= Maser state selection
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 $\mathcal E$ by
$$
W_\pm(\mathcal E)=\pm\sqrt{(h\nu_0/2)^2+d^2\mathcal E^2}.
$$
For 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> $\boldsymbol F_+=-\nabla W_+$ 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.<Chapter 9: The Ammonia Maser>[§9–2, Eq. (9.30)]{ref} The idealized <two-level system> omits the actual rotational and <hyperfine structure> sublevels and their different transmission efficiencies.
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