Dense retrieval systems are commonly used for information retrieval (IR). They rely on learning text representations through an encoder and usually require supervised modeling via labelled data which can be costly to obtain or simply unavailable. In this study, we introduce a novel unsupervised text representation learning technique via instruction-tuning the pre-trained encoder-decoder large language models (LLM) under the dual-encoder retrieval framework. We demonstrate the corpus representation can be augmented by the representations of relevant synthetic queries generated by the instruct-tuned LLM founded on the Rao-Blackwell theorem. Furthermore, we effectively align the query and corpus text representation with self-instructed-tuning. Specifically, we first prompt an open-box pre-trained LLM to follow defined instructions (i.e. question generation and keyword summarization) to generate synthetic queries. Next, we fine-tune the pre-trained LLM with defined instructions and the generated queries that passed quality check. Finally, we generate synthetic queries with the instruction-tuned LLM for each corpora and represent each corpora by weighted averaging the synthetic queries and original corpora embeddings. We evaluate our proposed method under low-resource settings on three English and one German retrieval datasets measuring NDCG@10, MRR@100, Recall@100. We significantly improve the average zero-shot retrieval performance on all metrics, increasing open-box FLAN-T5 model variations by [3.34%, 3.50%] in absolute and exceeding three competitive dense retrievers (i.e. mDPR, T-Systems, mBART-Large), with model of size at least 38% smaller, by 1.96%, 4.62%, 9.52% absolute on NDCG@10.