Fock state

The Fock state is any state of the Fock space with a well-defined number of particles in each state.

If we limit to a single mode for simplicity (doing so we formally describe a mere harmonic oscillator), a Fock state is of the type |n> with n an integer value. This means that there are n quanta of excitation in the mode. |0> corresponds to the ground state (no excitation). It is different from 0 which is the null vector.

Fock states form the most convenient basis of the Fock space. They are defined to obey the following relations in the bosonic algebra:

with a (resp. a^†) the annihilation (resp. creation) bose operator. Similar relations hold for fermionic algebra.

This allows to check that <a^†a>=n and Var(a^†a)=0, i.e., that measuring the number of particles a^†a in a Fock state returns always a definite value with no fluctuation.