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\begin{poster}
\large \sf

%%%%%%%%%%%%%%%%%%%%%
%%% Header
%%%%%%%%%%%%%%%%%%%%%
 %%% CQT_Logo
\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 Spectral Compression of \linebreak Narrowband Single Photons \\}
        \end{center}
      \end{minipage}
      %%% NUS-Logo
      \begin{minipage}[c]{0.05\textwidth}
        \begin{center}
          \includegraphics[width=9cm,angle=0]{NUS_Logo.pdf}
        \end{center}
      \end{minipage}
	\begin{center}
	\vspace{15mm}
	{\Large Mathias A. Seidler$^{1}$, Xi Jie Yeo$^1$, 
	 Alessandro Cer\`e$^1$ 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{2.0cm}
% \begin{center}
%    \begin{center}{\bf \Large Introduction}\end{center}
% \end{center}
%%% Abstract

% Based on our scheme, the spectral compression of a photon with bandwidth $\Gamma_{p}$ is found to be optimally achieved by using a dispersion cavity with a bandwidth of $0.25\,\Gamma_p$.

\vspace{1.5cm}
%%%%%%%%%%%%%%%%%%%%%
%%% Content
%%%%%%%%%%%%%%%%%%%%%
\begin{multicols}{2}
\setlength{\parskip}{1ex plus 0.5ex minus 0.2ex}
\begin{center}{\bf \Large Motivation}\end{center}
Efficient atom-light interaction at the single quantum level is at 
the core of many proposals for storing, processing, and relaying quantum
information~[1,2]. 
% \cite{Waks2009, Kimble2008}
Many of these schemes
require the single ``flying'' photons to match the spectrum of atomic transitions, which
can be a challenge with some of the photon preparation schemes. 
% A widely adopted solution for generating single photons that are spectrally
% matched to atomic transitions is passive filtering of bright, broadband sources [3,4],
% % \cite{Meyer-Scott2017, Schuck2010},
% with the unavoidable consequence of a drastic reduction of brightness.
% However, many photon-atom interaction experiments will require a high
% interaction rate; sometimes, photon loss can also completely compromise the
% feasibility of such experiments. 
Engineering spectral properties of single
photons is therefore an important task for scaling up hybrid quantum systems. In this experiment, we demonstrate a successful spectral compression of heralded 795\,nm narrowband single photons produced by four-wave mixing in an ensemble of cold $^{87}$Rb atoms.

\vspace{0.7cm}

%
% \begin{center}
       \begin{center}{\bf \Large Spectral compression}\end{center}
% \end{center}
Inspired by techniques to compress broadband ultra-fast pulses~[3,4],
%\cite{Lavoie,Karpinski2017}
we developed a method to compress the spectrum of narrowband photons with bandwidth a few times larger than the natural D transition linewidth of $^{87}$Rb (6.06\,MHz) using an asymmetric cavity for dispersion. % state the order of magnitude of the photon bandwidth
% using an asymmetric cavity as dispersion medium.

The dispersion medium stretches the temporal intensity profile of the photons in time. A subsequent temporal phase manipulation compresses the bandwidth.
 % to achieve the Fourier limited spectra.
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.9\columnwidth]{../figures/simple_concept/simple_concept.png}
  \end{center}
  \figcaption{
      Concept of spectral compression. Top row: temporal intensity profiles of a photonic wavepacket. Bottom row: corresponding power spectra. The color saturation represents the phase across the temporal intensity profile.
      % The initial pulse is dispersed by a cavity. The photon has now a new temporal shape, but the spectrum is unchanged. An EOM manipulates the phase $\phi^{\prime}(t)$ of the pulse which leads to a narrower spectrum.
      }
\end{figurehere}


\begin{center} {\bf \Large Heralded single photons}\end{center}
We generate time-ordered 762-795\,nm photon pairs by
four-wave mixing in a cold ensemble of $^{87}$Rb atoms in a cascade level scheme~[5]. We prepare the 795\,nm photon for spectral compression by heralding on the 762\,nm photon.
% ~\cite{Srivathsan:2013}.

\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.95\columnwidth]{../figures/experiment_setup/heralded_photons.png}
  \end{center}
  \figcaption{
      Left: Energy level scheme for four-wave mixing in $^{87}$Rb. Right: Schematic setup for generation of heralded single photons. MOT: Magneto-optical trap. IF: interference filter. 
    }
\end{figurehere}
 
% \begin{figurehere}
%   \begin{center}
%     \includegraphics[width=0.75\columnwidth]{../figures/photon_shapes_and_phase_correction/photon_shape_poster.pdf} \hspace*{0.5cm}
%   \end{center}
%   \figcaption{Photon coincidence probability density from the time-correlation measurement (blue circles).
%   Exponential decay fit to the data (blue line).
%   % matches our experimental data (filled dots) well. 
%   }
% \end{figurehere}

\begin{center} {\bf \Large Experimental overview}\end{center}
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.8\columnwidth]{../figures/experiment_setup/exp_poster.png}
  \end{center}
  \figcaption{
      Schematic setup for spectral compression of heralded single photons and the corresponding temporal intensity profiles in each step~[6]. D$_{s,i}$: single-photon detectors, EOM: electro-optical modulator, PBS: polarizing beam splitter, QWP: quarter-wave plate, IF: interference filter. }
\end{figurehere}
% \columnbreak
\columnbreak
\begin{multicols}{2}
\begin{figurehere}
  \begin{center}
    \includegraphics[width=\columnwidth]{../figures/experiment_setup/cavity_poster.png}
  \end{center}
\end{figurehere}
\begin{center}
\columnbreak
\begin{tabular}{ c|c } 
  \hline  \hline
  \multicolumn{2}{c}{Cavity specifications} \\
  \hline  \hline
   Reflectivity R$_{1}$ & 0.97  \\ 
   Reflectivity R$_{2}$ & $\approx$\,1  \\ 
   % Separation of mirrors                  & 10.1\,cm  \\
   Free spectral range     & 1.48\,GHz  \\ 
   Bandwidth                  & 7.3\,MHz  \\
   \hline
\end{tabular}
\end{center}
\end{multicols}
\figcaption{
Asymmetric dispersion cavity
}

