diff options
Diffstat (limited to 'mixed_domain')
| -rw-r--r-- | mixed_domain/chapter.tex | 100 |
1 files changed, 32 insertions, 68 deletions
diff --git a/mixed_domain/chapter.tex b/mixed_domain/chapter.tex index 308146b..7f8a8b4 100644 --- a/mixed_domain/chapter.tex +++ b/mixed_domain/chapter.tex @@ -137,9 +137,7 @@ from these measurement artifacts. % \section{Theory}
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=0.5\linewidth]{"mixed_domain/WMELs"}
\caption[Sixteen triply-resonant Liouville pathways.]{
The sixteen triply-resonant Liouville pathways for the third-order response of the system used
@@ -149,8 +147,7 @@ from these measurement artifacts. % are yellow, excitations with $\omega_2=\omega_{2'}$ are purple, and the final emission is gray.
}
\label{fig:WMELs}
-\end{figure}
-\clearpage}
+\end{dfigure}
We consider a simple three-level system (states $n=0,1,2$) that highlights the multidimensional
line shape changes resulting from choices of the relative dephasing and detuning of the system and
@@ -234,8 +231,7 @@ this paper. % The steady state and impulsive limits of Equation \ref{eq:rho_f_int} are discussed in Appendix
\ref{sec:cw_imp}. %
-\afterpage{
-\begin{figure}
+\begin{dfigure}
\includegraphics[width=\linewidth]{"mixed_domain/simulation overview"}
\caption[Overview of the MR-CMDS simulation.]{
Overview of the MR-CMDS simulation.
@@ -253,8 +249,7 @@ The steady state and impulsive limits of Equation \ref{eq:rho_f_int} are discuss help introduce our delay convention.
}
\label{fig:overview}
-\end{figure}
-\clearpage}
+\end{dfigure}
Fig. \ref{fig:overview} gives an overview of the simulations done in this work. %
Fig. \ref{fig:overview}a shows an excitation pulse (gray-shaded) and examples of a coherent
@@ -491,8 +486,7 @@ The driven limit holds for large detunings, regardless of delay. % \subsection{Convolution Technique for Inhomogeneous Broadening}\label{sec:convolution}
-\afterpage{
-\begin{figure}
+\begin{dfigure}
\includegraphics[width=\linewidth]{mixed_domain/convolve}
\caption[Convolution overview.]
{Overview of the convolution.
@@ -501,8 +495,7 @@ The driven limit holds for large detunings, regardless of delay. % (c) The resulting ensemble line shape computed from the convolution.
The thick black line represents the FWHM of the distribution function.}
\label{fig:convolution}
-\end{figure}
-\clearpage}
+\end{dfigure}
Here we describe how to transform the data of a single reference oscillator signal to that of an
inhomogeneous distribution. %
@@ -588,8 +581,7 @@ pulse delay times, and inhomogeneous broadening. % \subsection{Evolution of single coherence}\label{sec:evolution_SQC}
-\afterpage{
-\begin{figure}
+\begin{dfigure}
\centering
\includegraphics[width=0.5\linewidth]{"mixed_domain/fid vs dpr"}
\caption[Relative importance of FID and driven response for a single quantum coherence.]{
@@ -601,8 +593,7 @@ pulse delay times, and inhomogeneous broadening. % slightly detuned (relative detuning, $\Omega_{fx}/\Delta_{\omega}=0.1$).
}
\label{fig:fid_dpr}
-\end{figure}
-\clearpage}
+\end{dfigure}
It is illustrative to first consider the evolution of single coherences, $\rho_0 \xrightarrow{x}
\rho_1$, under various excitation conditions. %
@@ -639,8 +630,7 @@ We note that our choices of $\Gamma_{10}\Delta_t=2.0, 1.0,$ and $0.5$ give coher mainly driven, roughly equal driven and FID parts, and mainly FID components, respectively. %
FID character is difficult to isolate when $\Gamma_{10}\Delta_t=2.0$. %
-\afterpage{
-\begin{figure}
+\begin{dfigure}
\centering
\includegraphics[width=0.5\linewidth]{"mixed_domain/fid vs detuning"}
\caption[Pulsed excitation of a single quantum coherence and its dependance on pulse detuning.]{
@@ -661,8 +651,7 @@ FID character is difficult to isolate when $\Gamma_{10}\Delta_t=2.0$. % In all plots, the gray line is the electric field amplitude.
