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\begin{document}
% \vspace*{2cm}
\begin{poster}
\large \sf

%%%%%%%%%%%%%%%%%%%%%
%%% Header
%%%%%%%%%%%%%%%%%%%%%
\begin{minipage}[t]{\textwidth}

      \begin{minipage}[c]{0.05\textwidth}
        \begin{center}
          \includegraphics[width=14cm,angle=0]{CQT_Logo.pdf}
        \end{center}
      \end{minipage}
\hspace{8cm}
      %%% Title
      \begin{minipage}[c]{0.7\textwidth}
        \begin{center}
{\sc \Huge Narrowband Entangled Photon Pairs\\
from Four-Wave Mixing in Atomic Vapour\\}
        \end{center}
      \end{minipage}
      %%% NUS-Logo
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        \begin{center}
          \includegraphics[width=9cm,angle=0]{NUS_Logo.pdf}
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      \end{minipage}
	\begin{center}
	\vspace{15mm}
	{\Large  Gurpreet Kaur Gulati$^1$, Bharath Srivathsan$^1$, Alessandro Cer\`e$^1$,
	 Chng Mei Yuen Brenda$^1$,  Dzmitry Matsukevich$^{1,2}$ and Christian Kurtsiefer$^{1,2}$
            \\[4mm]
            $^1$Centre for Quantum Technologies, National University of
            Singapore, Singapore 117543\\
            $^2$Department of Physics, National University of Singapore,
            Singapore 117542\\}
	\end{center}
\end{minipage}

\vspace{1 cm}

%%%%%%%%%%%%%%%%%%%%%
%%% Content
%%%%%%%%%%%%%%%%%%%%%

%%% Abstract
\begin{multicols}{2}
% \begin{center}{\bf \Large Motivation} \end{center}
%\setlength{\parskip}{0.5ex plus 0.5ex minus 0.2ex}
% Correlated photon pairs offer a convenient quantum objects for applications that range from the demonstration of fundamental properties of quantum mechanics to the realization of quantum communication and computation protocols.
We present a source of photon pairs based on a four-wave mixing process in a cold ensemble of Rubidium 87 atoms that exploit a cascade decay scheme, similar to the one proposed by [1].
Here we present a characterization of the generated photon pairs bandwidth and polarization correlation. We also explore the rich structure offered by the hyperfine splitting of the intermediate energy level to observe quantum beats, a signature of the non-classicality of the pair generation process. 
\vspace{0.4cm}
\begin{center} {\bf \Large Non-collinear setup}\end{center}
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.85\columnwidth]{figures/Bandwidth_levelscheme.pdf}
  \end{center}
   \figcaption{Setup of the source.
     In the first realization  we used a non-collinear geometry for the pumps, signal, and idler beams.
     In the inset,
     the cascade level scheme used.}  
\end{figurehere}
\vspace{0.2cm}
\begin{center}{\bf \Large Pair correlation}\end{center} 
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.95\columnwidth]{figures/gsi.eps}
  \end{center}
  \figcaption{
    The two photon coincidences as a function of time delay between detection events on the signal and idler arms
    exhibit a strong time correlation.
    The asymmetric shape of the correlation is a consequence of the time-ordered cascade decay.
    The observed ${1}/{e}$ decay time is shorter than 
    the lifetime of the intermediate state, 27\,ns due to collective effects in the atomic ensemble (superradiance).
   } 
\end{figurehere}
\vspace{0.2cm}
\begin{center} {\bf \Large Optical bandwidth and collective effects}\end{center}
\vspace{0.2cm}
% We measured the bandwidth of the heralded idler photons  in the idler mode 
% The cavity has a bandwidth of  ???\,MHz, sufficiently narrow to resolve the spectral width of the atomic transition.
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.9\columnwidth]{figures/bandwidth.eps}
  \end{center}
  \figcaption{
    On the left, the spectral profile of idler photons,
    measured by scanning the Fabry-P\'erot cavity and recording the coincidence rate for each detuning.
    The measured bandwidth matches the one expected by calculating the Fourier transform of the two-photon correlation function.
    On the right, we can observe how the optical density affects the idler bandwidth.
    The linear dependence is a signature of superradiance, as presented in [2].}
\end{figurehere}
%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center} {\bf \Large Collinear setup}\end{center}
\begin{figurehere}
\begin{center}
  \includegraphics[width=0.9\columnwidth]{figures/schematic_beat.pdf}
\end{center}
\figcaption{
  % In its second realization, the source is based on a collinear geometry.
  The source can also be used in a collinear geometry.
  Using a  ``reversed'' level scheme, shown in the inset, the intermediate level offers two possible hyperfine levels contributing to the photon pair generation.}
\end{figurehere}
% 
% 
%%%%%%%%% Second column of the Poster  %%%%%%%%%
\columnbreak 
% 
% 
\vspace{-0.3cm}
 \begin{center}{\bf \Large Biphoton state}\end{center}
% We separate the two decay paths, A and B, using a 
% We then characterize the temporal correlation and the polarization state of the resulting biphoton in each case.
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.9\columnwidth]{figures/plot_decay.eps}
  \end{center} 
  \figcaption{
    Time correlation of the generated biphoton for decays A (left) and B (right).
    The decay path is selected using a temperature tuned \'etalon.
    The transitions involved in decay A are stronger than those of decay B. This leads to a stronger collective effect in the atomic ensemble and  hence faster decay.
    The rise time of 3.1\,ns is due to finite bandwidth of the \'etalon.}
\end{figurehere}
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.9\columnwidth]{figures/decay_time_tomo.eps}
  \end{center} 
  \figcaption{
    Tomographic reconstruction of the density matrix (real part only) for the biphotons generated via decay A (left) and B (right)
    % obtained by tomographic reconstruction and
    with pumps set to  orthogonal circular polarizations.
    % From a tomographic reconstruction of the biphoton polarization state for each decay path,
    The measured states
    are  well approximated by the pure states
    \mbox{$\ket{\psi_{A}}= 0.55\ket{LR}-0.82\ket{RL}$}, with a fidelity of 0.95,
    and 
    \mbox{$\ket{\psi_{B}}= 0.78\ket{LR}-0.60\ket{RL}$}, with a fidelity of 0.98.}
\end{figurehere}
 \vspace{0.2cm}
\begin{center}{\bf \Large Controlling quantum beats}\end{center}
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.8\columnwidth]{figures/plot_beat.eps}
  \end{center}
  \figcaption{
    Without the \'etalon, the probability amplitude of decay paths A and B interfere, generating the oscillations shown in these graphs.
    This behavior is well described by a model based only on the Clebsch-Gordan coefficients of the transitions:
    % The model for the fit, represented using a solid line, is 
    \begin{displaymath}
      G^{(2)}_{is}
      =
      \Theta(\Delta{t}_{is})\left[
      A^2e^{-\frac{\Delta{t}_{is}}{\tau_{A}}}+
      B^2e^{-\frac{\Delta{t}_{is}}{\tau_{B}}}+
      2ABe^{-\frac{\Delta{t}_{is}}{2(\tau_{A}+\tau_{B})}} \cos\left(2\pi\,\delta\!f \Delta t_{is}+\phi\right)
      \right],
    \end{displaymath}
    where A and B are the relative strengths of the transitions and $\phi$ is their phase difference.
    % All the parameters, apart from an overall amplitude factor, can be calculated directly from the C.G. coefficients of the transitions.
% 
    % For a given state, we can control the amplitude of the oscillations by setting the polarization projection for signal and idler modes.
    % In this case, the pumps are set to orthogonal linear polarization:
% 
    The oscillations are then determined by the polarization of the pumps, signal, and idler modes.
    
