% !TEX root = homodyne.tex

%Strong atom-light interaction at the single quantum level is a prerequisite for
%many quantum communication 
%and computation protocols~\cite{Cirac_1997,DLCZ:2001,Wilk_2007,kimble2008}.
%In free space the optimal coupling of photons to atoms requires 
%the temporal profile of the incoming photons to match the time reversal of photons generated by spontaneous decay from the transition of interest.~\cite{Yimin:2011,Syed_2013,Bader_2013}.
%Together with spectral and spatial mode matching~\cite{Nicolas_2001,Sondermann:07,Mengkhoon_2008}, the efficient preparation of single photons with an exponentially rising temporal envelope 
%remains an open challenge. 
%The generation of 
\textcolor{red}{Strong interaction in free space between a single 
% photons 
photon and a two-level quantum system is a
% fundamental physical process and is 
% a
prequisite for many quantum communication and computation protocols
\cite{Cirac_1997,DLCZ:2001,Wilk_2007,kimble2008}. This interaction has been
demonstrated to be optimal when the incident photon has an exponential rising
temporal envelope \cite{Sondermann:07,Yimin:2011,Syed_2013,Bader_2013}. }
 
 %Preparing single photon states with exponential rising temporal envelope is in particular of great interest  to enhance these interactions ~\cite{Yimin:2011,Syed_2013,Bader_2013}. }
 
 %The efficient interaction between the two is prequisite for many quantum communication and computation protocols~\cite{Cirac_1997,DLCZ:2001,Wilk_2007,kimble2008}. 
A common way to obtain single photons is to generate time correlated photon
pairs: the detection of one photon heralds the presence of the
other \cite{Clauser_1974,Grangier_1986,Hong:86}.
\textcolor{red}{
Heralding has already been used to generate single photons with rising exponential temporal envelopes:
the intensity of one photon of the pair
% generated in a cold atomic ensemble 
is modulated in time using fast modulators~\cite{Kolchin_2008, Zhang:2012}.\\
 % The intensity of one of the photon of the pair is then modulated in time using fast modulators~\cite{Kolchin_2008, Zhang:2012}.
 % that allows one to directly modulate the intensity of one of the photons of the pair in time domain~\cite{Kolchin_2008, Zhang:2012}. 
%This is done by using electromagnetically
%induced transparency and slow light
% However, the 
This modulation technique resulted in unavoidable losses due to the small overlap between the temporal shape of the generated photons (exponential decay) and the desired one (exponential rise).}
% However, the modulation techniques filter out the significant portion of the temporal envelope of  generated photons to obtain the desired (exponential rise) shape, thus results in unavoidable losses. 


 In the work presented here, we use a photon pair source based on four-wave mixing in a cold atomic ensemble via a cascade decay level scheme.
This process has been used in the past to generate narrow band photon
pairs~\cite{Chaneliere:2006}, and it has already been demonstrated that 
the resulting photon pairs are nearly Fourier-limited~\cite{Srivathsan:2013}
with a coherence time long enough to be resolved with various optical
detection techniques.
\textcolor{red}{We show 
% how this source 
how the use of a cascade decay scheme
allows the direct preparation of single photons with a rising exponential
temporal envelope 
by using the appropriate heralding scheme
without 
% recurring
resorting
to any intensity modulation.
% but only
% to
}
%{We demonstrate how this source allows the direct preparation of single photons with a rising exponential temporal envelope from the atoms.} 
