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-rw-r--r--mixed_domain/chapter.tex56
1 files changed, 28 insertions, 28 deletions
diff --git a/mixed_domain/chapter.tex b/mixed_domain/chapter.tex
index 12b0278..18af8d1 100644
--- a/mixed_domain/chapter.tex
+++ b/mixed_domain/chapter.tex
@@ -146,7 +146,7 @@ from these measurement artifacts. %
\section{Theory} % -------------------------------------------------------------------------------
-\begin{dfigure}
+\begin{figure}
\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
@@ -156,7 +156,7 @@ from these measurement artifacts. %
are yellow, excitations with $\omega_2=\omega_{2'}$ are purple, and the final emission is gray.
}
\label{fig:WMELs}
-\end{dfigure}
+\end{figure}
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
@@ -240,7 +240,7 @@ this paper. %
The steady state and impulsive limits of Equation \ref{eq:rho_f_int} are discussed in TODO
% Appendix \ref{sec:cw_imp}. %
-\begin{dfigure}
+\begin{figure}
\includegraphics[width=\linewidth]{"mixed_domain/simulation overview"}
\caption[Overview of the MR-CMDS simulation.]{
Overview of the MR-CMDS simulation.
@@ -258,7 +258,7 @@ The steady state and impulsive limits of Equation \ref{eq:rho_f_int} are discuss
help introduce our delay convention.
}
\label{fig:overview}
-\end{dfigure}
+\end{figure}
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
@@ -494,7 +494,7 @@ The driven limit holds for large detunings, regardless of delay. %
\subsection{Convolution Technique for Inhomogeneous Broadening} \label{sec:mixed_convolution} % --
-\begin{dfigure}
+\begin{figure}
\includegraphics[width=\linewidth]{mixed_domain/convolve}
\caption[Convolution overview.]
{Overview of the convolution.
@@ -503,7 +503,7 @@ 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{dfigure}
+\end{figure}
Here we describe how to transform the data of a single reference oscillator signal to that of an
inhomogeneous distribution. %
@@ -589,7 +589,7 @@ pulse delay times, and inhomogeneous broadening. %
\subsection{Evolution of single coherence}\label{sec:evolution_SQC}
-\begin{dfigure}
+\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{"mixed_domain/fid vs dpr"}
\caption[Relative importance of FID and driven response for a single quantum coherence.]{
@@ -601,7 +601,7 @@ pulse delay times, and inhomogeneous broadening. %
slightly detuned (relative detuning, $\Omega_{fx}/\Delta_{\omega}=0.1$).
}
\label{fig:fid_dpr}
-\end{dfigure}
+\end{figure}
It is illustrative to first consider the evolution of single coherences, $\rho_0 \xrightarrow{x}
\rho_1$, under various excitation conditions. %
@@ -638,7 +638,7 @@ 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 $\Gamma_{10}\Delta_t=2.0$. %
-\begin{dfigure}
+\begin{figure}
\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.]{
@@ -659,7 +659,7 @@ 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{dfigure}
+\end{figure}
Fig. \ref{fig:fid_detuning}a shows the temporal evolution of $\rho_1$ at several values of
$\Omega_{1x}/\Delta_{\omega}$ with $\Gamma_{10}\Delta_t=1$.
@@ -728,7 +728,7 @@ $\Gamma_{10}\Delta_t=1$. %
\subsection{Evolution of single Liouville pathway}
-\begin{dfigure}
+\begin{figure}
\centering
\includegraphics[width=\linewidth]{"mixed_domain/pw1 lineshapes"}
\caption[2D frequency response of a single Liouville pathway at different delay values.]{
@@ -741,7 +741,7 @@ $\Gamma_{10}\Delta_t=1$. %
compare 2D spectrum frame color with dot color on 2D delay plot.
}
\label{fig:pw1}
-\end{dfigure}
+\end{figure}
We now consider the multidimensional response of a single Liouville pathway involving three pulse
interactions. %
@@ -779,7 +779,7 @@ the changing resonance conditions for each of the four delay coordinates studied
Since $E_1$ is not the last pulse in pathway I$\gamma$, the tracking monochromator must also be
considered. %
-\begin{dtable}
+\begin{table}
\caption{\label{tab:table2} Conditions for peak intensity at different pulse delays for pathway
I$\gamma$.}
\begin{tabular}{c c | c c c c}
@@ -796,7 +796,7 @@ considered. %
2.4 & -2.4 & $\omega_1=\omega_{10}$ & $\omega_2=\omega_{10}$ & $\omega_2=\omega_{10}$ &
$\omega_1=\omega_2$ \\
\end{tabular}
-\end{dtable}
+\end{table}
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. %
@@ -870,7 +870,7 @@ in unexpected ways. %
\subsection{Temporal pathway discrimination} % ---------------------------------------------------
-\begin{dfigure}
+\begin{figure}
\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
@@ -885,7 +885,7 @@ in unexpected ways. %
(purple), and III or I (teal).
}
\label{fig:delay_purity}
-\end{dfigure}
+\end{figure}
In the last section we showed how a single pathway's spectra can evolve with delay due to pulse
effects and time gating. %
@@ -935,7 +935,7 @@ vanishing signal intensities; the contour of $P=0.99$ across our systems highlig
\subsection{Multidimensional line shape dependence on pulse delay time}
-\begin{dfigure}
+\begin{figure}
\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
@@ -950,7 +950,7 @@ vanishing signal intensities; the contour of $P=0.99$ across our systems highlig
$\tau_{22^\prime}=0$.
}
\label{fig:hom_2d_spectra}
-\end{dfigure}
+\end{figure}
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
@@ -1025,14 +1025,14 @@ 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 $\Gamma_{10}\Delta_t=0.5$. %
-\begin{dfigure}
+\begin{figure}
\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{dfigure}
+\end{figure}
It is also common to represent data as ``Wigner plots,'' where one axis is delay and the other is
frequency. \cite{KohlerDanielDavid2014a, AubockGerald2012a, CzechKyleJonathan2015a,
@@ -1051,7 +1051,7 @@ Again, these features can resemble spectral diffusion even though our system is
\subsection{Inhomogeneous broadening} \label{sec:res_inhom} % ------------------------------------
-\begin{dfigure}
+\begin{figure}
\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. %
@@ -1066,7 +1066,7 @@ 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{dfigure}
+\end{figure}
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
@@ -1118,7 +1118,7 @@ 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. %
-\begin{dfigure}
+\begin{figure}
\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
@@ -1135,7 +1135,7 @@ time-ordering III is decoupled by detuning. %
time-orderings V and VI unequal.
}
\label{fig:inhom_2d_spectra}
-\end{dfigure}
+\end{figure}
In frequency space, spectral elongation along the diagonal is the signature of inhomogeneous
broadening. %
@@ -1218,7 +1218,7 @@ 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. %
-\begin{dfigure}
+\begin{figure}
\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
@@ -1231,11 +1231,11 @@ $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space. %
Third column: The directly integrated response. %
}
\label{fig:steady_state}
-\end{dfigure}
+\end{figure}
\subsection{Extracting true material correlation} % ----------------------------------------------
-\begin{dfigure}
+\begin{figure}
\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
@@ -1252,7 +1252,7 @@ $\omega_{2^\prime}-\omega_2$ which is not explored in our 2D frequency space. %
area are connected). %
}
\label{fig:metrics}
-\end{dfigure}
+\end{figure}
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. %