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%\title{\huge Polarization of 41K by optical pumping for $\beta$-decay asymmetries}
%\author[]{J.A. Behr, S. Smale, A. Vantyghem, I. Craiciu, A. Gorelov, M. Anholm, S. Behling, D. Melconian, B. Fenker, D. Friesen, G. Gwinner}
%\institute[TRIUMF]{TRIUMF, Texas A\&M U., U. Manitoba}
\date[June 3, 2013]{June 3, 2013}

% abbreviations
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\def\etal{{et al}\onedot}
\makeatother

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\begin{document}
\begin{boldmath}
\begin{frame}{
%\Huge Polarization of 41K by optical pumping for $\beta$-decay asymmetries
{\Huge {\bfseries Optical pumping for $\beta$-decay}} \hspace*{0.1\linewidth} {\includegraphics[angle=0,width=0.06\linewidth]{TRIUMF_logo_1.ps}}
{\includegraphics[angle=0,width=0.04\linewidth]{ubc_logo_bw_gimp.eps}}
{\includegraphics[angle=0,width=0.04\linewidth]{TAM.eps}}
{\includegraphics[angle=0,width=0.04\linewidth]{banner_umlogo_home.eps}}
\hspace*{0.06\linewidth} {\large Support: NSERC, NRC through TRIUMF, U.S. D.O.E., State of Texas}
} 
{\Large J.A. Behr, A. Gorelov, E. Broatch, L. Lawrence, A. Forestell, L. Nguyen, TRIUMF; J. McNeil, UBC; B. Fenker, D. Melconian, Texas A\&M; M. Anholm, G. Gwinner, U. Manitoba}
\large
  \begin{columns}[t]
    \begin{column}{.3\linewidth}

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

      \begin{block}{\Large \bfseries Optical pumping of $^{37}$K for $\beta$ decay asymmetry}
{\bfseries
  
  $\beta$ angular distribution 
  $W(\theta)d\theta = 1 + {\color[rgb]{0,0,1} P}~ A_\beta \rm{cos}(\theta)$

  \vspace*{1mm}

  {\color[rgb]{0,0,1}
    $\bullet$ Achieved: laser-cooled, confined, polarized $^{37}$K atoms with

    \hspace*{5mm} vector polarization $P = 0.9913 \pm 0.0009$

  }

    \vspace*{1mm}


$\bullet$  $A_{\beta} [{\rm exp.}] = -0.5707 (13)_{\rm syst} (13)_{\rm stat} (5)_{\rm pol}$~~~Theory -0.5706(7)

  \hspace*{5mm}  Best fractional accuracy $A_{\beta}$ in nuclei or the neutron

  }     

\hspace*{3mm}  B. Fenker {\em et al.} Phys Rev Lett {\bfseries 120} 062502 (2018)


%{\color[rgb]{0,0,1}
%$\bullet$ Diagnostics:
%time dependence of excited state population after optical pumping light turns on%,
%%using nonresonant photoionization or fluorescence monitoring
%}


         \begin{columns}[T]
           \begin{column}{0.55\linewidth}
%             \includegraphics[angle=90,width=\linewidth]{myVud_mudensity_ACOT_diff_19NeOldNew_neutron.ps}
%             \includegraphics[angle=90,width=\linewidth]{myVud_mudensity_DAMOP.ps}
             \includegraphics[angle=90,width=\linewidth]{myVud_mudensity_trento.ps}
                        \end{column}
           \begin{column}{0.50\linewidth}
\hspace*{9mm}             {\bfseries \color[rgb]{1,0,0} Normal-handed $\nu$ forbids:}
             
%\hspace*{5mm}                         \includegraphics[angle=0,width=0.9\linewidth]{spins_skater.eps}
\hspace*{5mm}                         \includegraphics[angle=0,width=0.9\linewidth]{spins_skater_37.eps}

           {\bfseries \color[rgb]{1,0,0} $P < 1$ mimics wrong-handed $\nu$
  }
\end{column}
          \end{columns}
 
      \end{block}

      \vspace*{-7mm}

\vskip1ex
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       \begin{block}{\Large \bfseries Direct Optical Pumping}
        \begin{columns}[T]
          \begin{column}{0.5\linewidth}
{\bfseries
  $\bullet$ Optically pump $^{37}$K atoms

