How to 'activate' deep sleep ? Turn your screen off & leave your phone alone, when it's 'idling', it should be in deep sleep the majority of the time unless you have WiFi running or something else that's using the phone's resources.
You can't activate deep sleep as such.
If you find your phone isn't in deep sleep when it should be, there might be apps causing wakelocks which stop it entering deep sleep. If you suspect that's the case, install BetterBatteryStats & allow your phone to run normally for 8-10 hrs/overnight before you have a look at the stats in BBS.
If they show you've got wakelocks stopping the phone from sleeping, read the BBS thread on here. Info in the thread might be able to help you identify these wakelocks & perhaps eliminate or reduce them. There are also people who post to that thread a lot that might be able to help you identify/eliminate these.
One thing tho, you say you've used CPU Spy, what are the figures you're getting out of CPU SPY when you leave the phone idling/doing nothing with the screen off for say, an hour ?
If it's important enough to cause you grief if it's lost, back it up. No excuses
Trolling for thanks is lame
Does Samsung's auto-brightness implementation crap drive you to self-harm ? A solution !
Most retarded thread on XDA in 2013