Transformer structure has achieved great success in multiple applied machine learning communities, such as natural language processing (NLP), computer vision (CV) and information retrieval (IR). Transformer architecture's core mechanism\, -- \,attention requires $O(n^2)$ time complexity in training and $O(n)$ time complexity in inference. Many works have been proposed to improve the attention mechanism's scalability, such as Flash Attention and Multi-query Attention. A different line of work aims to design new mechanisms to replace attention. Recently, a notable model structure Mamba, which is based on state space models, has achieved transformer-equivalent performance in multiple sequence modeling tasks. In this work, we examine Mamba's efficacy through the lens of a classical IR task\, -- \,document ranking. A reranker model takes a query and a document as input, and predicts a scalar relevance score. This task demands the language model's ability to comprehend lengthy contextual inputs and to capture the interaction between query and document tokens. We find that \textbf{(1) Mamba models achieve competitive performance compared to transformer-based models with the same training recipe; (2) but also have a lower training throughput in comparison to efficient transformer implementations such as flash attention.} We hope this study can serve as a starting point to explore \mamba models in other classical IR tasks. Our \href{https://github.com/zhichaoxu-shufe/RankMamba}{code implementation} is made public to facilitate reproducibility. Refer to~\cite{xu-etal-2025-state} for more comprehensive experiments and results, including passage ranking.