    In these measurements, the pumps are set to orthogonal linear polarizations.
    In the top plot,
    % and signal and idler as indicated in the inset, 
    the visibility of the oscillation is maximized, reaching 94.1\%. 
    In the bottom one, we show how,
    choosing the appropriate polarizations,
    the oscillations can be damped, with the decay \mbox{path B} suppressed by a factor of 30.
  }
\end{figurehere}
% Controlling initial phase of oscillations $\phi_{0}$
\begin{figurehere} 
  \begin{center}
    \includegraphics[width=0.9\columnwidth]{figures/plot_phase.eps}
  \end{center}
  \figcaption{
      Similarly, the polarization projection allow us to control the phase of oscillation $\phi$.
      In these two cases, the two oscillations have a phase difference of $\pi$.
    }
\end{figurehere}
\begin{center} {\bf \large Pair source performance}\end{center}
\begin{center}
  \begin{tabular}{ l c c }
    \hline
    & \hspace*{1cm} 762 -- 795\,nm pairs  \hspace*{1cm} &  \hspace*{1cm} 776 -- 780\,nm pairs  \hspace*{1cm} \\
    \hline \hline
    Signal heralding efficiency 	&	 $23\,\%$ 					&	 $5\,\%$ 	\\
    Idler heralding efficiency 		&	 $19\,\%$ 					&	 $10\,\%$ 	\\
    Instantaneous pair rate 		& 	up to 18000\,s$^{-1}$ 	&	 up to 3000\,s$^{-1}$ 	 \\
    Bandwidth (FWHM) 				& 8 -- 25\,MHz 				& 10 -- 32\,MHz \\
    \hline
  \end{tabular}
\end{center}
\begin{flushleft}
      \begin{center}{\bf \large \textsf{References}}\end{center}
           [1] T.Chaneli\'er et. al., Phys. Rev.Lett. 96, 093604 (2006).
		\newline
	 [2] B. Srivathsan et.al., Phys. Rev. Lett. 111, 123602 (2013).
	  \newline
	 [3] G. K. Gulati, et.al. arXiv:1402.5800 (2014).
\end{flushleft}
     
\end{multicols}

\end{poster}

\end{document}

