Information retrieval in specialized domains (e.g., legal and medical) faces challenges in aligning user queries, often expressed in colloquial language, with highly structured, terminology-rich documents. This discrepancy creates a distribution gap in the text representation. Recent methods aim to enhance queries by generating intermediary elements (e.g., keywords, pseudo-documents) before performing retrieval with large language models (LLMs). However, by treating LLMs and retrievers separately, these approaches risk producing unreliable or irrelevant intermediaries, which can significantly degrade retrieval performance. To address this issue, we propose CoEvo, an alternating optimization framework that facilitates the coevolution of LLMs and retrieval models. CoEvo operates through two key steps: L-step directs the LLM in generating intermediaries by leveraging an archive of historical examples known to enhance retrieval. R-step trains the retriever using contrastive learning on the intermediaries produced by the LLM. Finally, we evaluate and flexibly leverage content generated by the LLM to amplify the effectiveness of coevolution. Experimental results demonstrate significant improvements in retrieval performance across both legal and medical domains.