In Federated Learning (FL), multiple clients collaboratively train a model without sharing raw data. This paradigm can be further enhanced by Differential Privacy (DP) to protect local data from information inference attacks and is thus termed DPFL. An emerging privacy requirement, ``the right to be forgotten'' for clients, poses new challenges to DPFL but remains largely unexplored. Despite numerous studies on federated unlearning (FU), they are inapplicable to DPFL because the noise introduced by the DP mechanism compromises their effectiveness and efficiency. In this paper, we propose Federated Unlearning with Indistinguishability (FUI) to unlearn the local data of a target client in DPFL for the first time. FUI consists of two main steps: local model retraction and global noise calibration, resulting in an unlearning model that is statistically indistinguishable from the retrained model. Specifically, we demonstrate that the noise added in DPFL can endow the unlearning model with a certain level of indistinguishability after local model retraction, and then fortify the degree of unlearning through global noise calibration. Additionally, for the efficient and consistent implementation of the proposed FUI, we formulate a two-stage Stackelberg game to derive optimal unlearning strategies for both the server and the target client. Privacy and convergence analyses confirm theoretical guarantees, while experimental results based on four real-world datasets illustrate that our proposed FUI achieves superior model performance and higher efficiency compared to mainstream FU schemes. Simulation results further verify the optimality of the derived unlearning strategies.

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