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\begin{document}

\vspace*{2cm}

\begin{poster}
\large \sf

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      %%% CQT_Logo
      \begin{minipage}[c][9cm][c]{0.15\textwidth}
        \begin{center}
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      \end{minipage}
      %%% Title
      \begin{minipage}[c][9cm][c]{0.67\textwidth}
        \begin{center}
          \begin{doublespacing}
          {\sc \Huge hong-ou-mandel interference\linebreak
          between photons from a single atom\linebreak
          and an atomic ensemble}\\[10mm]
          \end{doublespacing}
          {\Large Victor Leong$^1$, Gurpreet Kaur Gulati$^{1}$, Bharath Srivathsan$^{1}$, Sandoko Kosen$^{1}$,\\
          Alessandro Cer\`{e}$^1$, Christian Kurtsiefer$^1$ \\[7mm]
            $^1$Centre for Quantum Technologies, Department of Physics, National University of Singapore}
        \end{center}
      \end{minipage} 
      \begin{minipage}[c][9cm][c]{0.15\textwidth}
        \begin{center}
          \includegraphics[width=0.8\textwidth,angle=0]{NUS_Logo.pdf}
        \end{center}
      \end{minipage}

\vspace*{3cm}



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%%% Content
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  \begin{pcolumn}{0.485}
  \pbox{0.95\textwidth}{65cm}{framesep=1em}{
    \begin{center}
      {\bf \Large \textsf{Introduction}}
    \end{center}
    \vspace{1.25cm}
    
    Many proposed all-optical quantum-photonic networks are based on indistinguishable single photons carrying information between nodes and interacting with one another. It is important to demonstrate that single photons generated from different systems using different physical processes can indeed be indistinguishable and exhibit two-photon interference effects such as Hong-Ou-Mandel (HOM) interference \cite{hom}, where two indistinguishable photons interfering at a 50:50 beamsplitter will always exit on the same side. This had previously been demonstrated with sources such as quantum dots, single atoms and parametric down-conversion \cite{qdot,grangier,qdot_pdc}.
    \vspace{1.25cm}
    \begin{center}
     {\bf \Large \textsf{Single Photon Sources}}
    \end{center}
    \vspace{1.25cm}
    
    We interfere single photons generated by two different atomic systems. The first system is a cold atomic ensemble of $^{87}${Rb} atoms that generates photon pairs using a four-wave mixing (FWM) process via a cascade decay scheme \cite{fwm}. The second system is a single $^{87}${Rb} atom in an optical dipole trap that is excited by a short resonant optical pulse and produces a single photon via spontaneous emission.
    \vspace{0.5cm}
    \twofig{fwm_level_scheme.pdf}{D2_energy_level2.pdf}{0.25}{0.3}
    \mycaption{Energy level schemes of $^{87}${Rb} showing the cascade decay scheme of the FWM process (left) and the closed transition along which the single atom is excited and spontaneously emits a single photon (right).}
    
    %\vspace{0.5cm}
    \begin{center}
      %{\bf \Large Experimental Setup}
    \end{center}    
    \myfig[0.]{joint_setup_v1.pdf}{1}
    \mycaption{Pumps 1,2 are combined using filter F$_1$ and co-propagated through a cold atomic cloud of $^{87}${Rb} atoms. Photon pairs are generated and separated from residual pump light using filter F$_2$. A detection at D$_\text{T}$ triggers the electro-optic modulator (EOM) to generate a pulse to excite the single $^{87}${Rb} atom trapped at the focus of two AL (NA\,=\,0.55). A 230m long single-mode delay fiber and a variable delay box are used to match the photon arrival times at the BS. An acousto-optic modulator (AOM) compensates for the frequency mismatch of the photons. }
    
    %PBS: polarising beam splitter, $\lambda$/2, $\lambda$/4: half and quarter wave plates, F$_\text{1}$ - F$_\text{4}$: interference filters, 
%    due to the AC stark shift of the dipole trap and the Zeeman shift of the bias magnetic field in the single atom setup. 
   \vspace{1cm}
    \myfig[0]{photon_sources.eps}{0.85}
    \mycaption{APD measurements, normalised to the peak of their detection time distributions. (Top) 3 ns pulse used to excite the single atom. (Bottom) Single photons from the single atom (sa) via spontaneous decay and from the atomic ensemble via four-wave mixing (fwm), with exponential fits showing decay times.}
    
