To grasp the relationship between elixir and love in the poem "Love's Alchemy" by John Donne, it is first necessary to understand the meaning of the title. According to the Merriam-Webster Dictionary, alchemy is
A medieval chemical science and speculative philosophy aiming to achieve the transmutation of the base metals into gold, the discovery of a universal cure for disease, and the discovery of a means of indefinitely prolonging life; or, a power or process that changes or transforms something in a mysterious or impressive way.
Ancient alchemists often sought a potion known as the elixir of life or the elixir of immortality that they thought would cure diseases and bestow eternal life. This is what Donne refers to in the poem as the "elixir" that the "chemic" (or chemist) is creating in his "pregnant pot."
In "Love's Alchemy," the relationship between the elixir of life and love is one of comparison. Donne is comparing the wild claims of alchemists that the elixir they attempt to concoct will give life and health with the claims of lovers that being in love solves all their problems. However, Donne emphasizes that love is much more complex than that. He indicates that he has loved before, and even if he should continue to love until he is old, he will still not understand the "hidden mystery" of love. Lovers imagine that the elixir, or magic, of their love will give them a "rich and long delight," but all too often, love is cooler and briefer than they suppose it will be.
Just as the alchemist's elixir is a fantasy, so Donne calls love a "vain bubble" that can easily dissipate. Even marriage is not a guarantee of happiness, and women too often turn out to be disappointing.