}
\label{fig:fid_detuning}
-\end{figure}
-\clearpage}
+\end{dfigure}
Fig. \ref{fig:fid_detuning}a shows the temporal evolution of $\rho_1$ at several values of $\Omega_{1x}/\Delta_{\omega}$ with $\Gamma_{10}\Delta_t=1$.\footnote{
See Supplementary Fig. S3 for a Fourier domain representation of Fig. \ref{fig:fid_detuning}a.
@@ -729,8 +718,7 @@ $\Gamma_{10}\Delta_t=1$. % \subsection{Evolution of single Liouville pathway}
-\afterpage{
-\begin{figure}
+\begin{dfigure}
\centering
\includegraphics[width=\linewidth]{"mixed_domain/pw1 lineshapes"}
\caption[2D frequency response of a single Liouville pathway at different delay values.]{
@@ -743,8 +731,7 @@ $\Gamma_{10}\Delta_t=1$. % compare 2D spectrum frame color with dot color on 2D delay plot.
}
\label{fig:pw1}
-\end{figure}
-\clearpage}
+\end{dfigure}
We now consider the multidimensional response of a single Liouville pathway involving three pulse
interactions. %
@@ -783,11 +770,10 @@ Since $E_1$ is not the last pulse in pathway I$\gamma$, the tracking monochromat See Supplementary Fig. S5 for a representation of Fig. 5 simulated without monochromator frequency filtering ($M(\omega-\omega_1)=1$ for Equation \ref{eq:S_tot}).
}
-\begin{table*}
- \centering
+\begin{dtable}
\caption{\label{tab:table2} Conditions for peak intensity at different pulse delays for pathway
I$\gamma$.}
- \begin{tabularx}{0.7\linewidth}{c c | X X X X}
+ \begin{tabular}{c c | c c c c}
\multicolumn{2}{c}{Delay} & \multicolumn{4}{|c}{Approximate Resonance Conditions} \\
$\tau_{21}/\Delta_t$ & $\tau_{22^\prime}/\Delta_t$ & $\rho_0\xrightarrow{1}\rho_1$ &
$\rho_1\xrightarrow{2}\rho_2$ & $\rho_2\xrightarrow{2^\prime}\rho_3$ & $\rho_3\rightarrow$
@@ -800,8 +786,8 @@ Since $E_1$ is not the last pulse in pathway I$\gamma$, the tracking monochromat $\omega_1=\omega_{10}$ \\
2.4 & -2.4 & $\omega_1=\omega_{10}$ & $\omega_2=\omega_{10}$ & $\omega_2=\omega_{10}$ &
$\omega_1=\omega_2$ \\
- \end{tabularx}
-\end{table*}
+ \end{tabular}
+\end{dtable}
When the pulses are all overlapped ($\tau_{21}=\tau_{22^\prime}=0$, lower right, orange), all
transitions in the Liouville pathway are simultaneously driven by the incident fields. %
@@ -875,9 +861,7 @@ in unexpected ways. % \subsection{Temporal pathway discrimination}
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=\linewidth]{"mixed_domain/delay space ratios"}
\caption[2D delay response for different relative dephasing rates.]{
Comparison of the 2D delay response for different relative dephasing rates (labeled atop each
@@ -892,8 +876,7 @@ in unexpected ways. % (purple), and III or I (teal).
}
\label{fig:delay_purity}
-\end{figure}
-\clearpage}
+\end{dfigure}
In the last section we showed how a single pathway's spectra can evolve with delay due to pulse
effects and time gating. %
@@ -943,9 +926,7 @@ vanishing signal intensities; the contour of $P=0.99$ across our systems highlig \subsection{Multidimensional line shape dependence on pulse delay time}
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=\linewidth]{"mixed_domain/spectral evolution"}
\caption[Evolution of the 2D frequency response.]{
Evolution of the 2D frequency response as a function of $\tau_{21}$ (labeled inset) and the
@@ -960,8 +941,7 @@ vanishing signal intensities; the contour of $P=0.99$ across our systems highlig $\tau_{22^\prime}=0$.
