Question Generation (QG) is a fundamental NLP task for many downstream applications. Recent studies on open-book QG, where supportive answer-context pairs are provided to models, have achieved promising progress. However, generating natural questions under a more practical closed-book setting that lacks these supporting documents still remains a challenge. In this work, we propose a new QG model for this closed-book setting that is designed to better understand the semantics of long-form abstractive answers and store more information in its parameters through contrastive learning and an answer reconstruction module. Through experiments, we validate the proposed QG model on both public datasets and a new WikiCQA dataset. Empirical results show that the proposed QG model outperforms baselines in both automatic evaluation and human evaluation. In addition, we show how to leverage the proposed model to improve existing question-answering systems. These results further indicate the effectiveness of our QG model for enhancing closed-book question-answering tasks.