  \hspace*{3mm} for 2 ms after AC MOT off 

$\bullet$ 4S$_{1/2}$ $\rightarrow$ 4P$_{1/2}$ , $\sigma^{\pm}$

  $\bullet$  Diode laser with RF injected

  \hspace*{3mm} excites g.s F=1 and F=2 

  $\bullet$ Test with $^{41}$K, almost same

  \hspace*{3mm} hyperfine splitting as $^{37}$K}

\vspace*{1mm}

\hspace*{3mm} {\bfseries $\vec{F} = \vec{J} + \vec{I}$}

{\bfseries H$_{\rm hyperfine}$ = - $\vec{\mu_{\rm N}} \cdot \vec{B_{e}}$ = A $\vec{I} \cdot \vec{J}$ }

          \end{column}
          \begin{column}{0.5\linewidth}
            \includegraphics[angle=0,width=0.9\linewidth]{polarization2tsilevelsonly.eps}
            %            \includegraphics[angle=0,width=0.9\linewidth]{polarization2tsilevelsonly_plus.eps}
          \end{column}
         \end{columns}
      \end{block}
      \vskip1ex

      \begin{block}{\Large \bfseries Fluorescence Diagnostic stable $^{41}$K, 10$^6$ atoms}
        \begin{columns}[T]
          \begin{column}{0.4\linewidth}
            {\bfseries  
              $\bullet$ Burst of fluorescence

              \hspace*{3mm} as atoms are

              \hspace*{3mm} optically pumped

              \vspace*{0.5mm}

              $\bullet$ 1-photon counting

              \vspace*{0.5mm}

              $\bullet$ Modelled with rate

              \hspace*{2mm} equations and OBE's

              \hspace*{2mm} Including stray B$_\perp$ field

              \hspace*{2mm} and imperfect S$_3$

                            \vspace*{0.5mm}

                            $\bullet$ $P$ depends on ultimate B, not B$_{\rm quad}$[t] while MOT turns off


                                    {\color[rgb]{0,0,1} $\bullet$ Optimize parameters

                            \hspace*{3mm}                                      for $^{37}$K polarization}
}

%            tail/peak measures final polarization
          \end{column}
          \begin{column}{0.6\linewidth}
            \centering    
%            \includegraphics[angle=90,width=\linewidth]{sc_k1331sep1339_fit_nobtau_damop_norm_linearweights.ps}
            \includegraphics[angle=0,width=\linewidth]{sc_KR128I_withbtau_revised_minus_v2.ps}
          \end{column}
         \end{columns}
      \end{block}


      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    \end{column}
    \begin{column}{.3\linewidth}
      \begin{block}{\Large \bfseries $\beta$ decay geometry and optical pumping}
        \begin{columns}[T]
          \begin{column}{0.5\linewidth}
 %\centering
 %            \includegraphics[angle=0,width=1.1\linewidth]{alexfigure_laser_damop.eps}
            \includegraphics[angle=0,width=\linewidth]{jb_K37_geom_white_save_rev.eps}


            {\bfseries 

              $\bullet$ Combine OP and MOT beams

              \hspace*{5mm}
              with angle-tuned

              \hspace*{5mm}
              780 nm laser-line filter

              $\bullet$ Flip spin state with liquid

              \hspace*{7mm} crystal variable retarder


%            0.25mm thick SiC substrate mirrors in front of $\beta$ detectors


              $\bullet$ Relieve stress-induced

              \hspace*{7mm} birefringence with
              PCTFE

              \hspace*{7mm} (Neoflon) viewport seals

              \hspace*{7mm} C.Warner Rev Sci Instr {\bfseries 85}

              \hspace*{8mm} 113106 (2014)

              
              \hspace*{5mm} S$_3$=-0.9958(8), -0.9984(13),

              \hspace*{18mm} +0.9893(14), +0.9994(5)

              }

            
%            {\bfseries            efficiently combine 769.9 D1 and 766.49 D2 with an angle-tuned 780 nm laser-line filter}


          \end{column}
          \begin{column}{0.50\linewidth}
            \includegraphics[width=\linewidth,angle=0]{betas_2012_g.eps}

