipulation o photons can be regarded as the operation of qubit. And the interfernce visibility is the result of decoherence.The dissertation discusses the interference and distiguishability of the photons from parametric down conversion. The main work are listed below:1. Photonic interference and the application in quantum informationThe photon interference comes from the indistiguishability. If the system is indistigu-ishability, photon not only can interfere with itself, but also with other photons. Based on this indistiguishability principle, different single-photon, two-photon, and multi-photon interferences and their applications in quantum information, quantum computation, and quantum measurement are discussed. 2. Interference and distinguishability of multi-photon state in same spatial modeThe discussion of interference begins with the rotation properties of polarization of the multi-photon state in same spatial mode. It shows different result with single photon interference because all the photons interfere with each other. Then arbitrary two-mode multi-photon projection measurements were successfully proposed, including the maximally entangled photon number state (NOON state). With NOON state projection measurement and photons from parametric down conversion, we demonstrate multi-photon de Broglie wavelength. In the high resolution quantum phase measurement, we are able to use photons direct from parametric down conversion and corresponding projection measurement to obtain the phase uncertainty of Heisenberg limit, which is a true quantum limit and can not be improved. Moreover, the generalized multi-photon Hong-Ou-Mandel interference is realized in experiment based on the NOON state projection measurement. The visibility of Hong-Ou-Mandel interference shows the distinguishability of the multi-photon state.3. Stimulated emission and photon bunching. We directly observed the stimulation emission in parametric amplification. Both the stimulation emission and multi-photon interference can cause the photon bunching. In experiment and theory, we demonstrate that the two processes come from photon indistinguishability. Moreover, photon distinguishability is the result of quantum entanglement. So the photon bunching offers a method to measure the quantum entanglemeng. We use the parametric down conversion to generate pseudo two-fold copy of four-dimensional two-photons state and measure its I-concurrence by detecting the photon bunching effect.4. Interferece of photons with many degrees of freedomAll the interferences are regarded as the result quantum computation. There will be many degrees of freedom and many photons in the interference. With the boson permutation symmetry and quantum computation language, the photon interferences can be well described. It shows that the entanglement may exist between different photons and different degrees of freedom. These entanglement will drop the visibility in practical photonic interference.