What we know of the meaning of kykeon is as follows.

• The name comes from the verb stem kuka- 'stir'.
• Iliad 11.624-641 describes a kykeon prepared with onion 'as a spice for the drink, and pale honey', and made by mixing 'pramneian' wine (the meaning of pramneios is unknown), grated goat's milk cheese, and white barley flour.
• Odyssey 10.590 has Kirke put pharmaka, a magic spell or potion, into a kykeon to transform people into animals.
• Hymn to Demeter 208-211 describes a kykeon prepared by mixing barley flour with pennyroyal in water, and stirred directly before drinking to stop the barley sinking to the bottom.
• Hipponax fragment 39 (ed. West) corroborates that a kykeon is made with barley.
• A scholion (ancient gloss) on the Iliad passage compiles various medical sources on the subject, observes that in ancient medical thought cheese and barley were considered to encourage phlegm production, wine is good for bloodflow, and that onion is a diuretic; then states that 'The drink isn't given for medical treatment, but for refreshment. After all, Nestor drinks it too. The kykeon is suitable for people with ailments, since it provides both nourishment and drink at once.'
• At Eleusis, in Attica, a kykeon was a stage in the initiation procedure. A passage in Clement of Alexandria, a 2nd century CE Christian writers, suggests that a short fasting period may have been followed by consumption of a kykeon.

None of the ingredients mentioned in the Iliad or the Hymn to Demeter is psychotropic. There's no suggestion in the sources that the barley was treated in any way, or allowed to ferment.

The main bit of context for your question, then, is that there has been some speculation in the modern period that one of the ingredients might be psychotropic. There is no particular reason to imagine this. The reasoning always boils down to: 'people were impressed by the initiation ceremony at Eleusis, therefore they must have been high on drugs'. That's literally it. The rest is circumstantial wishful thinking: the fact that Kirke puts pharmaka into her kykeon, and that Hipponax refers to his kykeon as a 'pharmakon for wretchedness'. Pharmakon can mean 'poison, magic spell', but it can also just mean 'remedy'.

Absence of evidence doesn't stop it being a popular idea that it was psychotropic, unfortunately. The impressiveness of the initiation ceremony at Eleusis, according to ancient sources, actually lay in the sudden use of torchlight in a darkened gathering hall, but proponents tend to avoid mentioning that. Wasson, Hofmann, and Ruck speculated that the barley might have been infected with ergot; ergot can have psychotropic effects, but is inconsistent in its effects, and can be poisonous. Calvert Watkins speculated that it was the pennyroyal; pennyroyal is not psychotropic. Robert Graves suggested mushrooms, and Kerényi suggested opioids from poppies: these ones are virtually invented out of thin air (the opioid one is perhaps related to the fact that a poem by Ovid mentions Ceres in conjunction with opioids). I've never seen anyone suggest that feta cheese might be psychotropic (in the Iliadic kykeon), but after going through this kind of argumentation nothing would surprise me.

There's no evidence to suggest psychotropic effects, let alone intended psychotropic effects. What the available evidence actually indicates, especially the ingredients lists in the Iliad and the Hymn, and the commentary in the Iliad scholion, is that it was simply a barley drink that was both filling and refreshing.