As large language models (LLM) are increasingly used for text generation tasks, it is critical to audit their usages, govern their applications, and mitigate their potential harms. Existing watermark techniques are shown effective in embedding single human-imperceptible and machine-detectable patterns without significantly affecting generated text quality and semantics. However, the efficiency in detecting watermarks, i.e., the minimum number of tokens required to assert detection with significance and robustness against post-editing, is still debatable. In this paper, we propose, Duwak, to fundamentally enhance the efficiency and quality of watermarking by embedding dual secret patterns in both token probability distribution and sampling schemes. To mitigate expression degradation caused by biasing toward certain tokens, we design a contrastive search to watermark the sampling scheme, which minimizes the token repetition and enhances the diversity. We theoretically explain the interdependency of the two watermarks within Duwak. We evaluate Duwak extensively on Llama2 and Vicuna under various post-editing attacks, against four state-of-the-art watermarking techniques and combinations of them. Our results show that Duwak marked text achieves the highest watermarked text quality at the lowest required token count for detection, up to 70% tokens less than existing approaches, especially under post paraphrasing.