Research Article
Vol. 2, No. 2 / February 2015 / Optica
88
Micrometer-scale integrated silicon source of
time-energy entangled photons
DAVIDE GRASSANI,1 STEFANO AZZINI,1 MARCO LISCIDINI,1 MATTEO GALLI,1 MICHAEL J. STRAIN,2,3
MARC SOREL,2 J. E. SIPE,4 AND DANIELE BAJONI5,*
1
Dipartimento di Fisica, Universit degli Studi di Pavia, via Bassi 6, 27100 Pavia, Italy
School of Engineering, University of Glasgow, Glasgow G12 8LT, UK
Institute of Photonics, University of Strathclyde, Glasgow G4 0NW, UK
Department of Physics and Institute for Optical Sciences, University of Toronto, 60 St. George Street, Ontario, Canada
Dipartimento di Ingegneria Industriale e dellInformazione, Universit degli Studi di Pavia, via Ferrata 1, Pavia, Italy
*Corresponding author: daniele.bajoni@unipv.it
Received 17 September 2014; revised 18 November 2014; accepted 20 November 2014 (Doc. ID 223278); published 26 January 2015
Entanglement is a fundamental resource in quantum information processing. Several studies have explored
the integration of sources of entangled states on a silicon chip, but the devices demonstrated so far require
millimeter lengths and pump powers of the order of hundreds of milliwatts to produce an appreciable
photon flux, hindering their scalability and dense integration. Microring resonators have been shown
to be efficient sources of photon pairs, but entangled state emission has never been proven in these devices.
Here we report the first demonstration, to the best of our knowledge, of a microring resonator capable of
emitting time-energy entangled photons. We use a Franson experiment to show a violation of Bells inequality by more than seven standard deviations with an internal pair generation exceeding 107 Hz. The source is
integrated on a silicon chip, operates at milliwatt and submilliwatt pump power, emits in the telecom band,
and outputs into a photonic waveguide. These are all essential features of an entangled state emitter for a
quantum photonic network. 2015 Optical Society of America
OCIS codes: (270.0270) Quantum optics; (250.5300) Photonic integrated circuits; (270.5565) Quantum communications; (230.5750)
Resonators; (120.3180) Interferometry.
http://dx.doi.org/10.1364/OPTICA.2.000088
1. INTRODUCTION
Photonics is increasingly seen as an attractive platform for quantum information processing [14]. In quantum cryptography
[2,5] photons have several advantages as vectors of information,
due to their long coherence times at room temperature and the
possibility of being transmitted over the existing optical fiber
infrastructure. The potential scalability and integrability of
photonics also suggests its application in quantum simulation
and computing [69]. The most common strategy for producing entangled photon pairs at room temperature is the use of
the parametric fluorescence that can occur in a nonlinear crystal
[1012]. While having high generation rates, these sources are
very difficult to integrate. An ideal integrated source of
2334-2536/15/020088-07$15/0$15.00 2015 Optical Society of America
entangled photons should be CMOS compatible for cost-effective and reliable production, easily interfaced with fiber networks for long-range transmission in the telecom band, and
take up little real estate on the chip. For such sources the main
results have been obtained by exploiting third-order nonlinearities in silicon, in studies that have been focused on the generation of qubits based on polarization entangled photon pairs
[13,14] or entangled time-bins [15,16] in long waveguiding
structures. However, these devices require lengths ranging from
fractions of a millimeter to centimeters to produce an appreciable photon pair flux, hindering their scalability.
Another kind of quantum correlation of photon pairs is
time-energy entanglement. This is arguably the most suitable
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Vol. 2, No. 2 / February 2015 / Optica
89
format for the entanglement of photons, as it can be easily
manipulated in integrated optical circuits [8], and it can be
preserved over long distances in the fiber optical networks
[17,18] needed for communication between devices. Very recently, it has been shown that the use of time-energy entangled
photon pairs in quantum key distribution can enable a higher
key generation rate compared to entangled photon pairs in
lower-dimensional Hilbert spaces [19].
In this work we demonstrate that silicon ring resonators in a
silicon-on-insulator platform are an efficient source of timeenergy entangled photon pairs. Large field enhancements
can be obtained in resonant structures [20,21], and ring resonators in particular [22,23]. Combined with the large effective nonlinearities achievable in silicon ridge waveguides, of
which they are made, this allows the reduction of the emitters
footprint by orders of magnitude over other sources. There is
then a drastic improvement of the wavelength conversion efficiency, together with the spectral properties of the emitted
pairs, with respect to silicon waveguide sources.
