diff options
Diffstat (limited to 'content/know')
| -rw-r--r-- | content/know/concept/coupled-mode-theory/index.pdc | 6 | ||||
| -rw-r--r-- | content/know/concept/multi-photon-absorption/index.pdc | 4 | ||||
| -rw-r--r-- | content/know/concept/shors-algorithm/index.pdc | 2 |
3 files changed, 7 insertions, 5 deletions
diff --git a/content/know/concept/coupled-mode-theory/index.pdc b/content/know/concept/coupled-mode-theory/index.pdc index c9e9ad4..581dce4 100644 --- a/content/know/concept/coupled-mode-theory/index.pdc +++ b/content/know/concept/coupled-mode-theory/index.pdc @@ -109,6 +109,7 @@ After reversing time, $A$ evolves like so, where we have taken the complex conjugate to preserve the meanings of the symbols $A$, $S_\ell^\mathrm{out}$, and $S_\ell^\mathrm{in}$: + $$\begin{aligned} A(t) = A e^{-i \omega_0 t + t / \tau_\ell} @@ -129,7 +130,7 @@ $$\begin{aligned} = \frac{\alpha_\ell \tau_\ell}{2} S_\ell^\mathrm{in} \qquad \implies \qquad |\alpha_\ell|^2 |S_\ell^\mathrm{in}|^2 - = \frac{4}{\tau_\ell^2} |A| + = \frac{4}{\tau_\ell^2} |A|^2 \end{aligned}$$ But thanks to energy conservation, @@ -203,7 +204,8 @@ $$\begin{aligned} \boxed{ \begin{aligned} \dv{A}{t} - &= - i \omega_0 A - \sum_{\ell = 1}^N \frac{1}{\tau_\ell} A + &= \bigg( \!-\! i \omega_0 - \frac{1}{\tau_0} \bigg) A + - \sum_{\ell = 1}^N \frac{1}{\tau_\ell} A + \sum_{\ell = 1}^N \sqrt{\frac{2}{\tau_\ell}} S_\ell^\mathrm{in} \\ S_\ell^\mathrm{out} diff --git a/content/know/concept/multi-photon-absorption/index.pdc b/content/know/concept/multi-photon-absorption/index.pdc index a5f4ad7..337554d 100644 --- a/content/know/concept/multi-photon-absorption/index.pdc +++ b/content/know/concept/multi-photon-absorption/index.pdc @@ -253,7 +253,7 @@ $$\begin{aligned} This represents **two-photon absorption**, since it peaks at $\omega_{e0} = 2 \omega$: two identical photons $\hbar \omega$ are absorbed simultaneously to bridge the energy gap $\hbar \omega_{e0}$. -Suprisingly, such a transition can only occur when $\matrixel{e}{\vu{p}}{0} = 0$, +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 $|\vb{E}|^4$, so this effect is only noticeable at high light intensities. @@ -333,7 +333,7 @@ so this effect only appears at extremely high light intensities. ## N-photon absorption -A pattern has appeared in these calculcations: +A pattern has appeared in these calculations: in $N$th-order perturbation theory, we get a term representing $N$-photon absorption, with a transition rate proportional to $|\vb{E}|^{2N}$. diff --git a/content/know/concept/shors-algorithm/index.pdc b/content/know/concept/shors-algorithm/index.pdc index e3666a3..643337c 100644 --- a/content/know/concept/shors-algorithm/index.pdc +++ b/content/know/concept/shors-algorithm/index.pdc @@ -14,7 +14,7 @@ markup: pandoc # Shor's algorithm -**Shor's algorithms** was the first truly useful quantum algorithm. +**Shor's algorithm** was the first truly useful quantum algorithm. It can solve important problems, most notably integer factorization, much more efficiently than any classical algorithm. |