I comment on the experiment to realize an "on-demand," reversible
single-photon source by Kuhn, Hennrich, and Rempe [Phys. Rev. Lett. 89, 067901
(2002)].Comment: 2 pages, 1 figur

Kimble, H. J.

English

arXiv

A Comment on the Letter by Axel Kuhn, Markus Hennrich, and Gerhard Rempe, Phys. Rev. Lett. 89, 067901 (2002). The authors of the Letter offer a Reply

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1.5 1 0.5 0 0.5 1 1.5
1
2
10
1 2
(2)
,
( )D Dg τ
τ
0
FIG. 1 (color online). g2D1 ;D2  versus delay  for the fluores-
cent light from a beam of atoms with average number N 
 0:1.
The line at g2D1;D2  
 1 represents the Poisson limit for
coherent light of the same mean counting rates at D1; D2. 
is measured in units of the transit time t0. The generalized Rabi
frequency 0t0 
 25, and transverse decay rate t0 
 0:1. The
lower trace is for background to signal ratio 
 0:5 (appropriate
to Ref. [1]), while the upper trace has no background [3].
P H Y S I C A L R E V I E W L E T T E R S week ending20 JUNE 2003VOLUME 90, NUMBER 24Comment on ‘‘Deterministic Single-Photon Source for
Distributed Quantum Networking’’
A recent Letter [1] describes an experiment to generate
single photons within the setting of cavity QED. The
authors claim that ‘‘a sequence of single photons is emit-
ted on demand’’ and that their results represent ‘‘the
realization of an intrinsically reversible single-photon
source.’’ Although their work is certainly an advance
towards these goals, unfortunately the observational evi-
dence reported in Ref. [1] does not support the principal
claims of the demonstration of a deterministic source for
single photons, nor of emission that is suitable for the
coherent transfer of quantum states over a network. The
underlying difficulties are that (1) photons are emitted at
random and not ‘‘on demand’’due to the random arrival of
atoms into the interaction region, (2) the photon stream is
super-Poissonian because of fluctuations in atom number,
and (3) the pulse phase is random and unknown due to the
stochastic character of atomic trajectories.
The data presented in Fig. 4 of Ref. [1] display the
second-order intensity correlation function g2D1;D2 for
the cross-correlation of photoelectric counting events
from two detectors D1; D2 as a function of time sepa-
ration . Somewhat surprisingly, g2D1;D2  1, and, in
particular, g2D1;D20 ’ 1, so that the inferred photon sta-
tistics are super-Poissonian hn2i > hni [2]. This is in
marked contrast to the behavior required for an on-
demand single-photon source, for which g2t0 ’ 0 at
predetermined times t0, with sub-Poissonian photon sta-
tistics hn2i< hni [2]. The authors attribute this disparity
to detection events other than those arising from photons
emitted from the cavity. However, g2D1;D20 would remain
greater than unity even if the background light were
eliminated altogether, making ~g2 in [1] specious.
Furthermore, neither g2D1;D2 nor ~g
2 incorporate nonsta-
tionarity of the underlying processes, so that conclusions
about nonclassicality are not well supported.
To illustrate these points, consider the well-studied
problem of resonance fluorescence from a two-state
atom, with intensity correlation function g2A  [2]. If
observations are made not for a single atom but rather
from a volume with a stochastic variation in atom number
N, the resulting intensity correlation function g2D1;D2 is
of a markedly different form from g2A , as illustrated in
Fig. 1. Significantly, Fig. 1 for free-space emission repro-
duces the essential characteristics of Fig. 4 in Ref. [1] for
emission within a cavity, including that the light is super-
Poissonian [4]. The commonality of these two figures
arises because of fluctuations in the number of ‘‘source’’
atoms about which there is no a priori knowledge. For
independent single-atom emitters, the observation of sub-
Poissonian photon statistics requires sub-Poissonian atom
statistics, with g2D1;D20< 1 in direct correspondence to
the reduction QA  N
2N
N
< 0 [3]. Strategies to achieve
QA < 0 include conditional detection, both for Fig. 1 and
for Fig. 4 in Ref. [1] [2,5].249801-1 0031-9007=03=90(24)=249801(1)$20.00In addition to fluctuations in arrival time and atom
number, the experiment of Ref. [1] suffers from a lack
of atomic localization with respect to the spatially vary-
ing coupling coefficient g ~r. As as result, the output pulse
shapes and phases for photon emissions vary in a random
fashion. A typical atom in [1] moves 	 4 along the cavity
axis during its transit, leading to an unknown phase  for
the emitted field, which varies from one pulse to the next.
Such randomness in  makes the field unsuitable for the
quantum network protocols cited in Refs. [3,16–19] of
Kuhn et al. [1]. Moreover, reversible transmission to a
second atom-cavity system requires knowledge of the
actual time of the initial emission, as well as an ‘‘event’’
ready atom at the remote location. Neither of these capa-
bilities follows from the experiment reported in Ref. [1].
H. J. Kimble
California Institute of Technology 12-33
Pasadena, California 91125, USA
Received 4 October 2002; published 17 June 2003
DOI: 10.1103/PhysRevLett.90.249801
PACS numbers: 03.67.Hk, 03.67.–a, 32.80.Bx, 42.65.Dr 20[1] A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett.
89, 067901 (2002).
[2] Optical Coherence and Quantum Optics, edited by
L. Mandel and E. Wolf (Cambridge University Press,
Cambridge, 1995), Sec. 15.6.
[3] H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. A
18, 201 (1978), Eq. (31); see quant-ph/0210032.
[4] Quantitative differences (e.g., around  
 0) could be
resolved by a three-state model with pumping and
recycling.
[5] In [1] the mean number of photoelectric events per
atom per pumping cycle is n 0:04 1. This low effi-
ciency and the high background rate severely limit
any sub-Poissonian effect via conditional detection [2].03 The American Physical Society 249801-1


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