# Population inversion

** population inversion** is more exact a term from physics, quantum mechanics and describes the condition of a system, in which more particles occupy an energetically higher condition_{ N} 2 than the energetically lower condition N_{ 1}. This is inthermal equilibrium after the Boltzmann - distribution not possible, if a uniform temperature is presupposed. In the thermal equilibrium the Boltzmann equation applies:

- <math> N_2=N_1 \ cdot \ left (\ frac {g_2} {g_1} \ right) \ cdot {\ exp \ left (- \ frac {E_2-E_1} {k_b \ cdot T} \ right) } </math>,

<math> k_b = 1.38066 \ cdot 10 ^ {- 23} \, J\, K ^ {- 1} </math>: Boltzmann constant

<math> g_i< /math>: statistic weight of the condition <math> i< /math>

A population inversion is present, if <math> N_2 > g_2 \ cdot \ frac {N_1} {g_1}< /math>.

After the equation a higher temperature than the condition “1” can being assigned to the condition “2”. ThereSystem thereafter strives its entropy to maximize, is not not stable the population inversion and must by spending energy, which a pumping, artificially caused and upright will keep. Pumping must take place selectively, so that only selected levels of the particles more stronglyare occupied. The necessary energy can be brought in by optical pumping, whereby photo-flash lamps or the radiation of other lasers can be used.

The energy of the photon is proportional to the frequency or wavelength of the radiation:

<math> E = \, h \ cdot \ nu< /math>,

<math> h= 6.626076 \ 10^ cdot {- 34} \, J \, s </math> Planck constant

a population inversion is reached, if photon energy of the pump and the energy difference between the reason and agree a more highly put on electronic condition of the particle.

Another form of the selective suggestionthe impact with another lively particle is (B), which can exchange the energy difference by deexcitation, in order to bring the first particle (A) into the more highly put on condition. Around the particles of the sort B after the impact deexcitation again into thatput on condition to bring, them energy, z must. B. by electron collisions, to be supplied (see He-Ne-lasers). The energy can in form of an electrical discharge (e.g. Glow discharge, hollow cathode, microwave) into the medium to be brought.

becomes the source of suggestion (z. B. optical pumping, gas discharge) switched off, then is diminished the thermal overmanning of the inverted electronic condition by emission and impacts with other atoms or molecules. The localthermal equilibrium is reached, if put on electronic conditions, ionization degrees and the kinetic kinetic energy of the atoms/molecules are distributed according to the Boltzmann statistics. A condition is a high number density, in order to thus obtain a high stossrate and energy exchange.

## laser

a laseran arrangement represents to produce a ray of light its photons by same frequency, phase and oscillation direction (coherent radiation) is characterised. The usable radiation is uncoupled the radiation field in a resonator.

The condition for the enterprise of a laserthe reinforcement of a jet is by stimulated emission. In addition the occupation relationship of the two conditions must be inverted 1 and 2. This can be stationarily only achieved, if the lower condition 1 fast relaxiert and the life span is shorter thanthe life span of the upper condition determined by spontaneous emission. The lower condition must be emptied fast, so that the population inversion remains. On the other hand the upper condition must be long-lived 1, so that occupation is not so far reduced by spontaneous emission thatno sufficient rate of the stimulated emission arises.

In the detailed equilibrium the radiation processes in the equilibrium stand:

<math> A_ {21} \, N_2 \, + \, B_ {21} \, N_2 \, u_ {\ nu} \, = B_ {12} \, N_1 \, u_ {\ nu}

</math>,

spontaneous emission + stimulated emission = absorption

A_{ 21}: Einstein coefficient for spontante emission

B_{ 12}: Einstein coefficient for absorption

B_{ 21}: Transition probabilities represent Einstein coefficient for

stimulated emission the Einstein coefficients . The coefficient for stimulated emission stands with for absorption in connection: B_{ 21} = g_{ 1}/g_{ 2} B_{ 12}.

The detailed equilibrium applies in the Nichtgleichgewichtszustand only microscopically; the radiation intensity increases over the distance. In a laser radiation of the laser wavelength is optically strengthened. The population inversion is a necessary however not sufficient conditionfor the enterprise of a laser.