}
\label{fig:hom_2d_spectra}
-\end{figure}
-\clearpage}
+\end{dfigure}
In the previous sections we showed how pathway spectra and weights evolve with delay. %
This section ties the two concepts together by exploring the evolution of the spectral line shape
@@ -1036,17 +1016,14 @@ only the absorptive line shape along $\omega_2$. % This narrowing, however, is unresolvable when the pulse bandwidth becomes broader than that of the
resonance, which gives rise to a vertically elongated signal when $\Gamma_{10}\Delta_t=0.5$. %
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=\linewidth]{"mixed_domain/wigners"}
\caption[Wigners.]{
Transient ($\omega_1$) line shapes and their dependence on $\omega_2$ frequency.
The relative dephasing rate is $\Gamma_{10}\Delta_t=1$ and $\tau_{22^\prime}=0$.
For each plot, the corresponding $\omega_2$ value is shown as a light gray vertical line.}
\label{fig:wigners}
-\end{figure}
-\clearpage}
+\end{dfigure}
It is also common to represent data as ``Wigner plots,'' where one axis is delay and the other is
frequency.\cite{Kohler2014, Aubock2012,Czech2015,Pakoulev2007} %
@@ -1063,12 +1040,9 @@ This representation also highlights the asymmetric broadening of the $\omega_1$ pulse overlap when $\omega_2$ becomes non-resonant. %
Again, these features can resemble spectral diffusion even though our system is homogeneous. %
-\subsection{Inhomogeneous broadening}
+\subsection{Inhomogeneous broadening} \label{sec:res_inhom} % ------------------------------------
-\afterpage{
-\label{sec:res_inhom}
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=0.5\linewidth]{"mixed_domain/inhom delay space ratios"}
\caption[2D delay response with inhomogeneity.]{
2D delay response for $\Gamma_{10}\Delta_t=1$ with sample inhomogeneity. %
@@ -1083,8 +1057,7 @@ Again, these features can resemble spectral diffusion even though our system is (purple), III (teal, dashed), and I (teal, solid). %
}
\label{fig:delay_inhom}
-\end{figure}
-\clearpage}
+\end{dfigure}
With the homogeneous system characterized, we can now consider the effect of inhomogeneity. %
For inhomogeneous systems, time-orderings III and V are enhanced because their final coherence will
@@ -1138,9 +1111,7 @@ distortion has not been investigated previously. % Peak-shifting due to pulse overlap is less important when $\omega_1\neq\omega_2$ because
time-ordering III is decoupled by detuning. %
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=\linewidth]{"mixed_domain/inhom spectral evolution"}
\caption[Spectral evolution of an inhomogenious system.]{
Same as Fig. \ref{fig:hom_2d_spectra}, but each system has inhomogeneity
@@ -1157,8 +1128,7 @@ time-ordering III is decoupled by detuning. % time-orderings V and VI unequal.
}
\label{fig:inhom_2d_spectra}
-\end{figure}
-\clearpage}
+\end{dfigure}
In frequency space, spectral elongation along the diagonal is the signature of inhomogeneous
broadening. %
@@ -1241,9 +1211,7 @@ Only time-orderings V and VI are relevant. % The intermediate population resonance is still impulsive but it depends on
$\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space. %
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=\linewidth]{"mixed_domain/steady state"}
\caption[Conditional validity of the driven limit.]{
Comparing approximate expressions of the 2D frequency response with the directly integrated
@@ -1256,14 +1224,11 @@ $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space. % Third column: The directly integrated response. %
}
\label{fig:steady_state}
-\end{figure}
-\clearpage}
+\end{dfigure}
-\subsection{Extracting true material correlation}
+\subsection{Extracting true material correlation} % ----------------------------------------------
-\afterpage{
-\begin{figure}
- \centering
+\begin{dfigure}
\includegraphics[width=0.5\linewidth]{"mixed_domain/metrics"}
\caption[Metrics of correlation.]{
Temporal (3PEPS) and spectral (ellipticity) metrics of correlation and their relation to the
@@ -1280,8 +1245,7 @@ $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space. % area are connected). %
}
\label{fig:metrics}
-\end{figure}
-\clearpage}
+\end{dfigure}
We have shown that pulse effects mimic the qualitative signatures of inhomogeneity. %
Here we address how one can extract true system inhomogeneity in light of these effects. %
|