Fock state

A Fock state, in quantum mechanics, is any state of the Fock space with a well-defined number of particles in each state. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons The Fock space is an Algebraic system ( Hilbert space) used in Quantum mechanics to describe Quantum states with a variable or unknown number of In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made The name is for V. A. Fock. Vladimir Aleksandrovich Fock (or Fok, Владимир Александрович Фoк ( December 22 1898 &ndash December 27 1974

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 $|n\rangle$ with n an integer value. This article is about the harmonic oscillator in classical mechanics This means that there are n quanta of excitation in the mode. $|0\rangle$ 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. Basis vector redirects here For basis vector in the context of crystals see Crystal structure. They are defined to obey the following relations in the bosonic algebra:

$a^{\dagger}|n\rangle=\sqrt{n+1}|n+1\rangle$

$a|n\rangle=\sqrt{n}|n-1\rangle$

$|n\rangle={1\over\sqrt{n!}}(a^{\dagger})^n|0\rangle$

with a (resp. In Particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein $a^{\dagger}$ ) the annihilation (resp. creation) bose operator. Similar relations hold for fermionic algebra. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi.

This allows to check that $\langle a^{\dagger} a \rangle = n$ and $Var(a^{\dagger}a)=0$ , i. e. , that measuring the number of particles $a^{\dagger}a$ in a Fock state returns always a definite value with no fluctuation.

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Vladan Vuletic of MIT has used an ensemble of atoms to produce a Fock state (a.k.a single photon) source

Nonclassical light is any state of Light that cannot be described using Classical electromagnetism; its characteristics are described by the quantised Electromagnetic

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(quantum mechanics) Any state of the Fock space with a well-defined number of particles in each state.

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Fock state

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