Some people hypnotize their rabbits in order to groom them; some vets do it to take x-rays without having to anesthetize.
BUT being hypnotized isn’t fun for your rabbit and you shouldn’t do it for laughs. It isn’t “cute” from the bunny’s perspective!
It can be dangerous to “hypnotize” your rabbit. Rabbits are vulnerable to back injuries, especially when their feet aren’t on the ground: if the rabbit snaps out of the hypnosis and kicks into the air, it can break its own back.
Being “hypnotized” is very frightening for some rabbits. It isn’t good to frighten to your rabbit: acute stress can lead to panic and injury; repeated stress can lead to illness; and any stress caused by you will damage your relationship with your pet. This “sleeplike” reaction is probably rooted in a wild predator-prey behaviour, meaning the rabbit is terrified: this isn’t something you should do for fun.
Some rabbits hypnotize really well but others don’t. The more restless your rabbit is, the more precautions you should take when trying to “hypnotize” him. If your rabbit doesn’t hypnotize deeply, and is always snapping out of it and trying to get away, then you should stop trying, period.
More detailed instructions (again, keep in mind, this isn’t true for all rabbits):
To hypnotize your bunny you need to gently lay your rabbit on its back on a soft surface (pillow, blanket, carpet) and gently massage right between its jaw and neck, gently rub that for around 5 to 10 seconds and then let go of your rabbit and it won’t move. Don’t worry if you want to wake back up your rabbit just tap it or lay it back over on its feet.
NEVER let your rabbit’s feet rest in thin air no matter what you’re doing. ALWAYS support your rabbit’s feet! If the rabbit is hypnotized on its back, you can lean forward so that the rabbit’s feet are against your belly. If a rabbit kicks into thin air it can seriously injure itself.