This is not the Jewish way - no shortcuts! Spirituality is not about personal experiences. It is about the hard work of refining one's character, improving the world, engaging in acts of kindness, prayer and learning Torah. It is about forging a close, intimate relationship with one's fellow Jew, man and of course first and foremost - God.
If one picks up any work on Jewish Law, nowhere in it does it say one should be engaged in having "spiritual mystical experiences", certainly not with the assistance of psychedelic drugs - all you will find is a guide to living a normal, drug-free life in a way that is in sync with truth and spirituality.
In fact, such drugs are likely highly damaging to one's soul, and are likely to invite all sorts of unwanted impure forces into one's world. They will be profound experiences that might convince someone of something that they are convinced is a deep truth but is actually purely a hallucination. There would be no way to prove it or disprove it but this person might attach themselves to this false idea for the rest of their life and the damage that does is immeasurable! See this answer for more detail about this...
Even the shamans and native american tribes will not permit one to use them without guidance and assistance. They are dangerous, alter one's personality, cause mental illness and other negative effects. The guidance will invariably be from a priest of a pagan religion as well, and this is something the Torah and the children of Avraham have stood against for thousands of years.
On top of that, if, in (highly dubious) theory, such drugs actually worked and enabled someone to access spiritual truths, then what would be the point of coming down into this world? Before our soul was born, it had unlimited access to all spiritual truths, and clearly that wasn't good enough. Hashem created this world and sent us down here, and asks us to elevate this world and make it receptive to Him through the sweat of our brow, sincere effort and by following His guidelines. Cheating that system is not appropriate. See Midrash Tanhuma Pekudei 7; Shemot Rabbah 52:3 for one example of many many examples where the Sages had an opportunity to "cheat" and demonstrated that this is not permitted or wise.
They had opportunities to do so through saying special names of Hashem, with no need for drugs. For example, it is possible to recall one's previous lives through such practices. Faith and Folly by Chacham Hillel Shlita goes to length to explain how forbidden this is. Maybe a mashal can be drawn. A husband, if he had access to some super power that he could perform acts of romance and fulfil his wife's needs by simply sitting in his chair and pressing a button, his wife would wonder why she even married him and if she even has a real relationship with him. He's supposed to serve her himself and demonstrate his love through effort and struggle; get out of his chair and talk to her and get to know her over time; then his love is real and the relationship is proven and earned. Hashem doesn't want us "cheating" in relating to Him and serving Him. If He did, as I have said, then He wouldn't have created this world of effort and toil (see Mesilat Yisharim introduction and ch.1), He could have just kept us up in heaven and we could have adored Him for eternity...
Any spiritual mystical experiences in Jewish life are either very down to earth (such as visiting the holy land, the western wall etc) or they are accessible by the holiest sages who have dedicated their very being to the service of God and man for many decades, through effort we cannot comprehend. After all of that, they are granted, without drugs, communion with higher worlds. Even in such cases, such endeavours are dangerous and not all of them come out unscathed.
As such, every single time I've heard reference to psychedelic drugs anywhere in the Torah world, it has always been classed as strictly forbidden and damaging. Tinkering with one's soul like that is grossly negligent and irresponsible, causing unspeakable damage that one might never be able to recover from.
No shortcuts. If you want a spiritual experience, or access to higher truth, do it properly: through a lifetime of study, kindness and prayer.
EDIT: I had a non-Jewish friend who took magic mushrooms and told me how he had a profound mystical experience where he experienced "god" as some cosmic entity that loves us profoundly and also had a huge sexual nature. I wanted to assist this guy and I spoke to my own Rav about it to see if there was anything else going on (I thought maybe he came into contact with something to do with klipa etc). My Rav said:
"He was hallucinating!! That's what hallucinogens are, they make you hallucinate. Who is he kidding? Mushrooms, LSD. Takes you to a different reality. Far away from the true reality. All the euphoria is just effect of the drug. They just make you feel like you had a spiritual experience, but it was drug induced. After a trip you feel like you want to get spiritual or religious. That's because you want to experience the euphoria for real. If you keep going back to the drug for that, you will get wrecked. Just get this message across: Ok you had a spiritual experience, but where is it going? Just for the fun? Where is the Avodah? The service discipline? What is there to gain from it? How can you sustain this spiritual feeling without crashing?"
This is a tremendously dangerous force to get involved with. It makes you feel like you have a way to connect to God, and it feels great, and it will put you off ever wanting to do this for real, through the real work that it takes to achieve genuine spiritual euphoria that you own yourself (see Derech Hashem 1:2:2), the ultimate goal of creation.
Note, my friend left his wife for the person who supplied him those drugs. The supplier also killed herself a few weeks later. He's now moved to the far east, I don't hear from him much anymore. Oy vey, just stay away from this sort of stuff.