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  • Alexander KnochelQuantensalat@scicomm.xyz
    May 25, 2026, 6:34 AM

    Tl;dr: I recreated a key bit of the quantum mechanics in cesium clocks in Mathematica, and it is rather pretty because it's just three matrices multiplied. It explains why cesium clocks have two microwave cavities with a long gap in-between, as the gap makes it more sensitive to tuning errors

    So I just understood a cool aspect of Cesium beam clocks that I hadn't known before (you know, being a theorist and all...), namely Ramsey spectroscopy.

    So I looked at the schematic here, and was wondering why the microwave cavity in the Cesium standard is apparently divided into two cavities with a gap in between. That didn't seem to make sense and I first thought I maybe misunderstood it, but no: One actually subjects the cesium to the microwaves, then lets it fly a bit all unperturbed, and then subjects it to the microwaves once more.

    So why the gap? 1/3

    #physics #quantumphysics #hamradio # electronics #scienceedu #scicomm

    A schematic drawing of a cesium beam clock. The beam goes into the chamber from the left, and there it goes through a bit of cavity where the tentative clock frequency is applied, leaves it again to fly through space, and once again goes through a bit of cavity, before going to the magnetic final state filter where the excited atoms are separated and counted. Why the gap in the cavity?
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Replies

  • Alexander KnochelQuantensalat@scicomm.xyz
    May 25, 2026, 6:40 AM

    So it turns out that one could just make it one big cavity. In this case, the closer I am to the famous 9 GHz transition which now is the official definition of the Second, the closer I get the more atoms get kicked into the higher energy state, and I count them in the end and adjust the frequency to maximize that.

    Now, Ramsey had they genius idea to let nature do some more work in between. You see, in quantum mechanics, the phase of any quantum wave rotates with a frequency that is given by the energy, and the two cesium states have slightly different energy.

    So what happens is the following: In the first cavity we apply the microwaves just strongly enough to turn the cesium into a quantum superposition of excited and unexcited state, then let them rotate according to their own frequency for a bit, letting them collect a bigger phase difference, and then finish the rotation into the wanted excited state.

    The longer you make the flight time in-between, the more sensitive the final state will become to slight de-tunings of your frequency: the addiitonal phase that is collected during flight enhances the cancellation effects you get when the frequency is detuned.
    This looks like this when you plot the probability over the microwave frequency (in arbitrary units): 2/3

    #physics #electronics #hamradio #scienceedu

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  • Alexander KnochelQuantensalat@scicomm.xyz
    May 25, 2026, 6:47 AM

    So these are the rotation matrices inside the cavity (U1) and for free flight (U2), and the total action of the clock is then the triple matrix product U1.U2.U1. I plot the magnitude squared of the off-diagonal element which stands for the transition from lower to higher state which we want to count. In the first picture I chose a shorter gap time, in the second picture I chose a longer gap time.

    As you can see, the function oscillates much quicker and these so-called fringes become narrower for a longer gap time. Now your clock oscillator sits on the central one, tunes a bit to the left and a bit to the right, and makes sure that it sits on the spot where the change is symmetric. Thanks to these narrow fringes, this is super sensitive to small changes in the frequency.

    (the x axis shows the de-tuning, with the zero in the center meaning we are exactly on the cesium hyperfine frequency)

    Anyway, I thought that was neat.

    #physics #electronics #hamradio #scienceedu

    Mathematica notebook defining 2x2 rotation matrices mixing both components (U1) and just turning the phase of the second component (U2) for free flight. Then they are multiplied as U1.U2.U1 and the off diagonal element squared looks like an interference pattern of a double slit. The longer the time in between is, the narrower the peaks become, making the system super sensitive to small deviations
    The fringes, but for flight time T=10 instead of T=1, showing many more narrower fringes
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  • Alexander KnochelQuantensalat@scicomm.xyz
    May 25, 2026, 7:01 AM

    A bit of technical detail for the quantum mechanics savvy: the Delta in the free time evolution should actually be the full energy difference between the two hyperfine level states, but we make a basis change to absorb that into the definition of the states, and so what remains after the frame change is the frequency de-tuning between microwaves and atoms, Delta

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