Effective single-photon generator via entanglement between emitter and field
of a photonic-crystal reservoir near the band edge
D. Mogilevtsev and S. Kilin
Institute of Physics, Belarus National Academy of Sciences, F. Skarina Avenue 68, Minsk 220072, Belarus
Received 28 January 2008; published 8 September 2008
Long-living entanglement between the emitter and the field of a photonic-crystal reservoir near the band
edge is suggested for implementation of an effective single-photon generator. It can be efficiently driven by
incoherent excitation, is highly controllable, allows no two-photon generation, and provides for a high extrac-
tion probability of the emitted photon into a well-defined mode.
DOI: 10.1103/PhysRevA.78.033808 PACS numbers: 42.50.Dv, 03.67.Bg, 03.67.Lx, 42.70.Qs
Efficient and controllable single-photon generators able to
produce highly uniform single photons on demand are ulti-
mately a necessity for quantum informatics and communica-
tions. A number of proposals for implementation of a single-
photon generator include single emitters or ensembles of
them atoms, molecules, quantum dots, localized defects in
semiconductors, color centers in solid structures, etc. in ap-
propriately modified surroundings such as, for example, mi-
crocavities or photonic crystals, processing of the generated
quantum states for example, tuning down the coherent
states, using parametric nonlinear processes such as down-
conversion and generation by conditioning the multimode
state on results of some specific measurements 1.
Photonic crystals PCs open up an especially wide range
of possibilities for single-photon generators. They provide a
way to collect emitted radiation into a well-defined mode of
an appropriately designed defect in the photonic crystal, and
greatly enhance or inhibit the spontaneous emission 2–4.
However, up to now no attempts have been made to use
another nontrivial feature of PCs, namely, the possibility to
create strong coupling between an emitter and a field, if the
emitter transition frequency is close to the edge of a gap in
the density of states. It has been known for a long time that
the spontaneous decay of an emitter with a transition fre-
quency in the vicinity of a band edge might exhibit a “freez-
ing” behavior. After some initial period of decay, the popu-
lation of an excited level of the emitter comes to a stationary
nonzero value 5–8. Such a freezing or partial decay is a
consequence of the strong correlation appearing between the
emitter and the field modes of the reservoir with frequencies
close to the band edge. Due to the presence of the band gap,
in the process of emitter-field interaction a part of the emitted
radiation is localized in the spatial vicinity of the emitter.
So one has a natural cavity effect without making any
defect in which to localize the field 9. Actually, the struc-
ture of the reservoir distinguishes a superposition of the res-
ervoir modes with frequencies near the band edge, which
strongly interact with the emitter, whereas the rest of the
modes act like a Markovian reservoir. One has effectively
just a single-mode field interacting with the emitter, while
both of them are interacting with the common Markovian
reservoir 9. Thus, an entangled field-emitter bound state
FEBS is formed. The FEBS is quite robust to losses im-
perfections and finite size of the PC, nonzero gap, material
absorption, etc. provided the rates of these losses are smaller
than the inverse time of FEBS formation 10. Also, eventual
destruction of the FEBS via thermalization in a finite-
temperature reservoir is very slow on the time scale of FEBS
formation, if the average number of photons in the reservoir
modes is much less than unity, which is the case, for ex-
ample, for optical frequencies and room temperatures 11.
In this work we demonstrate that the FEBS in PCs can be
implemented for an efficient and highly controllable single-
photon generator, which potentially can have an advantage
over existing suggestions for “photon guns” using isolated
emitters. Two distinctive features make the FEBS a prospec-
tive candidate for such a role. The first is that, for a two-level
emitter in the absence of external excitations, the FEBS may
contain no more than one photon unlike the schemes imple-
menting cavities 1. The second is that the FEBS can be
effectively excited not only by coherent 9 but even by in-
coherent excitation 11which makes it unnecessary to pre-
pare a particular initial state before the next excitation-
emission process. Moreover, we demonstrate in this work
that one may achieve nearly an “ideal” single-photon FEBS
using incoherent excitation. Also, one can achieve nearly
complete collection of the emitted radiation into the chosen
waveguide mode and design a scheme in such a way as to
keep losses of this waveguide sufficiently low 12. It is to
be noticed that such collection is achievable by a coherent
exchange of excitation between the FEBS and the waveguide
mode, so one might expect a high degree of indistinguish-
ability of the emitted photons.
We suggest the following design of the single-photon gen-
erator. A two-level emitter is placed in a three-dimensional
3D PC in that spatial vicinity of an extended single-mode
waveguide Fig. 1. It is to be emphasized that no cavitylike
defect is necessary. Initially, the waveguide mode frequency
is inside the gap and far from the band edge and the emitter’s
transition frequency.
We also assume that the total rate of FEBS losses due to
material absorption, dephasing, etc. is much lower than the
time for FEBS formation. That is a prerequisite for the func-
tioning of the scheme. The suggested generator works as
follows. First, the emitter inside the PC is excited by an
incoherent source with a spectrum spanning the vicinity of
the band edge. The excitation should be present for a time
sufficient for the emitter to reach equilibrium with the reser-
voir. Then the excitation is switched off, and the system re-
laxes to a state that is a mixture of the ideal FEBS with the
PHYSICAL REVIEW A 78, 033808 2008
1050-2947/2008/783/0338085 ©2008 The American Physical Society 033808-1