The detection of human sleep stages is widely used in the diagnosis and intervention of neurological and psychiatric diseases. Some patients with deep brain stimulator implanted could have their neural activities recorded from the deep brain. Sleep stage classification based on deep brain recording has great potential to provide more precise treatment for patients. The accuracy and generalizability of existing sleep stage classifiers based on local field potentials are still limited. We proposed an applicable cross-modal transfer learning method for sleep stage classification with implanted devices. This end-to-end deep learning model contained cross-modal self-supervised feature representation, self-attention, and classification framework. We tested the model with deep brain recording data from 12 patients with Parkinson's disease. The best total accuracy reached 83.2% for sleep stage classification. Results showed speech self-supervised features catch the conversion pattern of sleep stages effectively. We provide a new method on transfer learning from acoustic signals to local field potentials. This method supports an effective solution for the insufficient scale of clinical data. This sleep stage classification model could be adapted to chronic and continuous monitor sleep for Parkinson's patients in daily life, and potentially utilized for more precise treatment in deep brain-machine interfaces, such as closed-loop deep brain stimulation.