# Timekeeping , optical clocks, and precision

I am having trouble understanding something:

The concept of time measurement.

So I want to simply this as much as possible to get an intuitive understanding:

We define the second by the time it takes cesium to oscillate 9.192631770 x 10^9 times. So in my head I am picturing someone watching a cesium atom, counting 1,2,3,4,5... 9.192631770 x 10^9 and then being BOOM a second -- that right there is a second, mark it down.

First:

(1) Why is this a second - why this specific number? I mean in essence isn't the second defined by counting ONE oscillation of cesium and multiplying it by 9.192631770 x 10^9? and since we can count these oscillations this gives a precision of about: (1 sec / 9.192631770 x 10^9) = 10^-10 seconds -- right?

(2) I am reading about optical clocks and how they can improve accuracy in time keeping, by reducing the uncertainty - which can be done using frequency combs. So i understand how we can improve our precision: namely just being able to count the the oscillations of a light wave at a high frequency -- but everywhere I keep reading they always refer to this bridge between 'microwave cesium radiation' and optical radiation. I don't fully understand the connection. Like say I am sitting there counting oscillations of the optical light - ok 1, 2, 3, 4, 5 in say X amount of time. My precision will be (X/5) = VERY SMALL NUMBER < 10^-10 (as we had in our cesium clock). And say for argument sake the second was defined by the amount of time it took cesium to oscillate once. So is an optical clock essentially counting the number of times the optical mode oscillates between cesium oscillations? E.G. Cesium oscillation = 0 -> Cesium oscillation = 1.

Whereas currently it is the time it takes for Cesium oscillation = 0 -> Cesium oscillation = 1 * 9.192631770 x 10^9 ?

(3) How do frequency combs aid in this matter?

• The caesium atom doesn't oscillate. The frequency is the frequency of the light emitted by a specific electronic transition. – ACuriousMind Apr 4 '16 at 21:37
• Question 1 is answered here (and in other questions linked from there). – The Photon Apr 4 '16 at 21:46
• @ThePhoton perhaps, since the question you linked is itself marked as a duplicate, better use this link – Floris Apr 4 '16 at 21:57
• @Floris, but the answer at the place I linked matches this question better than the ones at the earlier question. – The Photon Apr 4 '16 at 22:02
• For the answer to Q 2 and 3, maybe start here and here. – The Photon Apr 4 '16 at 22:18

but everywhere I keep reading they always refer to this bridge between 'microwave cesium radiation' and optical radiation. I don't fully understand the connection.

The optical frequency comb is generated by a laser source generating periodic very short pulses. Such a source will have peaks in its spectrum at frequencies

$$f_n = n f_r + f_0$$

where $f_r$ is the repetition rate of the the pulses, and $f_0$ is an offset frequency.

The "bridge" to the microwave frequency is made by generating $f_r$ from a source that is locked to a microwave or rf frequency standard.

Finding $f_0$ is more complicated, requiring passing the comb signal through a nonlinear optical medium to obtain a comb spanning at least one octave, and then further passing it through a frequency doubler. This done, we can combine a line from the doubled comb (at $2nf_r+2f_0$) with one from an octave away on the original comb (at $2nf_r + f_0$), to obtain a beat frequency $f_0$, which we can compare with a microwave frequency standard using electronics. (source)

Like say I am sitting there counting oscillations of the optical light - ok 1, 2, 3, 4, 5 in say X amount of time.

A key issue is that there is currently no known method to do that. We don't have any electronic means to count oscillations of optical light. Currently the best we can do is to compare the spectrum of an unknown source with a known reference. Traditionally we'd use, for example, emission lines from a mercury vapor lamp. But with optical combs we get more closely and more uniformly spaced lines to compare with.