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Shown are the magnetic field dependence of
the hyperfine energy levels in the ground state of the cesium atom (nine in
the upper state, seven in the lower).
The magnetic field is plotted up to the value HO. The solid arrow represents the “clock”
transition; the dashed arrows depict the magnetic-field-sensitive (Zeeman)
transitions. F is the hyperfine
quantum number, and mF is the magnetic quantum number of the atom.
The atomic resonance utilized is at
9,192,631,770 Hz - by definition (of the second*), which corresponds to the
(3,0) to (4,0) hyperfine transition, called the clock transition. Referring
back to “Generalized Atomic Resonator” earlier in this chapter, the (3,0) and
(4,0) levels are the A and B levels.
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This (3,0) to (4,0) transition has a small
quadratic dependence on magnetic field. The C-field must be stable and
uniform; high degree of shielding is
required for ±1x10-13/gauss magnetic field sensitivity (e.g., one
laboratory Cs standard uses a triple magnetic shield).
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It would be desirable to operate at zero
magnetic field - all transitions would then behave as a single transition,
the signal would be 7X larger, but that would require < 10-8
gauss for errors < 1 x 10-12.
This is not feasible; a C-field must be applied. A 0.06 gauss C-field separates the
sublevels by 40 kHz, and the the (3,0) and (4,0) levels, the level with the
minimum magnetic field sensitivity are utilized in making a Cs frequency
standard. The way these levels are utilized is shown schematically on the
next two pages.
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See “Magnetic Field Sensitivities of Atomic
Clocks” later in this chapter.
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* See “The Second”
in chapter 8.
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