            {\bfseries $\bullet$ Trap and optical pumping share Z axis:
              Larger $\beta^+$ d$\Omega$}
%            {\bfseries $\bullet$ atomic e$^-$ coincidences: A$_{\rm recoil}$, remove backgrounds}

%            {\bfseries $\bullet$ $\beta^+$ passes through 0.25mm SiC mirror substrates 
%}

%           {\bfseries $\bullet$ AC MOT turns off Bquad fast ($<$~1\% after 0.1 ms)}

      \includegraphics[width=1.2\linewidth,angle=99]{polopticsflip3.eps}~\includegraphics[width=0.525\linewidth,angle=0]{trinat_2ndtrap_optics_2018_gimpnarrow.eps}


          \end{column}
        \end{columns}
 %     \end{block}


      \end{block}

\vskip1ex

      \begin{block}{\Large \bfseries           Improvements in progress}

          \begin{columns}[T]
    \begin{column}{0.4\linewidth}

%    \includegraphics[angle=0,width=\linewidth]{pellicle_gimp.eps}
    \includegraphics[angle=0,width=\linewidth]{AuPellicle.eps}

    \end{column}
    \begin{column}{0.6\linewidth}

      {\bfseries
        $\bullet$ Trim B$_\perp$ field gradients

        \vspace*{1mm}

%        $\bullet$ Improve $S_3$, flipping:
%        (S$_3$=-0.9958(8), -0.9984(13), +0.9893(14), +0.9994(5))
$\bullet$ Twisted nematic liquid crystal:
        \hspace*{3mm} \alert{$S_3 \rightarrow \pm 0.9996$}

        \vspace*{1mm}

        %        $\bullet$ Add flipping of $B_z$
        $\bullet$ PMT $\rightarrow$ \alert{100 $\mu$s CMOS} $\Rightarrow$ d$P$/dz ?

        \vspace*{1mm}

        $\bullet$ higher-power 355 nm photoionizing

        \hspace*{3mm} laser by 3x to improve statistics

                \vspace*{1mm}

                $\bullet$ \alert{gentler RAC-MOT} with

                \hspace*{3mm} lower-frequency half-sinusoid
                to

                \hspace*{3mm} dissipate 1/10 the power while

                \hspace*{3mm} maintaining confinement%\\
               % (L. Lawrence, McMaster, Poster EA.00150)

      }
    \end{column}
  \end{columns}
          {\bfseries       $\bullet$ Lower E$_{\beta}$ threshold (0.5 MeV) by changing mirror substrates

           % \hspace*{5mm} from
             250$\mu$m SiC \alert{$\rightarrow$ 70 nm Au 4$\mu$m  Kapton pellicles}  {\color[rgb]{1,0,1} $\leftarrow$ [Stern Family }
          }


          \end{block}

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


    \end{column}

%    \end{columns}
%\end{frame}
%\end{document}
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \begin{column}{.3\linewidth}

      \begin{block}{\Large \bfseries Polarization probe t$_{1/2}$=1 s $^{37}$K, 10$^{4}$ atoms}
        %: 10\% of data}
 
{\bf   B. Fenker {\em et al.} New Jour Phys 18 073028 (2016)~~~~10\% of data}


\begin{columns}[T]
\begin{column}{0.25\linewidth}


%\includegraphics[angle=0,width=2.4in]{fig2.eps}
%\includegraphics[angle=0,width=\linewidth]{polarization2tsilevelsonly.eps}
%\includegraphics[angle=0,width=1.1\linewidth]{polarization2tsilevels_767_b.eps}
\includegraphics[angle=0,width=1.05\linewidth]{pol_level_dnp_nonuc_uv.eps}

\vspace*{1mm}


{\bfseries $\bullet$ Photoionize

  \hspace*{5mm} $\sim$ 1\%

\alert{  $\bullet$ {\em in situ} probe

  \hspace*{3mm} of $P$ of

  decaying nuclei}} 


\end{column}
%\vskip1ex
\begin{column}{0.75\linewidth}

%{\bfseries P=99.1$\pm$0.4\% $^{37}$K }


\includegraphics[angle=0,width=\linewidth]{photoion_spectrum_final.eps}

\includegraphics[angle=0,width=1.1\linewidth]{fig8_njp_fromnjp_screendump.eps}


%\includegraphics[angle=90,width=\linewidth]{solvay_fit_plus019.ps}




%{\bfseries P=99.6\% $^{41}$K (pyrex cell)}




\end{column}
\end{columns}

%{\bfseries 
%  all data $\Rightarrow$ P = $\pm$ 0.9913 $\pm$ 0.0009
%  %(e.g. we know 1st 2 of 100 cycles is hurt by 
%%a transient B$_{\perp}$)
%}

