### Ytterbium Atomic Clock

March 16, 2012

When physicists mention the Heisenberg uncertainty principle, it's usually in its you can't step in the same river twice context; namely,
ΔxΔp ≥ h/4π,

where Δx is the uncertainty of a particle's position, Δp is the uncertainty of a particle's momentum, and h is the Planck constant. This inequality essentially states that if you attempt to accurately determine a particle's momentum, it won't be where you first found it.

There's an alternate formulation of this principle,
ΔEΔt ≥ h, approximately,
where ΔE is the uncertainty of an energy measurement and Δt is the uncertainty in a time measurement. The interpretation of this inequality, as perceived by no less than Niels Bohr, is that a short-lived state will not have a definite energy. Since the energy is proportional to the frequency, ν, by the equation, E = hν, the complementary interpretation is that only long-lived states will have a definite frequency.

What this means in the real world is that transitions from excited states with a long lifetime have a very narrow linewidth. This second formulation of the uncertainty principle is important when you're building atomic clocks.

Atomic clocks function by measuring the frequency of an atomic transition at microwave or optical frequencies. The most common such clocks use rubidium. There's a hyperfine transition in rubidium that occurs at 6,834,682,610.904324 Hz.[1]

 The hyperfine splitting of the 5S1/2 energy level in Rubidium-87.(Drawing by author, rendered using Inkscape).

A rubidium clock is actually easy to make. You build a rubidium discharge lamp, expose it to a variable frequency microwave oscillator near the 6.835 GHz frequency, and monitor its light output. When the microwave oscillation matches the transition frequency, the light output will decline slightly. A control loop can be used to lock the microwave oscillator onto the rubidium frequency.

As time marches on (pun intended), scientists seek to make more accurate clock sources. Scientists at the Physikalisch-Technische Bundesanstalt (Braunschweig, Germany), have created an atomic clock using a "forbidden" transition in ytterbium-171 (171Yb).[2-4] This device, combined with a recent measurement of the frequency of this 2S1/2-2F7/2 optical transition (642,121,496,772,646.22 Hz),[5] makes this a clock with an error of about 10−16.

This frequency of 642 terahertz corresponds to a wavelength of 467 nm. The German research team captured a single 171Yb+1 ion in an ion trap for their measurements. This forbidden transition is nearly, but not completely, impossible because of conservation of symmetry and angular momentum. The transition is so unlikely that it has a lifetime of about six years and a correspondingly small linewidth. This small linewidth corresponds to a timekeeping error of just thirty seconds in the age of the universe.[5]

 The ion trap used in the Physikalisch-Technische Bundesanstalt experiments.The 467 nm laser radiation is a pretty blue color.(Physikalisch-Technische Bundesanstalt photograph).

The downside of all this forbidding is that it takes a large laser energy to force the transition, which disturbs the ion and causes measurement errors. The advance made by the German team is finding that they could alternate low and high intensity laser beams to get a better measurement.[5] They also found another less forbidden transition at 436 nm, so it might be possible to have a self-checking atomic clock in a single ion.[5]

 Another type of atomic clock. The Doomsday Clock of the Bulletin of the Atomic Scientists is a representation of the health of the world. It shows the minutes before an apocalyptic "midnight." It was conceived in 1947 because of the possibility of nuclear war. Now, other environmental issues, such as global warming and biotechnology, are rolled into this scoring. (Via Wikimedia Commons).

### References:

Linked Keywords: Physicist; Heisenberg uncertainty principle; you can't step in the same river twice; position; momentum; Planck constant; inequality; energy; time; Niels Bohr; frequency; excited state; linewidth; atomic clock; atomic transition; microwave; optical; rubidium; hyperfine transition; Inkscape; discharge lamp; oscillator; control loop; pun; scientist; Physikalisch-Technische Bundesanstalt (Braunschweig, Germany); "forbidden" transition; ytterbium-171; terahertz; wavelength; nanometer; nm; German; ion; ion trap; symmetry; angular momentum; universe; laser; Doomsday Clock; Bulletin of the Atomic Scientists; 1947; nuclear war; global warming; biotechnology; Wikimedia Commons.

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