Although Sufism is an esoteric school within the Muslim tradition, it's aims in meditation are exactly the same as those in Buddhism and Hinduism, to experience the non-dual nature of reality first hand.
An extract from 'Sufism and Quantum Physics' by Ibrahim B.Syed
"...For Sufis “Enlightenment” is an experience to become aware of the unity and mutual interrelation of all things, to transcend the notion of an isolated individual self, and to identify themselves with the ultimate reality.
An exact science is expressed in the highly sophisticated language of modern mathematics, whereas Tasawwuf is based on meditation and insists on the fact that Sufis’ insight cannot be communicated verbally. Reality as experienced by the Sufis is completely indeterminate and undifferentiated. Sufis never see the intellect as their source of knowledge but use it merely to analyze and interpret their personal Tasawwuf experience. The parallel between scientific experiments and Tasawwuf experiences may seem surprising in view of the very different nature of these acts of observation. Physicists perform experiments involving an elaborate teamwork and a highly sophisticated technology, whereas the Sufis obtain their knowledge purely through introspection, without any machinery, in the privacy of meditation or Dhikr. To repeat an experiment in modern elementary particle physics one has to undergo many years of training. Similarly, a deep Tasawwuf experience requires, generally, many years of training under an experienced master. The complexity and efficiency of the physicist’s technical apparatus is matched, if not surpassed, by that of the mystic’s consciousness-both physical and spiritual-in deep Dhikr. Thus the scientists and the Sufis have developed highly sophisticated methods of observing nature which are inaccessible to the layperson.
DHIKR
The basic aim of Dhikr is to silence the thinking mind and to shift the awareness from the rational to the intuitive mode of consciousness. The silencing of the mind is achieved by concentrating one’s attention on a single item, like one’s breathing, the sound of Allah or La Ilaha Illallah. Even performing Salat is considered as Dhikr to silence the rational mind. Thus Salat leads to the feeling of peace and serenity which is characteristic of the more static forms of Dhikr. These skills are used to develop the meditative mode of consciousness. In Dhikr, the mind is emptied of all thoughts and concepts and thus prepared to function for long periods through its intuitive mode. When the rational mind is silenced, the intuitive mode produces an extraordinary awareness; the environment is experienced in a direct way without the filter of conceptual thinking. The experience of oneness with the surrounding environment is the main characteristic of this meditative state. It is a state of consciousness where every form of fragmentation has ceased, fading away into undifferentiated unity.