A digital twin (DT), with the components of a physics-based model, a data-driven model, and a machine learning (ML) enabled efficient surrogate model, behaves as a virtual twin of the real-world physical process. In terms of Laser Powder Bed Fusion (L-PBF) based additive manufacturing (AM), a DT can predict the current and future states of the melt pool and the resulting defects corresponding to the input laser parameters, evolve itself by assimilating in-situ sensor data, and optimize the laser parameters to mitigate defect formation. In this paper, we present a deep neural operator enabled DT framework for closed-loop feedback control of the L-PBF process. This is accomplished by building a physics-based computational model to accurately represent the melt pool states, an efficient Fourier neural operator (FNO) based surrogate model to approximate the melt pool solution field, followed by a physics-based procedure to extract information from the computed melt pool simulation that can further be correlated to the defect quantities of interest (e.g., surface roughness). An optimization algorithm is then exercised to control laser input and minimize defects. On the other hand, the constructed DT also evolves with the physical twin via offline finetuning and online material calibration. For instance, the probabilistic distribution of laser absorptivity can be updated to match the real-time captured thermal image data. Finally, a probabilistic framework is adopted for uncertainty quantification. The developed DT is envisioned to guide the AM process and facilitate high-quality manufacturing in L-PBF-based metal AM.