Post B6eOZrIp2HhTsXmka0 by brettm@swarm.coiloptic.org
(DIR) More posts by brettm@swarm.coiloptic.org
(DIR) Post #B6eOZqnGvaSmIh1YP2 by Quantensalat@scicomm.xyz
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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
(DIR) Post #B6eOZrIp2HhTsXmka0 by brettm@swarm.coiloptic.org
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@Quantensalat@scicomm.xyz unfortunately i can't read post 2 or 3 cause i click on the link and your instance redirects to some ground rules then i click ok and it redirects to a 'lets get you set up' page
(DIR) Post #B6eOZsM37lsN8qIqFU by Quantensalat@scicomm.xyz
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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
(DIR) Post #B6eOZtEdqnXps9qRLE by Quantensalat@scicomm.xyz
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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
(DIR) Post #B6eOZu42lgf4RZtUSe by Quantensalat@scicomm.xyz
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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
(DIR) Post #B6enEGpZwIELXKuSGG by dj3ei@mastodon.radio
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@brettm - is that what happens if you go to https://scicomm.xyz/@Quantensalat/116633820429618173 in your browser?Works for me. I get the 🧵.@Quantensalat
(DIR) Post #B6enEH0vG7Iw6WDVwW by brettm@swarm.coiloptic.org
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CC: @Quantensalat@scicomm.xyzthat works (firefox from my browser on laptop). but I think the link I clicked on earlier (from subway tooter app on android) should have just gone to same link? that is what normally happens...anyway I can read the other 2 posts now 🙂