Zen is very unlikely to produce LSD-like effects. It is just sitting. There isn't an object like breath or visualization to focus on, it's more like un-focusing the mind.
According to some ancient sources, some ritual substances produce effects that are called "siddhis," or in laymens' terms, psychic phenomenon. Ancient texts in yoga and Buddhism contain descriptions of states of consciouness associated with siddhis, or iddhis.
"Psychic powers arise by birth, drugs, incantations, purificatory acts or concentrated insight." - Patanjali Yoga Sutra
This web site is about Mindfulness Meditation, which like Zen practice, moves one AWAY from altered states, rather than to them. The effects of this are not "powerful" but are more permanent, if that interests you.
Siddhis: In Tibetan Buddhism it's much the same as Shaivism (not sure why Wikipedia did not list for Buddhism here):
In Shaivism, siddhi are defined as "Extraordinary powers of the soul, developed through consistent meditation and often uncomfortable and grueling tapas, or awakened naturally through spiritual maturity and yogic sādhanā."
Eight primary siddhis according to Shaivism
According to some forms of Shaivism, the eight classical siddhis (Ashta Siddhi) or eight great perfections are:
Aṇimā: reducing one's body to the size of an atom
Mahimā: expanding one's body to an infinitely large size
Garimā: becoming infinitely heavy
Laghimā: becoming almost weightless
Prāpti: ability to be anywhere at will
Prākāmya: realizing whatever one desires
Īśiṭva: supremacy over nature
Vaśiṭva: control of natural forces"
Or in Pali text its called "iddhi" or "rddhi"
According to Bowker, there are eight ṛddhi powers:
Replicate and project bodily-images of oneself,
Make oneself invisible,
Pass through solid objects,
Sink into solid ground,
Walk on water,
Touch the sun and moon with one's hand,
Ascend to the world of the god Brahmā in the highest heavens
According to the Iddhipada-vibhanga Sutta (SN 51.20)
Having been one he becomes many; having been many he becomes one.
He appears. He vanishes.
He goes unimpeded through walls, ramparts, & mountains as if through space.
He dives in and out of the earth as if it were water.
He walks on water without sinking as if it were dry land.
Sitting crosslegged he flies through the air like a winged bird.
With his hand he touches & strokes even the sun & moon, so mighty & powerful.
He exercises influence with his body even as far as the Brahma worlds.
In the book Great Disciples of the Buddha by Nyanaponika Thera and Hellmuth Hecker, there are several additional powers described:
The Divine Eye (Clairvoyance)- this power allows one to see beings in other realms as well as see the future
The Divine Ear (Clairaudience)
Travel by Mind-Made Body(Astral Travel)
Travel with the Physical Body (to other realms)
Telekinesis (Supernormal Locomotion)
The power of Transformation
The ability to replicate one's body
Penetration of others' minds (Thought Reading)
Passing through solid objects
Diving in and out of the Earth as if through water
Walking on water
Touching the sun and the moon with one's fingers
Recollection of past lives (some would call this a power, some would call it true knowledge)
Even in the case of those who seek to develop these powers, it's not a matter of something temporary such as a drug. It's more like a life-long pursuit. Most Buddhist, even advanced ones, see this a a trap, only further attachment, and will try to avoid these as much as possible.