2. SAMPLE STRUCTURE AND TRANSMISSION
SPECTRA
The sample geometry is illustrated in Fig. 1(a): the device is a
ring resonator with a radius of 10 m, evanescently coupled to
a straight silicon waveguide on one side of the ring; both the
ring and the waveguide have transverse dimensions of 500 nm
(width) and 220 nm (height) and are etched on a silicon-oninsulator wafer. The gap between the ring and the waveguide is
150 nm. The coupling of light onto and off the chip is implemented by mode field converters, and the emission is extracted
through a tapered optical fiber. A tunable continuous wave
laser is used for characterizing the sample, and as a pump
for the nonlinear optical experiments (see Supplement 1).
While such ring resonators would act as all-pass devices in
the absence of scattering losses, they are somewhat akin to
integrated FabryPerot cavities in that the modes of the
electromagnetic field are identified by a comb of resonances.
The transmission spectrum from our sample is shown in
Fig. 1(b), where the dips occur due to scattering losses at
the resonances. The free spectral range is about 9 nm, and
the resonance quality factors (Qs) are, on average, around
15,000. The minimum transmission is about 3%5% on
resonance, meaning that the ring almost satisfies the critical
coupling condition, which maximizes the coupling between
the ring and the bus waveguide.
3. NONLINEAR SPECTROSCOPY AND
COINCIDENCE MEASUREMENTS
The nonlinear process responsible for the generation of photon
pairs is spontaneous four-wave mixing (SFWM) [2327]: two
pump photons at frequency p are converted into signal and
idler photons at frequencies s and i [as sketched in the inset
of Fig. 1(b)]. When using resonant structures, energy conservation implies three equally spaced resonances in energy
(s i 2p ). Another advantage in using ring resonators is that the process is greatly amplified by the resonance,
and it has been shown [28] that the generation rate goes as
Fig. 1. Sample structure and characterization. (a) Sketch of the sample
together with the input/output light coupling mechanism. The R
10 m ring resonator is evanescently coupled to a silicon nanowire waveguide via a deep-etched 150 nm gap point coupler. An optical microscope
image of the ring is shown in the inset. The waveguide ends at both sides
with spot-size converters: 300 m long silicon inverse tapers ending in a
20 nm tip width covered by 1.5 m 2.0 m polymer waveguides.
Light injection from a collimated pump laser is achieved by the use
of an aspheric lens with numerical aperture NA 0.5. The output from
the sample is collected with a PM lensed fiber with a working distance of
3 m. (b) Transmission spectrum of the resonator. The pump resonance
is highlighted in green, and the signal and idler resonances employed in
the experiment are indicated in blue and red, respectively.
R Q 3 P 2 r 2 , where Q is the quality factor of the resonances,
r is the rings radius, and P is the pump power. In our ring
resonators, waveguide dispersion limits the bandwidth over
which pairs can be generated for a fixed pump wavelength
to a spectral range of about 80 nm, resulting in a plentiful
choice of possible signal and idler pairs. We have also verified
that the generation rate is almost the same for all resonances up
to the fourth neighboring resonances from the pump [28].
Thus the pump can generate a number of entangled signal
and idler pairs in parallel, with each entangled pair easily
separated from the others because of their frequencies. In this
work we study only one pair, as highlighted by colors in
Fig 1(b): we use a resonance around 1550 nm (at the center
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Vol. 2, No. 2 / February 2015 / Optica
90
Fig. 2. SFWM and coincidences. (a) Spectra of the SFWM experiment for five different coupled pump powers; signal and idler intensities are divided
by the corresponding pump power to underline the superlinear growth of the intensity. The slight difference in intensity between the two peaks is due to
slightly different coupling to the input/output bus of the signal and idler modes. For coupled pump powers above 1 mW, the pump wavelength was
retuned to compensate the red shift of the resonance due to the thermo-optic effect [22]. The horizontal scale is expanded around the signal and idler
resonances, while the complete absence of detected photons at the pump resonance confirms the excellent rejection of the transmitted pump intensity in
the setup. (b) Scaling of the internal generation rates of signal (blue squares) and idler (red circles) photons in SFWM, varying the coupled pump power.
The black dashed line is a guide to the eye proportional to the square of the pump power. The left axis indicates the photon flux measured at the sample
output. (c) Measured coincidence histogram for a coupled pump power P p 1 mW. The time resolution is 75 ps, and it is driven by the response time of
the detectors.
of the telecommunication c-band) for the pump and its second
nearest neighbor resonances for the signal and idler; this
spectral distance is chosen to optimize filtering of the laser
background noise at the signal and idler frequencies.
