Step 4: The distance between the observed and simulated transition frequencies is computed for all parameter points (Table 1, column 5).

Using this device he succeeded to measure the transition frequency of the Balmer line of atomic hydrogen with a much higher precision than before.

The atomic term is given by the Hamiltonian of a spin 1/2 system with being the transition frequency and the Pauli matrix.

This provides the possibility to read out the atomic (qubit) state by measuring the transition frequency.

As the hyperfine splitting is very small, the transition frequencies usually are not optical, but in the range of radio- or microwave frequencies.

This score is a normalised version of the transition frequency.

Let the energy difference between the states be so that is the transition frequency of the system.

The cavity frequency is and atomic transition frequency is .

The frequency difference of the two beams is exactly equal to the transition frequency between the two hyperfine levels.

A new beam is then switched on, whose frequency is exactly the transition frequency between and .