% !TEX root = homodyne.tex

In summary, we have demonstrated a source of heralded single
photons based on an ensemble of cold rubidium atoms. We observe antibunching
with $g^{(2)}(0)<0.03$, conditioned on the
photon in the signal (idler) mode.
Depending on which of the modes is chosen as a herald, we find either an
exponentially decaying or rising temporal envelope of the heralded photon.

% We do recognize that with this scheme, photon presenting the rising
% exponential envelope is not resonant with a transition from the ground
% state.  But this photon can be at the basis of a scheme for the generation
% of on resonant single photon with the desired (exponential rise) envelope
% [work in preparation]. 
If heralded single photons are practically not distinguishable from ``true''
single photons, the latter should at least in principle 
be
efficiently 
% be
absorbed by a two-level system in free-space in a time-reversed
Weisskopf-Wigner situation.
Such an experiment also would provide a better understanding to what extent
heralded photons are equivalent to single photons emerging from a setup with a
well-defined initial condition.

% \textcolor{red}{
% Such an experiment with a two-level system would ideally have the photon with
% the exponentially rising envelope resonant with a ground state transition,
% which in the presented scheme this is not the case.
% However, this is not a fundamental obstacle, and techniques for photon
% reshaping demonstrated in \cite{Bader_2013} may be employed to address this
% problem.}

% or

% \textcolor{red}{
% In case of an atom as a two level system, one would ideally require a photon with exponential rising envelope resonant  with a ground state transition,
% which is not the case in the presented scheme.
% However, this is not a fundamental obstacle, and waveform reshaping techniques 
% demonstrated in \cite{Bader_2013} may be employed to address this
% problem}


% or

% \textcolor{blue}{
% 	The ideal two level system to perform this experiment is a ground state transition of a single atom.
% 	The photons with the exponentially rising waveform generated by our scheme are instead resonant with an excited transition and cannot be used directly to verify this hypothesis.
% 	However, this is not a fundamental obstacle, and waveform reshaping techniques demonstrated in \cite{Bader_2013} may be employed to address this problem
% }

\textcolor{blue}{This test would require a photon driving a ground state
 transition of a two level system. The heralded photons with the exponentially
 rising waveform
 generated by our scheme are resonant with an excited transition and therefore
 cannot be used directly. However, 
% this is not a  fundamental obstacle because 
  waveform reshaping techniques demonstrated in
 \cite{Bader_2013} can be employed to address this problem.
}