FWM spectra are shown in Fig. 2(a): two clear peaks of
generated photons are evident at the signal and idler frequencies. It is important to notice that the pump laser is completely
filtered out, so that only spontaneously generated photons are
detected. The parametric nature of the emission process is confirmed by the superlinear increase of the generation rate with
increasing pumping powers: the quadratic behavior of the
generated beams is reported in Fig. 2(b), where we plot the
estimated generation rate of photon pairs inside the ring resonator together with the output rate [28]. The output rate
was directly measured at the sample output, as detailed in
Supplement 1. The internal generation rate was estimated
in the following way: we have directly measured a total insertion loss of 7 dB for the sample. Due to the sample symmetry,
we assume propagation and coupling losses from the ring resonator to the output fiber to be 3.5 dB. The internal generation rate is then estimated from the flux measured at the
output by subtracting the 3.5 dB.
The generation rate can exceed 107 Hz; this is an extremely
high rate, and will be beneficial for all experiments involving
coincidence counting. The first step necessary to verify entanglement is to check that signal and idler photons are emitted in
pairs: this was assessed via a coincidence experiment, in which
the relative times of arrival of idler and signal photons were
statistically analyzed [26]. The coincidence measurement
shown in Fig. 2(c) is obtained employing the setup described
in Fig. 3(a) (detailed in Figure S1 of Supplement 1) by masking the short arm of each interferometer. The total losses
undergone by the signal and idler in the coincidence experiment are 31 and 34 dB, respectively.
An instance of a histogram of the arrival times is shown in
Fig. 2(c), where a distinct coincidence peak is visible over a
small background of accidental counts; this is a clear signature
of the concurrent emission of the signalidler pairs. The 3.5 ns
offset is determined by the different path lengths of the signal
and idler photons. The coincidence measurements, for experimental consistency, were taken using the same setup used to
measure the entanglement as described below, by masking one
arm in each interferometer. The losses from the setup were
directly measured for each component, and amount to
31 dB for signal photons and 34 dB for idler photons, giving
a total loss of 64 dB on the coincidence rate. Almost all of these
losses, as discussed in Supplement 1, are outside the source and
are mainly given by the interferometers and the low quantum
efficiency of the detectors used in these experiments.
Accidental counts are primarily due to emitted pairs of
which only one photon is detected. The accidentals in the
coincidence curve mainly come from the detection of signal
and idler photons belonging to different pairs. As all emission
times are equivalent, the signal-to-noise ratio (SNR) is also an
indication of how likely it is for multiple pairs to be generated
at the same time [29]. In our case the SNR is about 65 in
Fig. 2(c), and higher than 100 in some of the measurements
(see Supplement 1).
4. ENTANGLEMENT TEST ON THE EMITTED
PHOTON PAIRS
The photon pairs are emitted simultaneously, but, because of
the continuous wave pumping, the emission time is indeterminate to within the coherence time of the pump laser; this
is several microseconds in our experiments. This systematic
lack of information can lead to the pairs being time-energy
entangled, as first pointed out by Franson [30]. In order to
Research Article
Fig. 3. Correlations at the output of a double interferomenter.
(a) Sketch of the signal and idler Michelson interferometers. The arm
length difference of the two interferometers is the same to well within
the coherence length of the generated photons (Supplement 1). The
movable mirrors on the short arms are connected to a piezo actuator
and are used to control the relative phase between the short and long
arms. At the outputs of the interferometers are two superconducting
single-photon detectors (SSPDs). (b) Instance of coincidence histogram
measured at the output of the interferometers, taken for a coupled pump
power of 1.5 mW. The integration time is 120 s. The error bars indicate
the error on the counts. The inset shows the absolute intensity at the
output of each interferometer while varying the respective phase: the
complete absence of interference confirms that the arm length difference
is much larger than the coherence time on the generated photons.
experimentally measure the entanglement we have used a double interferometer [30,31], as shown in Fig. 3(a). Photons at
idler frequencies enter one interferometer, while photons at
signal frequencies enter the other [Fig. 3(a)]. The unbalanced
T between the two arms of the interferometers must be
much greater than the coherence time of the signal and idler
photons to avoid first-order interference. In our case T
0.67 ns while 10 ps ( was extracted from the linewidth
of the modes).
