Transcript Diapositiva 1

Single photon sources
M.Bertolotti
Dipartimento di Scienze di Base ed Applicate per l’Ingegneria – Sapienza Università
di Roma
Via A. Scarpa 16, I-00161 Roma, ITALY.
Email: [email protected]
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Introduction
The generation of quantum states of the radiation field
has been a topic of growing interest in recent years. This
is because of possible applications in quantum
communication, information processing and quantum
computing, such as quantum networks, secure quantum
communications, and quantum cryptography
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An ideal single-photon source would produce exactly one
photon in a definite quantum state, in contrast with a
“classical” source, such as attenuated laser pulses, for
which the photon number follows a Poisson distribution.
A more stringent request would be to have the single
photon generation on demand, that is a determinate
time. More stringent requests could be high repetition
frequency, high efficient extraction into free space or
fibre, good coherence.
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We may divide the single photon sources into three main
categories:
1. Random sources so much attenuated that one may
assume photons arrive one at the time
2. Real single photon sources that however emit at
random
3. Single photon sources ondemand
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1.Strongly attenuated sources
G.I.Taylor [Proc. Cambridge Phil.Soc. 15(1909)114] could
be the first to be mentioned to have performed an
interference experiment with a single photon obtained by
a strongly attenuated classical source.
The result was the same as in the classical case.
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Strongly attenuated sources
Faint laser pulses deliver Poisson distributions of photons
from which multi-photon events can never be entirely
suppressed.
Nevertheless, such sources are much easier to build and
operate than single-photon sources.
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Strongly attenuated sources
With an attenuated pulsed laser source, the probability of
having 0,1,2,3, or more photons present at a time is
controllede by Poisson statistics
p(m) = <n>m e<n> /m!
where <n> is the mean photon number
Single-photon number-states may be approximated by
coherent states with a very low average photon number.
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Strongly attenuated sources
One may introduce a probability pm that a non-empty
weak coherent pulse contains more than one photon
pm = p2 /p1 = [1-p(0)-p(1)]/[1-p(0)] = <n>/2
Where p1 and p2 are the probabilities that a pulse
contains at least one and at least two photons,
respectively
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Strongly attenuated sources
The value of pm could therefore be made arbitrary small
by decreasing <n>. However when <n> is small most
pulses are empty. The probability to find no photon is
p(0) = 1 - <n>
To overcome this difficulty one may increase the pulsed
laser rate, but in this way also dark counts increase and
the ratio of detected photons to dark counts decreases
with <n>
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2.Real single-photon sources emitting at random
These sources are built around a single emitting
nanometric object, producing photon distributions which
are far from Poissonian. In most cases, for ex., the
probability density of emitting two photons at the same
time can be completely neglected, whereas it is still high
for an attenuated Poisson source with the same
brightness. In most cases, the emission process is
spontaneous and takes place after a rapid excitation of
the emitter.
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Single photon sources
Much progress has been made recently towards such
devices, especially in suppressing the probability of
emitting two photons in the same pulse. Large twophoton suppression has been observed using singlequantum emitters such as molecules [1], diamond
colour centres [2], atoms [3], impurities in
semiconductors [4] and quantum dots [5]. Significant
progress has also been made in increasing the purity of
the quantum states produced [6].
(1)C.Brunel et al. PRL 83 (1999) 2722; B.Lounis and W.E.Moerner, Nature 407 (2000) 491 (2)C.Kurtsiefer
et al. PRL 85 (2000) 290; A.Beveratos et al. Eur.Phys. J. D18 (2002) 191 (3)A.Kuhn et al. PRL 89
(2002)67901 (4)S.Strauf PRL 89 (2002) 177403 (5)P.Michler et al. Science 290 (2000) 2282 C.Santori
et al. PRL 86 (2001) 1502 V.Zwiller et al. APL 78 (2001) 2476 Z.Yuan et al. Science 295 (2002) 102 J.
Vuckovic APL 82 (2003) 3596 (6)C.Santori et al. Nature 419 (2002) 594
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2.Real single-photon sources emitting at random
Quantum dots (QDs) are the ideal sources. The emission
can be controlled by putting the QDs in a cavity and
changing the density of states.
However, the emission process is spontaneous and takes
place after a rapid excitation of the emitter.
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2.Real single-photon sources emitting at random
Semiconductor quantum dots (QDs) have already
produced promising results as single photon emitters. The
main difficulty with QDs is that they interact with a solid
state environment, necessitating cryogenic operation
temperatures, and yet environment induced decoherence
is still a problem. However these difficulties are offset by
advantages such as being fixed in place, large dipole
moments, and the possibility of integration into
monolithic optical microcavity structures
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Control of spontaneous emission from atoms or
molecules
In 1946, Purcell [1] first predicted that nontrivial boundary
conditions of an electromagnetic field in the vicinity of an excited
atom could alter its decay rate. The rate  for spontaneous
transitions from an initial state |i > with no photons to a final state
|f > with one photon is given by the well-known Fermi golden rule
[2]
2
 = h  (  c ) | <f | H |i> |
2
where H is the interaction Hamiltonian and ρ(νc) is the density of
states at the transition frequency νc, that for radiation in free space is
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 (  c )= 2 (4  c /c ).