%     $\tau_{\mathrm{fwm}}$ can be tuned by adjusting the optical density of the atomic cloud.
%     \vspace{.5cm}
%     \begin{center}
%      {\bf \Large Temporal Overlap}
%     \end{center}
%     \vspace{.5cm}
%     
%     Incomplete temporal overlap between the two photons due to different decay times or different arrival times at the beamsplitter will result in a decreased HOM interference visibility. We consider two exponentially decaying photon wavepacket amplitudes
%      \begin{equation}
%        \xi_{\mathrm{sa}}(t)=\frac{1}{\sqrt{\tau_{\mathrm{sa}}}}\;\Theta(t)\;\exp\left(\frac{-t}{2\;\tau_{\mathrm{sa}}}\right) \quad\qquad\qquad , \qquad\qquad 
%        \xi_{\mathrm{fwm}}(t)=\frac{1}{\sqrt{\tau_{\mathrm{fwm}}}}\;\Theta(t-\Delta t_a)\;\exp\left(\frac{-t}{2\;\tau_{\mathrm{fwm}}}\right)
%       \end{equation}
%     where $\mathrm{sa}$ and $\mathrm{fwm}$ denote single atom and four-wave mixing respectively, $\Theta(t)$ is the Heaviside step function, and $\Delta t_a$ is the arrival time delay between the photons at the beamsplitter. We define the temporal overlap integral $J$ and the HOM visibility $V$ as follows: 
%     
%     \vspace*{0.5\baselineskip}
%     \begin{minipage}{.47\linewidth}
%       \begin{equation}
%        J=\int\xi^{*}_{\mathrm{sa}}(t)\cdot\xi_{\mathrm{fwm}}(t)\;\mathrm{d}t \qquad
%       \end{equation}
%       \end{minipage}
%       \begin{minipage}{.53\linewidth}
%       \begin{equation}
%        V=1-A|J|^2 \label{eq:vis}
%       \end{equation}
%       \end{minipage} 
%     
%     \vspace*{0.5\baselineskip}
%     The coefficient $A=1$ if the two photons are otherwise indistinguishable in their spatial, frequency and polarisation modes; any distinguishability will lead to a smaller value of $A$, and hence a diminished visibility $V$. For instance, by setting orthogonal polarisations for the input photons, $V=0$ and the photons do not interfere.
  }
  \end{pcolumn}
%%
%% Second column of the Posterrrr
%%
  \begin{pcolumn}{0.485}
  \pbox{0.95\textwidth}{65cm}{framesep=1em}{

    \begin{center}
      {\bf \Large \textsf{HOM Interference}}
    \end{center}
    
    \myfig[0]{HOM_withcorrection.eps}{0.80}
    \mycaption{Coincident photons at D$_\text{A}$ and D$_\text{B}$ as a function of the arrival time delay between the two photons at the HOM beamsplitter $\Delta t_a$. Coincidence counts within a 80ns window are normalised to the non-interfering case and corrected for accidental events due to background noise. The solid line represents theoretical predictions based on a temporal overlap integral. A normalised coincidence value of 0.5 marks the quantum limit.} 

    \begin{center}
      {\bf \Large \textsf{HOM Visibility}}
    \end{center}
    
    \myfig[0]{hom_g2.pdf}{0.75}
    \mycaption{Probability of detecting coincident photons at D$_\text{A}$ and D$_\text{B}$ with parallel and perpendicular polarisations, as a function of the delay between the detection times $\Delta t_d$. The HOM visibility is calculated from the ratio of the integrals of $P_{\parallel}$ and $P_{\perp}$ over the range $-15\,\text{ns}\leq \Delta t_d \leq 15\,\text{ns}$.}
    
%     $\tau_{\mathrm{sa}}=27\;\text{ns}$ and $\tau_{\mathrm{fwm}}=14\;\text{ns}$.
%     $V=1-\frac{\int P_{\parallel}\; \mathrm{d}\Delta t_d}{\int P_{\perp}\; \mathrm{d}\Delta t_d}$

%      given the photon decay times of $\tau_{\mathrm{sa}}=27\;\text{ns}$ and $\tau_{\mathrm{fwm}}=14\;\text{ns}$
%     \myfig[0]{decayplot.eps}{0.4}
%     \mycaption{!!PLACEHOLDER!! for decay time plot. Still need a final decision on how to handle the normalisation etc for this plot! will make a nice one if we decide to include this...}
% ; measured data points below this value indicate the quantum nature of the HOM inteference effect, which cannot be explained with classical physics.
    
    \begin{center}
      {\bf \Large \textsf{Quantum Beats}}
    \end{center}
        
    \myfig[0]{beat.eps}{0.75}
    \mycaption{Probability of detecting coincident photons at D$_\text{A}$ and D$_\text{B}$ as a function of the delay between the detection times $\Delta t_d$. Here, the FWM photon bypasses the AOM, resulting in a frequency difference of 75$\pm$1\,MHz with the photon from the single atom, which is consistent with the beat frequency in the coincidence probability.}


       %% References
      \begin{thebibliography}{1}

      \bibitem{hom}{C. Hong, Z. Ou, L. Mandel, Phys. Rev. Lett. {\bf 59}, 2044 (1987)}
      \bibitem{qdot}{C. Santori et al., Nautre {\bf 419}, 594 (2002)}
      \bibitem{grangier}{J. Beugnon et al., Nature {\bf 440}, 779 (2006)}
      \bibitem{qdot_pdc}{S. Polyakov et al., Phys. Rev. Lett. {\bf 107}, 157402 (2011)}
      %\bibitem{mk_nature}{M. K. Tey, et al., Nature Physics {\bf 4}, 924 (2008)}
      \bibitem{fwm}{B. Srivathsan et al., Phys. Rev. Lett. {\bf 111}, 123602 (2013)}
      \end{thebibliography}        
    }
    
  \end{pcolumn}

\end{poster}

\end{document}

