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.  %