From 46eb6bad8700abdfef52fd83445607228016b10b Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Sat, 24 Mar 2018 16:45:13 -0500 Subject: 2018-03-24 16:45 --- mixed_domain/chapter.tex | 56 ++++++++++++++++++++++++------------------------ 1 file changed, 28 insertions(+), 28 deletions(-) (limited to 'mixed_domain') 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. % -- cgit v1.2.3