The rule applies also to photonic crystals [3]
[1] E.M. Purcell, Phys. Rev. 69, 681 (1946).
[2] R. Loudon, The Quantum Theory of Light, Oxford Univ. Press (2000).
[3] S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, A. Menna, Phys. Rev. E70, 56614 (2004).
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History
The application to a small cavity for which the density of modes may
be modified was considered by Klepper [1]. In particular, when the
transition frequency νc is near resonance with a mode
eigenfrequency, the spontaneous emission rate can be considerably
increased.
The effect was experimentally observed [2] with a sodium Rydberg
atom set through a resonant superconducting cavity. Also inhibited
spontaneous emission was observed by studying the cyclotron
motion of a single electron [3].
[1] D. Klepper, Phys. Rev. Lett. 47, 233, (1981).
[2] P. Goy, J.M. Raimond, M. Gross, S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[3] G. Gabrielse, H. Dehmelt, Phys. Rev. Lett. 55, 67 (1985).
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Photonic crystals may influence atomic
emission
The decay rate could be suppressed for atoms located inside a
PBG when their resonant emission frequency is in the PBG gap. In
this frequency range, the electromagnetic density of modes is very
small.
Resonance enhancement of the decay rate is on the contrary
expected at the photonic band edges where the DOM is
anomalously large [1,2]. Computer simulations have confirmed
changes in the rate of emission in photonic structures [3].
[1] V. Bykov, Phys. Rev. Lett. 58, 2486 (1987). S. John, Phys. Rev. Lett. 58, 2486 (1987). S. John, T. Quang,
Phys. Rev. A50, 1764 (1994).
[2] E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987). E. Yablonovitch, T. Gmitter, Phys. Rev. Lett. 63, 1950
(1989).
[3] Dowling J P 1999 J. Lightwave Technol. 17 2142. Dowling J P and Bowden C M 1992 Phys. Rev. A 46
612. Bendickson J M, Dowling J P and Scalora M 1996 Phys. Rev.E 53 4107. Fogel I S, Bendickson J M,
Tocci M D, Bloemer M J, Scalora M, Bowden C M and Dowling J P 1998 Pure Appl. Opt. 7 393. Scalora M,
Dowling J P, Tocci M, Bloemer M J, Bowden C M and Haus J W 1995 Appl. Phys. B 60 557. Pereira S and
Sipe J E 2000 Phys. Rev. E 62 5745.
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Density of modes and group velocity in PBG
T
1 .0
0 .5
DOM
(u n its o f 1 /c)
0
9
6
3
g ro u p ve lo citiy
(u n its o f c)
0
6
4
2
0
0 .6
0 .8
1 .0
 /
0
1 .2
1 .4
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The effect may be seen as a modification of
the exponential decaying emission with
respect to an atom in free space and can be
generated by embedding the atom in photonic
crystals
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The effect may be seen as a modification of the exponentially
decaying emission with respect to an atom in free space and can be
generated by embedding the atom in photonic crystals [2].
Spontaneous emission of CdSe quantum dots embedded in a 3D
photonic crystal consisting of air spheres in titanium dioxide has
shown changes in the fluorescence decay curves of the quantum
dots inside photonic crystals with different lattice parameters [3–5].
[2] Sprik R, Von Tiggelen B A and Lagendijk A 1996 Europhys. Lett. 35 265. Yang Y, Fleischhaner M and Zhu
S Y 2003 Phys. Rev. A 68 43805. Zhu S Y, Li G X, Yang Y P and Li F L 2003 Europhys. Lett. 62 210. Yu
Zhang J, Wang X Y and Xiao M 2003 Opt. Photon. News 14 (December) 33.
[3] Busch K and John S 1998 Phys. Rev. E 58 3896. Nikolaev I, Lodahl P, Vos W and van Driel F 2005
ECLEO (Munich 2005).
[4] Lodahl P, von Driel A F, Nikolaev I S, Irman A, Overgaag K, Vanmalkelberg D and Vos W 2004 Nature
430 654.
[5] Nikolaev I S, Lodahl P and Vos W L 2005 Phys. Rev. A 71 53813.
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An example.
Spontaneous emission of CdSe quantum dots embedded in a 3D
photonic crystal consisting of air spheres in titanium dioxide shows
changes in the fluorescence decay curves of the quantum dots
inside photonic crystals with different lattice parameters.
Lodahl P, von Driel A F, Nikolaev I S, Irman A, Overgaag K, Vanmalkelberg D and Vos W 2004 Nature 430
654.
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Using quantum dots embedded in pillar microcavities, one may
have two-photon suppression factors as large as 40 [1], improved
efficiencies [2] and photon state purities such that the mean
wavepacket overlap between consecutive photons is as high as 0.8
[3].
