Timeline for Drive frequency for second order quantum transitions
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2018 at 6:01 | history | tweeted | twitter.com/StackPhysics/status/1044104428842872832 | ||
| Sep 19, 2018 at 4:27 | answer | added | wcc | timeline score: 0 | |
| Sep 18, 2018 at 16:08 | vote | accept | DanielSank | ||
| Sep 18, 2018 at 15:59 | history | edited | DanielSank | CC BY-SA 4.0 |
edited body
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| Sep 18, 2018 at 11:55 | comment | added | Emilio Pisanty | Just for the record, I think the time-ordering issues have been perfectly well handled here, and they do not even need the condition $[V(t),V(t')]=0$ to work. Explicit time-ordering requirements come in if you want to re-express the (infinite) Dyson series as an exponential, but that's not been done here. The requirement that $0\leq t'' \leq t' \leq t$ is plenty obvious in the integration throughout the question. | |
| Sep 18, 2018 at 9:48 | history | edited | Emilio Pisanty | CC BY-SA 4.0 |
Removed ugly space at the top of the post caused by the mathjax-on-its-own-line.
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| Sep 18, 2018 at 9:48 | answer | added | Emilio Pisanty | timeline score: 5 | |
| Sep 18, 2018 at 4:52 | comment | added | DanielSank | @IamAStudent Perhaps the notation I used isn't clear, but the second integral goes from $0$ to $t'$, so the constrained ordering you have written is there. | |
| Sep 18, 2018 at 4:49 | comment | added | wcc | I think we do...In the perturbative expansion, the integration limit tells us that $0 \leq t' \leq t$ and $0 \leq t'' \leq t'$ so $0 \leq t'' \leq t' \leq t $ but this is not apparent in the final expression. Regarding the book, If you can't find it I will give a try tomorrow at working out what I mentioned (or least provide the expressions from the book to work on) | |
| Sep 18, 2018 at 4:39 | comment | added | DanielSank | @IamAStudent thanks for the comments. I don't think we need time ordering here because $[V(t), V(t')]=0$ for all $t$ and $t'$. I appreciate the reference. Will see if a coworker has the book. | |
| Sep 18, 2018 at 4:33 | comment | added | wcc | I think the Dyson series integral should have time ordering. Also, Cohen-Tannoudji works out the transition amplitude for second order transition in pg 28-30 of "Atom-Photon Interaction" for time-independent $\hat{V}$, and I feel the generalization to time-dependent case should be straightforward. The drive frequency should appear in the $\delta^{(T)}(E-E_{f,i})$ that he talks about, and the right choice of drive frequency should maximize the value of the product of two $\delta^{(T)}$. | |
| Sep 18, 2018 at 3:50 | history | asked | DanielSank | CC BY-SA 4.0 |