The absence of interference in each single interferometer
was verified by varying the path differences independently
Vol. 2, No. 2 / February 2015 / Optica
91
Fig. 4. Entanglement between signal and idler photons. (a)(d) Histograms of the coincidence rate for four different phase settings. (e) Twophoton interference of the double interferometer configuration: the
coincidence count rate of the central peak is plotted as a function of
the phase s i . The integration time is 120 s for each point, and the
pump power is 1.5 mW. The dotted black curve is a best fit of the
experimental data.
in each of the interferometers and confirming that there
was no change in the counting rate detected by the superconducting single-photon detectors (SSPDs), as shown in the inset
of Fig. 3(b). Then with the interferometer arms fixed [32] we
measured the arrival time of idler photons with respect to signal photons [Fig. 3(b)]; the generated histograms reveal three
relative arrival times. The earliest peak is due to the signal photon having taken the long path in the interferometer and the
idler photon having taken the short path; the reverse holds for
the latest peak. The middle peak is due to two indistinguishable paths, both photons taking the long path or both
taking the short path. The inability to distinguish from
which of these two cases the coincidence event arises, due
to the long coherence time of the pump, causes second-order
interference [30]. The coincidence rate for the central peak is
expected to be
Research Article
Vol. 2, No. 2 / February 2015 / Optica
C 2C 0 1 cos ;
(1)
where C 0 is the detected coincidence rate measured by covering one arm in each interferometer. Since signal and idler photons propagate in the same direction once they exit the sample,
the phase term in the above expression is given by the sum of
the phases acquired by the photons passing through the long
arms with respect to the short ones, S I , and is a
constant phase term dependent on the unknown actual lengths
of the interferometer arms.
The effect of varying is shown in Fig. 4; the full experimental dataset is shown in Figs. S4 and S5 of Supplement 1.
While the side peaks, corresponding to distinguishable events,
have heights that are independent of , the number of coincidence counts of the central peak oscillates between minima,
close to zero events, and a maximum, close to four times
the height of the side peaks, as shown in Figs. 4(a)4(d).
The height of the central peak as a function of is summarized
in Fig. 4(e). The trend is well fitted by a sinusoid curve of the
type of Eq (1). For the raw data of Fig. 4(e), the best fit yields
p a
visibility V Meas 89.3% 2.6% (greather than 1 2),
proving a violation of Bells inequality by 7.1 standard
deviations, and so we can conclude that we are generating
time-energy entangled photon pairs [33].
5. DISCUSSION
The experiment was performed for various pumping powers P
(see Fig. S6 of Supplement 1 for the data), and the results are
summarized in Table 1. Bells inequality is violated in all cases,
and by more that 11 standard deviations in the best case. The
visibility is limited by the background due to emission of
multiple couples and possibly other parasitic luminescent processes, such as FWM and Raman scattering in the access waveguide and in the optical fibers in the setup. The SNR, as
expected, decreases with increasing pumping power, but it
is always sufficiently high to lead to entanglement. It is worth
noticing that the values of the measured visibility V Meas reported in the table are obtained by a single fit operation on
the raw data without performing any data correction, e.g.,
without subtracting the dark counts of the detectors. Finally,
the maximum measurable visibility is limited by the first-order
visibility of the interferometers, in our setup w 0.95, which
gives the expected visibility V V Meas w (see the last column
of Table 1).
In conclusion, we have experimentally demonstrated a
microstructured, CMOS-compatible source of entangled
92
photons, operating at room temperature with unprecedented
capabilities. While ring resonators have long been studied
theoretically as a source of quantum correlated states, and pairs
of photons emitted from spontaneous FWM in silicon ring
resonators have been detected, with this work the oft-quoted
promise that these devices could serve as sources of entangled
photons has finally been fulfilled. We confirmed the violation
of Bells inequality by more than seven standard deviations,
and we demonstrated the generation of time-energy entangled
photon pairs particularly relevant for telecommunication applications. The source has incomparable operating characteristics. Beyond the high purity of the emitted two-photon
states, the spectral brightness per coupled pump power is remarkable, at about 6 107 nm1 mW 2 s1 . This is more than
four order of magnitudes larger than that reported for entangled photon pairs emitted by long silicon waveguides
[13,15,23]. Even when compared to room temperature
sources of entangled photons based on 2 nonlinearities, which
are typically not CMOS compatible, the emission rate reported
here is remarkable. It is two orders of magnitude larger than
that obtained from GaAs-based waveguides [34] for 1 mW of
coupled pumping power and, for the given bandwidth, is of
the same order of magnitude as the emission rate of centimeter
long waveguides in periodically poled crystals [11] (see
Table 2), while having a footprint of a few hundred square
micrometers. This small footprint has great advantages for scalability: all the existing know-how of integrated photonics can
be directly applied with our source, and its micrometric size
makes it ideal for integration with other devices on the same
chip, such as integrated filters for the pump and the routing of
signal and idler, for what integration strategies are well established. In particular, with quantum cryptography protocols in
mind, one perspective for this work would be to take advantage
of the silicon photonics industrial know-how to integrate the
pump filtering and signal/idler demultiplexing stages on a
single transmitter chip [35] and implement two receiver
chips with integrated interferometers. Considering the
receiving chips, the coherence time of the signal and idler
photons in this work corresponds to a coherence length of
about 1 mm in a silicon waveguide, and thus an arm unbalance
of some centimeters would be needed in the interferometers;
this can be easily achieved on chip using spiraled waveguides.
