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High dimensional quantum entanglement based on orbital angular momentum (OAM) can provide infinite freedom theoretically, providing a significant improvement on the capacity of the quantum communication. However, the vortex beam that carries OAM signal can be easily distorted by atmospheric turbulence and can degrade the performance of the system. Consequently, for the operation, administration and maintenance of quantum system, an accurate digital twin model of the turbulent channel is necessary. Digital twin model is a mathematical model which can reflect the influence of atmospheric channel on quantum system by theoretical analysis. Nevertheless, it is challenging to achieve for the complex mechanism of atmospheric turbulence. To address this problem, deep learning (DL) techniques have been studied recently. Whereas, for the training of DL, a massive number of labeled samples are needed, i.e., the actual free-space channel, which are hard to be obtained in practical systems. The pool generalization also hinders the use of these DL-based algorithms in practice. To overcome the above challenges, we propose a self-supervised DL algorithm, which does not need any labeled samples in advance, meaning the training of the algorithm can be restarted any time once the environment changes. Compared with previous studies, the proposed algorithm can better suite as the digital twin of the turbulent channel. To verify the performance of the proposed algorithm, we perform extensive verification, whose results demonstrate the superior performance of the proposed method. [ABSTRACT FROM AUTHOR]