Experimental evidence confirms that AI tools raise worker productivity, but also that sustained use can erode the expertise on which those gains depend. We develop a dynamic model in which a decision-maker chooses AI usage intensity for a worker over time, trading immediate productivity against the erosion of worker skill. We decompose the tool's productivity effect into two channels, one independent of worker expertise and one that scales with it. The model produces three main results. First, even a decision-maker who fully anticipates skill erosion rationally adopts AI when front-loaded productivity gains outweigh long-run skill costs, producing steady-state loss: the worker ends up less productive than before adoption. Second, when managers are short-termist or worker skill has external value, the decision-maker's optimal policy turns steady-state loss into the augmentation trap, leaving the worker worse off than if AI had never been adopted. Third, when AI productivity depends less on worker expertise, workers can permanently diverge in skill: experienced workers realize their full potential while less experienced workers deskill to zero. Small differences in managerial incentives can determine which path a worker takes. The productivity decomposition classifies deployments into five regimes that separate beneficial adoption from harmful adoption and identifies which deployments are vulnerable to the trap.