creation operator
The creation operator, usually written a-dagger, is the ladder operator that raises an oscillator by exactly one rung. Apply it to a state and you get the next state up, with one more quantum of energy ℏω added. In the language of particles it 'creates' one more quantum — hence the name — turning a state of n quanta into a state of n plus one.
Acting repeatedly, the creation operator builds the entire family of states from the very bottom. Start with the ground state, apply a-dagger once and you have the first excited state, twice and you have the second, and so on. Every state of the oscillator can be written as the creation operator applied some whole number of times to the ground state, which makes it the natural construction kit for the whole spectrum.
It carries a numerical factor, the square root of n plus one, so that the states stay properly normalised as you climb. In quantum field theory this same operator adds a real particle — a photon to a light field, a phonon to a crystal — and the entire content of a field can be described by how many times various creation operators have acted on the empty vacuum.
Adds one quantum and bumps the state up to the next rung, |n⟩ → |n+1⟩.
Despite the vivid name, the creation operator does not conjure energy from nothing; it is a mathematical map between already-existing states of the system. It is also not Hermitian, so it is not itself something you measure.