We propose a stochastic Schrödinger equation (SSE) approach to investigate the dynamics of giant atoms coupled to a waveguide, addressing two critical gaps in existing research, namely, insufficient exploration of continuous coupling and multiple excitations. A key finding is that continuous coupling, unlike discrete coupling at finite points, breaks the constant phase difference condition, thereby weakening the interference effects in giant-atom–waveguide systems. In addition, a key technical advantage of the SSE approach is that auto- and cross-correlation functions can directly reflect the complex photon emission-absorption processes and time-delay effects in giant-atom–waveguide systems. Moreover, the SSE approach also naturally handles multiple excitations, without increasing equation complexity as the number of excitations grows. This feature enables the investigation of multiexcitation initial states of the waveguide, such as thermal and squeezed initial states. Overall, our approach provides a powerful tool for studying the dynamics of giant atoms coupled to a waveguide, particularly for continuous coupling and multiexcitation systems.

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