What is the connotation of slumber?

I've always thought "to slumber" meant to sleep deeply or for a long period of time. Several colloquial but less reputable dictionaries agree with me (http://www.urbandictionary.com/define.php?term=slumber, http://www.yourdictionary.com/slumber) but Merriam-Webster and the OED disagree, defining slumber as "to sleep lightly" and "to sleep, esp. to sleep lightly; to doze or drowse," respectively.

Which is correct in modern usage?

It just means sleep. Although it is not an archaism, the word isn't used much in everyday English. Google Ngram shows the usage of slumber compared with sleep.

Google Books Ngram Viewer

It is an old verb, not commonly used nowadays:

Slumber:

• mid-14c. alteration of slumeren (mid-13c.), frequentative form of slumen "to doze," probably from Old English sluma "light sleep" (compare Middle Dutch slumen, Dutch sluimeren, German schlummern "to slumber"). Frequentative on the notion of "intermittent light sleep." (Etymonline)

To slumber literary :

• Sleep - ‘Sleeping Beauty slumbered in her forest castle’ figurative ‘the village street slumbered under the afternoon sun’' (ODO)