Fock state
A Fock state is a state of the oscillator with a perfectly definite number of quanta, written |n⟩, where n is a whole number. The ground state |0⟩ has none, the first excited state |1⟩ has exactly one, and so on. Each Fock state is an energy eigenstate, meaning it has a sharp, well-defined energy and sits motionless on a single rung of the energy ladder.
Fock states form an orthonormal basis: any state of the oscillator whatsoever, however complicated, can be written as a combination of them. They are the natural alphabet for describing the system, especially in quantum field theory, where |n⟩ means a mode is occupied by exactly n particles — n photons in a light mode, n phonons in a crystal vibration.
Pure Fock states with definite particle number are oddly non-classical: because their energy is perfectly sharp, their phase is completely uncertain, and the average position of |n⟩ just sits at the centre, not swinging like a classical oscillator. They are also surprisingly hard to prepare in the laboratory, especially for many photons, even though they are the simplest states to write down on paper. The named honour belongs to Vladimir Fock.
Each Fock state is built from the vacuum by raising operators and has a sharp energy.
A Fock state has definite energy but maximally uncertain phase — it is in this sense the opposite of a coherent state. Confusingly, |0⟩ is called the vacuum but is not 'nothing': it still carries the zero-point energy.