Sleep is regulated by homeostatic processes, yet the biological basis of sleep pressure that accumulates during wakefulness, triggers sleep, and dissipates during sleep remains elusive. We explored a causal relationship between cellular synaptic strength and electroencephalography delta power indicating macro-level sleep pressure by developing a theoretical framework and a molecular tool to manipulate synaptic strength. The mathematical model predicted that increased synaptic strength promotes the neuronal "down state" and raises the delta power. Our molecular tool (synapse-targeted chemically induced translocation of Kalirin-7, SYNCit-K), which induces dendritic spine enlargement and synaptic potentiation through chemically induced translocation of protein Kalirin-7, demonstrated that synaptic potentiation of excitatory neurons in the prefrontal cortex (PFC) increases nonrapid eye movement sleep amounts and delta power. Thus, synaptic strength of PFC excitatory neurons dictates sleep pressure in mammals.