With this first set of measurement we have demonstrated how the generated heralded state is close to a true single photon state and we confirm the measured bandwidth we already measured in ref.

\textbf{Motivation of the second experiment}

An important characteristic that affects the efficiency of the interaction between a single photon and an atom is the temporal shape of the photon \cite{Yimin:2011}. 
We use  a balanced homodyne detection scheme (BHD) to measure directly a quadrature of the field. 
Since there isn't any asymmetry in the 

We measured the temporal shape of field of the heralded state generated by our source by using a balanced homodyne detection scheme (BHD) \cite{Chi:2011,Kumar:2012}.% the single photon field is combined with an intense local oscillator. 
 
 The experimental schematics is shown in Figure~\ref{fig:homodyne_setup.eps}(b): the signal mode is mixed with the orthogonally polarized local oscillator (LO) beam at a polarizing beam splitter (PBS1) with a measured overlap of $\approx97\%$. 
The LO  is  provided by diode laser a locked to the $5\text{P}_{1/2},\,F=2$$\rightarrow$  $5\text{D}_{3/2},\,F=3$ transition such that its frequency matches the generated signal photon one. 
The combined modes are sent to a second polarizing beam splitter (PBS2). A half wave plate is used to balance the power at the two output ports of PBS2.
%after passing through a half wave plate. 
The output modes of PBS2 are focused on the active area of a balanced detector photodiodes D+ and D- (Hamamatsu S5972, quantum efficiency $\approx87\%$). The variance in the resulting photocurrent is proportional to a quadrature of the field of the signal mode.
To measure it we pass the difference current of the two photodiodes through a high pass filter (cut-off frequency 100kHz) followed by a trans-impedance amplifier G (Analog devices, AD8015, bandwidth 210\,MHz). With a LO power of 4.2\,mW the detector is quantum noise limited with the optical signal 5dB above the electronic noise in the bandwidth of interest. 
We record the signal on a fast digital oscilloscope to measure the temporal shape of the field.
The heralding is obtained using detection of the idler photon as trigger for the oscilloscope acquisition.

We have repeated the same measurement switching roles for the signal and idler modes, using  a different laser diode as LO, locked in this case to the $5\text{S}_{1/2},\,F=2$$\rightarrow$  $5\text{P}_{1/2},\,F=2$ transition to match the frequency of the idler photons. 

In Figure ~\ref{fig:combined_field.eps} we plot the average variance of $5 \times 10 ^5$ traces as a function of the delay with respect to the trigger events. 

\begin{figure}
  \begin{center}
	\includegraphics[width=\columnwidth]{figures/combined_field.eps}
   \caption{(a) Exponential rise field for heralded signal photon(b) Exponential decay field heralded idler photon}   
  \end{center}
\end{figure}


