Variation around "sleeping"

To hit the sack:
Syn: to go to bed

• Very often we would not hit the sack until one o'clock in the morning. - aller se coucher

Forty winks 

Syn: a brief and light sleep

• I´m going to catch forty winks before getting ready to go out.- piquer un petit roupillon 
• He usually has forty winks going home on the train. 

To turn in

Syn: to go to bed (familiar)

• It's getting very late, I'm going to turn in. - se pieuter, se coucher

To get/put your head down
Meaning 1: going to sleep, to sleep for a short while

• I'm just going to put my head down for an hour - I feel so tired.

Meaning 2: to work hard at something that involves reading or writing, to direct all your efforts into the particular task you are involved in

• I'm sure I can finish the article - I just need to get my head down this afternoon.
• They will have to wind down their business and get their heads down to studying 
• I'm going to get my head down and try and finish this report before I go home today.

To run on empty

Meaning 1: to continue working when you have no energy or enthusiasm

• I get the impression he's been running on empty for months now. A holiday will do him good.

Meaning 2: If a person or an organization is running on empty, they have no new ideas or are not as effective as they were before.

• The fund-raising campaign was running on empty after ten years under the same leader.

VISUAL THESAURUS http://www.visualthesaurus.com

 Source: http://www.bbc.co.uk/worldservice/learningenglish/general/sixminute/2013/05/130516_6min_sleeping_for_learning.shtml