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Diffstat (limited to 'source/know/concept/multi-photon-absorption/index.md')
| -rw-r--r-- | source/know/concept/multi-photon-absorption/index.md | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/source/know/concept/multi-photon-absorption/index.md b/source/know/concept/multi-photon-absorption/index.md index 80dbc9b..481c19d 100644 --- a/source/know/concept/multi-photon-absorption/index.md +++ b/source/know/concept/multi-photon-absorption/index.md @@ -30,7 +30,6 @@ Here, we have made the to neglect the $$e^{i \omega t}$$ term, because it turns out to be irrelevant in this discussion. - We call the ground state $$\Ket{0}$$, but other than that, the other states need *not* be sorted by energy. However, we demand that the following holds @@ -187,7 +186,7 @@ i.e. for any odd-numbered final state $$\Ket{u}$$. ## Two-photon absorption Next, we go to second-order perturbation theory. -Based on the previous result, this time +Thanks to the previous result $$c_e^{(1)}(t) = 0$$, this time all odd-numbered states $$\Ket{u}$$ are unaffected: $$\begin{aligned} @@ -248,7 +247,7 @@ two identical photons $$\hbar \omega$$ are absorbed simultaneously to bridge the energy gap $$\hbar \omega_{e0}$$. Surprisingly, such a transition can only occur when $$\matrixel{e}{\vu{p}}{0} = 0$$, i.e. for any even-numbered final state $$\Ket{e}$$. -Notice that the rate is proportional to $$|\vb{E}|^4$$, +The rate is proportional to $$|\vb{E}|^4$$, so this effect is only noticeable at high light intensities. @@ -339,7 +338,7 @@ due to the dependence on $$\vb{E}$$. If $$N$$ is odd, only odd-numbered destinations $$\Ket{u}$$ are allowed (assuming the electron starts in the ground state $$\Ket{0}$$), and if $$N$$ is even, only even-numbered destinations $$\Ket{e}$$. -Note that nothing has been said about the energies of these states +Nothing has been said about the energies of these states (other than $$\Ket{0}$$ being the minimum); everything is determined by the matrix elements $$\matrixel{f}{\vu{p}}{i}$$. |