The 795\,nm photons are reflected from the dispersion cavity and then sent to the electro-optic modulator where the phase removal is performed by applying a synchronised $\pi$ phase-flip.
% We obtain the spectral profiles of the photons before and after compression by measuring the photon transmission rate through the Fabry-Perot cavity at different cavity detunings.
% \vspace{-0.5cm}
%% START OF SECOND COLUMN
% \begin{center}
 \begin{center}{\bf \Large Temporal envelope}\end{center}
% \end{center}
% We measure the effect of the dispersion cavity on the single photons and compared it with our simulation to confirm the accuracy.
We measure a time correlation between the 762-795\,nm photon pairs; the probability of detecting a 795\,nm photon after a 762\,nm photon is recorded. By fitting this time-correlation measurement to an exponential decay, we infer the bandwidth of the 795\,nm photons to be 20(2)\,MHz. We also measured the time correlation of the photons after the dispersion cavity which matches well with our simulated temporal profile. 
\begin{figurehere}
  \begin{center}
    \includegraphics[width=0.75\columnwidth]{../figures/photon_shapes_and_phase_correction/photon_shape.pdf} \hspace*{0.5cm}
  \end{center}
  \figcaption{Observed photon coincidence probability density before and after the dispersion cavity. Exponential decay fit to initial time-correlation measurement (blue line).
  Simulated temporal profile after the photon passed through the dispersion cavity (red line).
} 
\end{figurehere}

\begin{center} {\bf \Large Results}\end{center}
We measure the spectrum of the photons by recording the photon transmission rate through a scanning Fabry-Perot spectroscopy cavity with a bandwidth of 2.65\,MHz. The bandwidth of these photons, defined as the spectral window containing 50\% of total spectral power, was compressed by a factor of 2.39(4), from 20(2)\,MHz to 8(2)\,MHz.
% , almost matching the targeted natural D transition linewidth of $^{87}$Rb of 6.06\,MHz.
 


% % \begin{center}{\bf \Large Results}\end{center}
% \columnbreak
% \begin{figurehere}
%   \begin{center}
%     \includegraphics[width=0.9\columnwidth]{../figures/spectra/output.pdf} \hspace*{0.5cm}
%   \end{center}
% \end{figurehere}
\begin{figurehere}
  % \begin{center}
  %   \includegraphics[width=\columnwidth]{../figures/combined_results/combined_results.png} \hspace*{0.5cm}
  % \end{center}
    \begin{center}
    \includegraphics[width=0.8\columnwidth]{../figures/spectra/output.pdf} \hspace*{0.5cm}
  \end{center}
  % \figcaption{Left: Photon coincidence probability density before (open blue circles) and after
  % (filled red dots) the dispersion cavity.
  % Exponential decay fit to initial time-correlation measurement (blue line).
  % Simulated temporal profile after the photon passed through the dispersion cavity (red line).
  % % matches our experimental data (filled dots) well. 
  % 
  \figcaption{
Measured spectra of the photons before (blue dots) and after (red dots) compression.  
 % The solid line is a Lorentzian with full-width half maximum of 8 MHz.
  Initial photon spectrum inferred from the time-correlation measurement of the photons (blue line). Simulation of spectrum after compression (red line).
 % To measure the spectrum we scan a fabry-perot cavity, with a bandwidth of 2.65\,MHz, and record the photon transmission rate. 
Spectral windows defining the initial spectral bandwidth (blue shaded area) and post-spectral compression bandwidth (red shaded area).}
\end{figurehere}
% \bibliographystyle{apsrev4-1}
% \bibliography{compress}


% \end{multicols}
\begin{center}{\bf \Large References}\end{center}
{\large
% \begin{multicols}{2}
\begin{flushleft}
  \begin{tabular}[]{cl}
          {[1]}&E.~Waks et al., \textit{Phys. Rev. A \textbf{80}, 062330 (2009).} \\
          {[2]}&H.J.~Kimble, \textit{Nature \textbf{453}, 1023 (2008).} \\
          % {[3]}&E.~Meyer-Scott et al., \textit{Phys. Rev. A \textbf{95}, 1 (2017).}\\
          % {[4]}&C.~Schuck et al., \textit{Phys. Rev. A \textbf{81}, 1 (2010).}\\
          {[3]}&J.~Lavoie et al., \textit{Nat. Photon. \textbf{7}, 363 (2013).}\\
          {[4]}&M.~Karpi\'{n}ski, et al., \textit{Nat. Photon. \textbf{11}, 53 (2016).}\\
          {[5]}&B.~Srivathsan, et al., \textit{Phys. Rev. Lett. \textbf{111}, 123602 (2013).}\\
          {[6]}&M.A.~Seidler, et al., Manuscript in preparation\\
  \end{tabular}
\end{flushleft}
% \end{multicols}
}
\end{multicols}
\end{poster}
\end{document}
	