The main problem hindering this goal is, for the moment,
the unavailability of single-photon counters for the telecom
band working at room temperature and integrated on a silicon
chip.
Table 1. Violation of Bell Inequalitiesa
P (mW)
R (MHz)
SNR
V Meas (%)
0.25 0.025
0.5 0.05
1.0 0.1
1.5 0.15
2.0 0.2
0.4 0.11
1.7 0.3
5.8 0.8
14 1.9
27 3.1
131.6 16.5
120.4 7.9
64.4 3.3
45.1 2.2
22.9 1.0
94.8 3.8
88.2 4.8
91.8 1.9
89.3 2.6
83.8 3.2
p
V Meas 1 2
V Meas
6.4
3.6
11.2
7.1
4.1
V (%)
99.8 4
92.8 5.1
96.6 2.0
94.0 2.7
88.2 3.4
a
Summary of the measured parameters for five values of the coupled
p pump power P. R, pair emission rate; SNR, signal-to-noise ratio; V Meas , visibility of the two-photon
interference extracted from the experimental raw data; V Meas 1 2 V Meas , number of standard deviation by which Bells inequality is violated. Finally, the visibility V
is V Meas corrected for the limited visibility w 0.95 of the interferometers: V V Meas w.
Research Article
Vol. 2, No. 2 / February 2015 / Optica
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Table 2. Comparison between Room Temperature, Integrated Entangled Photon Sourcesa
Reference
Structure
Material
Device Area ( m2 )
SNR
[11]
[34]
[15]
[16]
Present work
Waveguide
Waveguide
Waveguide
CROW
Ring
PPLN
AlGaAs
Si
Si
Si
180000
10000
5000
8000
300
6b
7c
30
8
64
Spectral Brightness (P 1 mW)
7.5 107
6 105
4 105
3 106
6 107
(s1
(s1
(s1
(s1
(s1
nm1 )
nm1 )
nm1 )
nm1 )
nm1 )
The values of spectral brightness refer to the coupled pump power and the internal generation rate.
The SNR is inferred from the HOM experiment reported in the article.
c
The SNR is calculated from the experimental value of the fidelity reported in the article.
b
A further advantage of the source reported here is that ring
resonators are also a well-established industrial standard,
already used in modulators. Here we have demonstrated a
new, compelling functionality of ring resonators: they can
be used as sources of entangled states of light. Immediate
applications should follow, especially because their production
readiness gives them advantages even over structures characterized by larger nonlinearities, but with less mature integration
technologies [21]. The signal and idler beams have a bandwidth of 13 GHz, which would allow their use in DWDM
network systems without the need for any spectral filtering; the
pump powers used here, on the order of dBm, are characteristic of those used in fiber networks; and the pump, signal, and
idler frequencies lie in the telecommunications band. We can
confidently expect that silicon mircoring resonators will become the dominant paradigm of correlated photon sources
for quantum photonics, both for applications involving the
transmission of quantum correlations over long distances, such
as quantum cryptography, and for applications involving quantum information processing on-a-chip.
FUNDING INFORMATION
Engineering and Physical Sciences Research Council (EPSRC);
Fondazione Cariplo (2010-0523); MIUR (RBFR08XMVY);
Natural Sciences and Engineering Research Council of Canada
(NSERC).
ACKNOWLEDGMENT
We acknowledge the technical staff of the James Watt
Nanofabrication Centre at Glasgow University. J. E. Sipe acknowledges support from the Natural Sciences and Engineering Research Council of Canada. M. J. Strain and M. Sorel
acknowledge support from the EPSRC, UK.
See Supplement 1 for supporting content.
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