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In ammonia, the nitrogen chemical atom can lie on either side of the plane of the three hydrogen chemical atoms. Quantum tunnelling couples these configurations; the resulting pair of energy levels permits an electric dipole transition. This geometrical inversion is distinct from population inversion, which concerns how many molecules occupy each level.^[ref]

For an idealized pair of energy levels with equal quantum degeneracy, the Boltzmann distribution gives $N_u/N_l=\exp [-h{\nu }_0/(k_{\mathrm{B}}T)]<1$ at positive temperature $T$. A warm source therefore supplies upper-state molecules together with an unwanted lower-state population. Selecting the former can produce population inversion in the transmitted beam without exciting each transmitted molecule during selection. The energy per net downward transition isHere $h$ is the Planck constant. Taking the reported ${\nu }_0=23.87\mathrm{GHz}$ as a rounded input gives $ϵ\approx 1.582\times 10^{-23}\mathrm{J}$. This calculation is a conversion of the reported frequency, not a new measurement of the ammonia inversion transition.

An ammonia maser uses an ammonia molecular beam, maser state selection and a maser cavity to obtain amplification or sustained microwave oscillation. In the 1954 experiment by James Power Gordon, Herbert Jack Zeiger and Charles Hard Townes, a quadrupolar static electric field focused upper-state molecules toward the cavity and deflected lower-state molecules away. The reported $J=K=3$ ammonia inversion transition lies near $23.87\mathrm{GHz}$.^[ref]

Maser state selection separates paths according to the Stark effect, the dependence of a molecule's energy levels on an electric field. It prepares a transmitted population by sorting. Optical pumping, by contrast, changes populations through absorption of light and subsequent transitions. Both can produce a useful population imbalance, but they are different preparation mechanisms.

A simple two-level system explains the sign of the focusing force. Ignore additional splittings and let the magnitude of the relevant projected electric dipole moment be $d$. Model the two local energy levels in an electric field of magnitude $\mathcal{E}$ byFor an ideal quadrupolar electrostatic potential $\Phi =A(x^2-y^2)$, the electric field magnitude is $\mathcal{E}=2|A|r$, where $r=\sqrt{x^2+y^2}$. Since $W_{+}$ increases with $r$, the force ${\mathbf{F}}_{+}=-\nabla W_{+}$ points inward. The lower branch has the opposite sign and is defocused. The upper branch is thus low-field seeking. This argument uses the gradient of internal energy, rather than a net electric charge on the molecule. The square-root splitting is the usual two-state description.^[ref] The idealized two-level system omits the actual rotational and hyperfine structure sublevels and their different transmission efficiencies.