We show an example from the work of Santori [3].
(1) J.Vuckovic et al. APL 82 (2003) 3596
(2) M.Pelton et al. PRL 89 (2002) 233602
(3) C.Santori et al. Nature 419 (2002) 594-
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Santori realized a single-photon device embedding a quantum
dot in a distributed Bragg structure[fig 1(a)]. One or more InAs
quantum dots, surrounded by a GaAs matrix, are embedded in
a micropillar optical cavity. The QDs serve as the single-photon
emitters. The optical microcavity serves to modify the
spontaneous emission properties of the QD through the
Purcell effects. When a radiative transition of the QD is on
resonance with a cavity mode, if the QD couples much more
strongly with this mode than to the background “leaky” modes,
the spontaneous emission rate can increase substantially and
light is emitted mainly into the cavity mode.
C.Santori et al.
New J.Phys. 6(2004)89
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The operation scheme is shown in figure 1(c). A short (2-3 ps) optical
pulse generated by a tunable Ti-sapphire laser raises the quantum
dot into an excited state containing one electron-hole pair.
The QD then quickly relaxes (with a timescale of the order of 10 ps) to
a lowest excited state. This state then decays through a much slower
spontaneous emission process (100-300 ps) to emit a single photon.
The spontaneous emission is collected and sent through a narrowband (0.1 nm) spectral filter. This not only removes background
emission from the sample, but also protects against events in which
the quantum dot receives multiple excitations.
In these events, multiple photons
are emitted, but each photon has
a unique wavelength, as a result
of the electrostatic interactions
between particles inside the
quantum dot, leading to energy
shifts of the order of meV.
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The sample needs to be cooled
temperatures ranging from 3 to 10 K.
to
The efficiency can be studied through
photon correlation with a Hanbury-Brown
and Twiss-type set-up.
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A single photon state is one that should
exihbit antibunching. This property was
already found by Mandel and Wolf
measuring the conditional probability g2(τ)
that having detected a photon at time t
another photon comes at time t + τ.
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single-photon sources on demand
In the nanosecond time regime the emitted photons from
a single quantum system are expected to show
antibuching, that is the probability for two photons to
arrive at the same time is zero
To observe antibunching correlations, the second-order
correlation function g2(t) is generally measured by
determining the distribution of time delays N(τ) between
the arrival of successive photons in a dual beam detector.
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Single photon generation is examined by measuring the
second-order intensity autocorrelation function (g(2)(τ))
using the Hanbury-Brown and Twiss arrangement.
g
(2)
(r) 
n (t )n (t  
n
2

P (t / t  )
P (t )
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Cahotic, laser, and nonclassical light
The behaviour
of the g(2)(τ) as
a function of the
time delay τ
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g(2) (τ) for different Fock
states
A Fock state with 9 photons
B Fock state with 5 photons
C Fock state with 1 photon
g2(τ ) = 1 – 1/n
where n is the number
of Fock states
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Antibunching for a single photon
• From A.Beveratos PR A64(2001)061802
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In the Santori experiment the emission from the QD is spectrally
filtered and split into two paths by a beamsplitter, each path leading
to a photon counter. Coincidence-counting electronics generates a
histogram of the relative delay  = t2 – t1 between photon detection
events at counters 1 and 2. The peak at  = 0 corresponds to events in
which two photons were detected in the same pulse, and thus the first
goal in developing a single-photon source is to make the area of this
peak as small as possible.
The peaks at times nTrep where
Trep = 13 ns is the laser repetition
period, correspond to events in
which one photon was detected
from each of two different pulses.
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3.single-photon sources on demand
A particularly novel non-classical source of light is a
deterministic (or triggered) single-photon source: a source
that has the property to emit with a high degree of
certainty one (and only one) photon at a user specific
time.
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One method for preparing an approximation to a singlephoton state is by generating a pair of photons.
This can be achieved using the creation of two photons by
a parametric downconversion process
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Parametric down conversion is a second order nonlinear
process where a wave impinging on a nonlinear crystal
creates two new light beams obeying energy and
momentum conservation
ω1 k1
ωo ko
ω2
ωo = ω1 + ω2
k2
ko = k1 + k2
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Essentially the process is one of conditional preparation:
given that either two photons exist or no photon exists,
the detection of one photon acts as a signal that a second
photon is present in the field.
The frequency and direction of propagation of the second
photon are related to those of the first by conservation
laws, and can be determined by analysing the first “gate”
photon.
The second photon field can then be regarded as being in
a one-photon Fock state
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Luminescent centres in diamond have recently emerged
as an alternative
. T.M.Babinec et al. Nature Nanotechnology 5 (2010)195Single photon sources
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A schematic of the SEM/FIB with nickel-ion
source. The yellow cubes represent diamond
uninplanted diamond crystals while the blue one
is the only crystal which was implanted with
nickel. B is SEM image from I.Aharonovich et
al. PRB79, 235316 (2009)
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