Closed-loop sleep modulation is an emerging research paradigm to treat sleep disorders and enhance sleep benefits. However, two major barriers hinder the widespread application of this research paradigm. First, subjects often need to be wire-connected to rack-mount instrumentation for data acquisition, which negatively affects sleep quality. Second, conventional real-time sleep stage classification algorithms give limited performance. In this work, we conquer these two limitations by developing a sleep modulation system that supports closed-loop operations on the device. Sleep stage classification is performed using a lightweight deep learning (DL) model accelerated by a low-power field-programmable gate array (FPGA) device. The DL model uses a single channel electroencephalogram (EEG) as input. Two convolutional neural networks (CNNs) are used to capture general and detailed features, and a bidirectional long-short-term memory (LSTM) network is used to capture time-variant sequence features. An 8-bit quantization is used to reduce the computational cost without compromising performance. The DL model has been validated using a public sleep database containing 81 subjects, achieving a state-of-the-art classification accuracy of 85.8% and a F1-score of 79%. The developed model has also shown the potential to be generalized to different channels and input data lengths. Closed-loop in-phase auditory stimulation has been demonstrated on the test bench.