udpate

Author: mhjensen

doc/src/FuturePlans/bellfig.pdf

@@ -0,0 +1,115 @@
+\documentclass{article}
+\usepackage{quantikz}
+\begin{document}
+\begin{center}
+\begin{quantikz}
+  \lstick{$\ket{0}$} & \gate{H} & \ctrl{1} & \qw  & \rstick[2]{$\ket{\Phi^+} = \frac{1}{\sqrt{2}}(\ket{00} + \ket{11})$} \\
+  \lstick{$\ket{0}$} & \qw      & \targ{}  & \qw  &
+\end{quantikz}
+\end{center}
+
+
+\begin{tikzpicture}[>=latex]
+  % Draw axes
+  \draw[->] (-3.5,0) -- (3.5,0) node[right] {$x$};
+  \draw[->] (0,0) -- (0,5) node[above] {$E$};
+  % Draw potential curve V(x) = 1/2 x^2 (parabola)
+  \draw[thick] (0,0) parabola (3,4.5);
+  \draw[thick] (0,0) parabola (-3,4.5);
+  % Draw quantized energy levels E_n = n+0.5
+  \draw[dashed] (-3,0.5) -- (3,0.5) node[right] {$n=0$};
+  \draw[dashed] (-3,1.5) -- (3,1.5) node[right] {$n=1$};
+  \draw[dashed] (-3,2.5) -- (3,2.5) node[right] {$n=2$};
+  \draw[dashed] (-3,3.5) -- (3,3.5) node[right] {$n=3$};
+  \draw[dashed] (-3,4.5) -- (3,4.5) node[right] {$n=4$};
+\end{tikzpicture}
+
+
+\begin{tikzpicture}[>=latex, line cap=round, line join=round]
+  % Axes
+  \draw[->] (-3.7,0) -- (3.7,0) node[right] {$x$};
+  \draw[->] (0,0) -- (0,5.2) node[above] {$E$};
+
+  % Harmonic oscillator potential V(x) = (1/2) x^2 (in units where ħω=1)
+  \draw[thick] (0,0) parabola (3,4.5);
+  \draw[thick] (0,0) parabola (-3,4.5);
+  \node[anchor=west] at (0.2,4.9) {$V(x)=\tfrac12 m\omega^2 x^2$};
+
+  % Energy levels En = n + 1/2 (units ħω)
+  \foreach \n/\E in {0/0.5,1/1.5,2/2.5,3/3.5,4/4.5}{
+    \draw[dashed] (-3,\E) -- (3,\E);
+    \node[anchor=west] at (3.1,\E) {$n=\n$};
+  }
+% --- Two particles in the lowest level n=0 ---
+  % Place two circles on the n=0 line
+  \filldraw[fill=white, thick] (-0.6,0.5) circle (0.12);
+  \filldraw[fill=white, thick] ( 0.6,0.5) circle (0.12);
+
+  % Spin arrows: up on left, down on right
+  \draw[->, thick] (-0.6,0.53) -- (-0.6,0.85);  % spin up
+  \draw[->, thick] ( 0.6,0.85) -- ( 0.6,0.53);  % spin down
+
+  % Optional labels
+  \node[anchor=south] at (-0.6,0.88) {$\\uparrow$};
+  \node[anchor=north] at ( 0.6,0.50) {$\\downarrow$};
+
+  % Highlight the n=0 level a bit
+  \draw[very thick] (-3,0.5) -- (3,0.5);
+
+\end{tikzpicture}
+
+
+
+\begin{tikzpicture}[>=latex, line cap=round, line join=round, scale=1.0]
+
+  % ---- Axes (optional) ----
+  %\draw[->] (-7,0) -- (7,0) node[right] {$x$};
+  %\draw[->] (0,0) -- (0,6) node[above] {$E$};
+
+  % Parameters
+  \def\xL{-3.5}      % left well center
+  \def\xR{ 3.5}      % right well center
+  \def\a{1.2}        % horizontal scale of each parabola
+  \def\Emax{4.5}     % top energy level drawn
+  \def\yBridge{5.2}  % height of smooth connecting curve on top
+  \def\R{0.13}       % particle radius
+
+  % ---- Left harmonic well: V_L(x) = 0.5 * ((x-xL)/a)^2 ----
+  \draw[thick, domain=\xL-3:\xL+3, samples=120]
+    plot (\x, {0.5*((\x-\xL)/\a)^2});
+
+  % ---- Right harmonic well: V_R(x) = 0.5 * ((x-xR)/a)^2 ----
+  \draw[thick, domain=\xR-3:\xR+3, samples=120]
+    plot (\x, {0.5*((\x-\xR)/\a)^2});
+
+  % ---- Smooth curve joining the two wells on top ----
+  % A smooth arch/bridge drawn as a Bézier curve:
+  \draw[thick]
+    (\xL+2.6, {0.5*((2.6)/\a)^2})
+      .. controls (-1.5, \yBridge) and (1.5, \yBridge) ..
+    (\xR-2.6, {0.5*((-2.6)/\a)^2});
+
+  % ---- Energy levels in each well ----
+  % (units where ħω=1): E_n = n + 1/2 for n=0..4
+  \foreach \n/\E in {0/0.5,1/1.5,2/2.5,3/3.5,4/4.5}{
+    % Left levels (short segments inside left well)
+    \draw[dashed] (\xL-2.2,\E) -- (\xL+2.2,\E);
+    % Right levels (short segments inside right well)
+    \draw[dashed] (\xR-2.2,\E) -- (\xR+2.2,\E);
+  }
+
+  % Optionally emphasize the n=0 lines
+  \draw[very thick] (\xL-2.2,0.5) -- (\xL+2.2,0.5);
+  \draw[very thick] (\xR-2.2,0.5) -- (\xR+2.2,0.5);
+
+  % ---- One particle (circle) in lowest level in each well ----
+  \filldraw[fill=white, thick] (\xL,0.5) circle (\R);
+  \filldraw[fill=white, thick] (\xR,0.5) circle (\R);
+
+  % Optional labels
+  %\node[anchor=south] at (\xL,0.5) { };
+  %\node[anchor=south] at (\xR,0.5) { };
+
+\end{tikzpicture}
+
+\end{document}