%{\bfseries $\bullet$ TRIUMF cyclotron B field produces 0.26$\pm$0.02 Gauss }



      \end{block}
      \begin{block}{\Large \bfseries Uncertainty Budget for $^{37}$K Polarization}
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \centering
        \begin{columns}[T]
\begin{column}{0.75\linewidth}
  {\bfseries

    %    Uncertainty Budget:

%    {\bfseries
      
    \begin{tabular}{lllllc}
      Source & \multicolumn{2}{c}{$\Delta{P}~[\times10^{-4}]$} &  \multicolumn{2}{c}{$\Delta{T}~[\times10^{-4}]$} & {\color[rgb]{0.6,0,1} Fix} \\  
                  &    $\sigma^-$   &  $\sigma^+$ & $\sigma^-$ & $\sigma^+$ & \\
      \hline \\
      SYSTEMATICS &                &              &            &         & \\
      Initial $T$   &            3 &         3    &       10   &      8  & {\color[rgb]{0.6,0,1}Prep state} \\
Global fit v. ave  &       2      &         2    &        7   &      6   \\
$S_3^{\rm out}$ Uncertainty &  1 &         2    &       11   &      5   &{\color[rgb]{0.6,0,1}Better flips} \\
Cloud temp       &        2    &         0.5   &        3   &      2   \\
Binning            &        1    &         1     &        4   &      3   \\
$B_z$ Uncertainty &      0.5  &         3     &        2   &      7   \\
Initial $P$          &      0.1  &         0.1   &        0.4 &    0.4\\
Require $\mathcal{I}_+ = \mathcal{I}_-$ & \underline{0.1} & \underline{0.1} &     \underline{0.1} &      \underline{0.2} \\
Total Systematic     &      5    &         5     &       17   &     14   \\
STATISTICS           &      7    &         6     &       21   &     17  & {\color[rgb]{0.6,0,1} More 355nm}\\
      \end{tabular}

%  \includegraphics[angle=0,width=1.08\linewidth]{uncertainties_notot.eps}
    
}
%  \tableofcontents
\end{column}
        \end{columns}

        \vspace*{3mm}
        
        {\bfseries \color[rgb]{0,0,1}

          1-$P$ = 0.87\% $\pm$ 0.09\%~~~~I.e. we know the `tail' to $\sim$
          10\%. 

          We hope to bring the polarization closer to 1, which will naturally increase the precision.

          \vspace*{1mm}

          The accurate polarization probe of the atoms as they decay is enabling more accurate angular correlations of the

          $\beta$ and $\nu$ w.r.t. the nuclear spin

          to test Standard Model predictions.
        }



      \end{block}

      \vspace*{12mm}
      
                {\bfseries \color[rgb]{1,0,1} of National Photocolor]}

    \end{column}
  \end{columns}
\end{frame}

\end{boldmath}

\end{document}

        \begin{columns}[T]
          \begin{column}{.49\linewidth}
{\bfseries
            $\bullet$ Atoms trapped in the coherent dark state would have poor
nuclear polarization

            $\bullet$ Signature: at t= 80 $\mu$s, detune RF sidebands by 1 MHz

            $\bullet$ Eliminate CPT by counter-propagating beams and by RF detuning


%g.s. hyperfine splitting to add 1 MHz. CPT state is then optically pumped and more fluorescence is seen.
}  
           \end{column}
          \begin{column}{.49\linewidth}
%            \includegraphics[width=\linewidth,angle=0]{polarization2tsilevelsonly_cpt.eps}
              \includegraphics[width=0.7\linewidth,angle=90]{sc_cpt_jb_1211_12.ps}
%            \includegraphics[width=\linewidth,angle=0]{sc_cpt_jb.ps}
          \end{column}
        \end{columns}

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