From dedb366c3a78f61c64f6be627ea091e71e009f7d Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sat, 2 Oct 2021 15:40:20 +0200
Subject: Expand knowledge base

---
 content/know/concept/rabi-oscillation/index.pdc | 24 +++++++++++++++---------
 1 file changed, 15 insertions(+), 9 deletions(-)

(limited to 'content/know/concept/rabi-oscillation/index.pdc')

diff --git a/content/know/concept/rabi-oscillation/index.pdc b/content/know/concept/rabi-oscillation/index.pdc
index cf393a4..a488de0 100644
--- a/content/know/concept/rabi-oscillation/index.pdc
+++ b/content/know/concept/rabi-oscillation/index.pdc
@@ -87,11 +87,15 @@ while $\exp\!(i (\omega \!-\! \omega_0) t)$ does not.
 Dropping the respective terms thus leaves us with:
 
 $$\begin{aligned}
-    \dv{c_a}{t}
-    = - i \frac{V_{ab}}{2 \hbar} \exp\!\big(i (\omega \!-\! \omega_0) t \big) \: c_b
-    \qquad \quad
-    \dv{c_b}{t}
-    = - i \frac{V_{ba}}{2 \hbar} \exp\!\big(\!-\! i (\omega \!-\! \omega_0) t \big) \: c_a
+    \boxed{
+        \begin{aligned}
+            \dv{c_a}{t}
+            &= - i \frac{V_{ab}}{2 \hbar} \exp\!\big(i (\omega \!-\! \omega_0) t \big) \: c_b
+            \\
+            \dv{c_b}{t}
+            &= - i \frac{V_{ba}}{2 \hbar} \exp\!\big(\!-\! i (\omega \!-\! \omega_0) t \big) \: c_a
+        \end{aligned}
+    }
 \end{aligned}$$
 
 Now we can solve this system of coupled equations exactly.
@@ -186,7 +190,7 @@ the special case of exact resonance $\omega = \omega_0$:
 
 $$\begin{aligned}
     \Omega
-    \equiv \frac{V_{ab}}{\hbar}
+    \equiv \frac{V_{ba}}{\hbar}
 \end{aligned}$$
 
 As an example, Rabi oscillation arises
@@ -195,7 +199,7 @@ where $\hat{H}_1$ is:
 
 $$\begin{aligned}
     \hat{H}_1(t)
-    = - q \vec{r} \cdot \vec{E}_0 \cos(\omega t)
+    = - q \vec{r} \cdot \vec{E}_0 \cos\!(\omega t)
 \end{aligned}$$
 
 After making the rotating wave approximation,
@@ -203,12 +207,14 @@ the resulting Rabi frequency is given by:
 
 $$\begin{aligned}
     \Omega
-    = \frac{\vec{d} \cdot \vec{E}_0}{\hbar}
+    = - \frac{\vec{d} \cdot \vec{E}_0}{\hbar}
 \end{aligned}$$
 
 Where $\vec{E}_0$ is the [electric field](/know/concept/electric-field/) amplitude,
-and $\vec{d} \equiv q \matrixel{a}{\vec{r}}{b}$ is the transition dipole moment
+and $\vec{d} \equiv q \matrixel{b}{\vec{r}}{a}$ is the transition dipole moment
 of the electron between orbitals $\ket{a}$ and $\ket{b}$.
+Apparently, some authors define $\vec{d}$ with the opposite sign,
+thereby departing from its classical interpretation.
 
 
 
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