Question:

Why is exile likened to a state of sleep?

Answer:

"When G-d will return the exiles of Zion, we will have been like dreamers." (Psalms 126:1) When we will be redeemed from exile, the experience will be like awakening from a long sleep.

A dream can fuse two opposites; in a dream state, we can visualize things that are logically impossible.  In the present time of exile, likewise, our lives can have a paradoxical quality.  While praying, we can become aroused with love for G-d. When the prayer is over, though, the love vanishes and we go back to our preoccupation with material, mundane matters.

However, we should not assume that our spiritual service while in exile has no value.  Even if the inspiration later vanishes, every spiritual success is real and permanent.  Our G-dly soul is always complete, and its accomplishments can never be erased.

The fact that we are in a "dream-state" has a positive component.  It means that we are able to overcome boundaries that to our sane, rational mind seem insurmountable.  Our rational mind tells us that we must progress in an orderly, systematic fashion.  We mustn't think too big or get ahead of ourselves.  However, in a dream state we ignore all these limitations and can make a huge spiritual leap all at once, out of proportion to our previous level.

The prelude to the Egyptian exile was Pharaoh's dream, which Joseph interpreted, which lead to his being appointed viceroy and to finally bringing his entire family to settle in Egypt.  However, in the end the Jewish people left Egypt with great wealth.  Our present exile is likewise a state of "sleep," but through increasing in Torah and Mitzvot we can awaken in an instant to the ultimate state of redemption.

(Likutei Sichos vol. I, pp. 85-87.  Torah Or Vayeshev 28:3)