High-dimensional interference through a multimode fiber using long coherence single photon from warm atomic ensemble

The light passing through the scattering medium makes speckle pattern. It is the result of interference in all paths of the light. it means that when we can control all paths, we can make specific mode we want and we can control the interference.

well-controlled scattered light can also make quantum properties robust and can be used to create multidimensional spatial entanglement.

It has to know transmission matrix(T-matrix) to control scattered lights. It uses iteration method to measure T-matrix. This method has the problem that it spends a lot of time to measure T-matrix and we have to measure properties of light, like interference fringe, in the optimization maintaining time.

However, phase conjugation can be measured at once and we can make spatial mode we want by controlling input beam shape and its phase. For example, we can make like a beam splitter. It means that the two output states are phase difference is pi. Furthermore, if we can make 4 output states that the phase difference is pi/2 each states.

These results demonstrate to be able to control multiple inputs and output states. Furthermore, these may have potential application in quantum information processing.