PHYSICAL REVIEW RESEARCH 4, L022011 (2022)
LetterEvidence for near-unity radiative quantum efficiency of bright excitonsin carbon nanotubes from the Purcell effect
H. Machiya,1,2 D. Yamashita,3 A. Ishii,1,3 and Y. K. Kato
1

1,3,*

Nanoscale Quantum Photonics Laboratory, RIKEN Cluster for Pioneering Research, Saitama 351-0198, Japan2
Department of Electrical Engineering, The University of Tokyo, Tokyo 113-8656, Japan
3
Quantum Optoelectronics Research Team, RIKEN Center for Advanced Photonics, Saitama 351-0198, Japan(Received 19 March 2021; revised 27 February 2022; accepted 23 March 2022; published 15 April 2022)

The efficiencies of photonic devices are primarily governed by radiative quantum efficiency, which is aproperty given by the light-emitting material. Quantitative characterization for carbon nanotubes, however, hasbeen difficult despite being a prominent material for nanoscale photonics. Here we estimate the radiative quantum
efficiency of bright excitons in carbon nanotubes by modifying the exciton dynamics through cavity quantum
electrodynamical effects. Silicon photonic crystal nanobeam cavities are used to induce the Purcell effect on
individual carbon nanotubes. Spectral and temporal behavior of the cavity enhancement is characterized byphotoluminescence microscopy and the fraction of the radiative decay process is evaluated. We find that theradiative quantum efficiency can reach near unity for bright excitons in long air-suspended carbon nanotubes atroom temperature.
DOI: 10.1103/PhysRevResearch.4.L022011

Radiative quantum efficiency is a fundamental physicalquantity that ultimately limits the efficiency of optoelectronic
devices. Type III-V direct gap semiconductors with radiative
quantum efficiencies close to 100% have played a central rolein the development of efficient light emitting diodes (LEDs)
that are now used ubiquitously [1]. Modern high-power diodelasers see extensive use in industries including telecommunications [2], materials processing, and medical treatments [3],but the performance needed for broad applications would havenot been possible without the high quantum efficiencies of
the gain materials. Organic semiconductors have likewise seencommercial success in LED displays [4], but only after substantial improvement of their radiative quantum efficiencies[5,6].
Carbon nanotubes (CNTs), also as a direct gap semiconductor, have demonstrated their potential as a key material
for nanoscale photonic devices. Electrically gated pn-junction
devices can be constructed from nanotubes with diameters
significantly smaller than the wavelength, where extremely
efficient photocurrent generation [7,8] and excitonic electroluminescence [9,10] have been demonstrated. Unique exciton
physics can be exploited to generate telecom-band single
photons at room temperature [11–13], and the compatibilityof nanotube emitters with silicon photonics [14–19] offers
opportunities in integrated quantum optics [20]. The device
performance is again limited by the radiative quantum effi-*

Corresponding author: yuichiro.kato@riken.jp

Published by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Further
distribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.
2643-1564/2022/4(2)/L022011(7)L022011-1

ciency, but the uncertainty of absorption cross section andsensitivity to nanotube quality have made quantitative characterization difficult.
Here we experimentally estimate the radiative quantum
efficiencies of excitons in air-suspended CNTs. Quantum
electrodynamical effects in nanoscale photonic cavities areused to selectively modify the radiative decay rate of excitons, allowing us to gain insight to the fractions of radiativeand nonradiative processes before the modification. Individual
CNTs are coupled to air-mode photonic crystal nanobeam
cavities, and photoluminescence (PL) measurements are performed to quantitatively evaluate the spectral and temporalenhancements induced by the Purcell effect. We find that theradiative quantum efficiency can reach near unity for bright
excitons in long air-suspended carbon nanotubes at room temperature. Statistically, 40% of nanotubes are found to exhibit
radiative quantum efficiencies larger than 70%.
Microcavities alter the decay dynamics of excitons througha quantum electrodynamical phenomenon known as the Purcell effect [21]. In free space, the total exciton decay rate
can be written as γr + γnr where γr and γnr are the radiativeand nonradiative decay rates, respectively. When excitons arecoupled to a microcavity, the increased photon density ofstates gives rise to an additional radiative decay rate F γr ,where F is the Purcell factor [14–17,22,23]. Combined withthe unchanged free-space emission, the resulting total radiative decay rate within the microcavity is then given by(1 + F )γr . The accelerated radiative recombination appears inthe spectral domain as an increased intensity in a spectrally
narrow region around the cavity resonance. If the radiative
quantum efficiency η = γr /(γr + γnr ) is low, the Purcell effectalso increases the radiative fraction of the recombination. The
acceleration is more directly observed in the time domain asa shortening in the lifetime. The overall change in the decay
Published by the American Physical Society

MACHIYA, YAMASHITA, ISHII, AND KATO

PHYSICAL REVIEW RESEARCH 4, L022011 (2022)

FIG. 1. (a) Schematic of the device. (b) Simulated spatial distribution of the y component of the electric field Ey for the fundamental
transverse-electric mode at z = 0.00 μm. The lattice constant a =350 nm is used and the cavity center period is 1.18a. The beamwidth is 600 nm and the holes are 140 nm by 400 nm. The Si layer
thickness of 260 nm is chosen to match the actual devices. The
scale bar is 1 μm. (c)–(e) Spatial profiles of the calculated Purcell
factor at x = 0.00 μm. Cross sections through the dashed lines at (c)z = 0.38 μm and (d) y = 0.00 μm. Position-dependent Purcell factor
is calculated from F (r) = 4π3 2 VQ λ3 |Ey (r)|2 / max |Ey (r)|2 , where Q isthe emitter quality factor, V is the mode volume, and Ey (r) is the ycomponent of the electric field amplitude at position r. For (b)–(e),The coordinate origin is taken to be the center of the cavity.

rate can be characterized by the acceleration factor defined as
the enhancement of the total decay rate by the Purcell effectA=(1 + F )γr + γnr= 1 + F η.
γr + γnr(1)

If F and A are known, Eq. (1) allows us to estimate η without making further assumptions. By performing spectral- andtime-domain measurements on excitons coupled to a microcavity, we independently evaluate the Purcell factor and theacceleration factor.
As our primary interest is in the intrinsic properties of
excitons, we use as-grown air-suspended CNTs for the determination of the quantum efficiency. These tubes are known
to exhibit high PL yields, indicative of their pristine nature[24]. To modify the radiative decay rates by the Purcell effect,
the air-suspended tubes are coupled to silicon photonic crystal
nanobeam cavities [14,17] as shown in Fig. 1(a). We utilize
air-mode cavities characterized by ultrasmall mode volumes

and large electric fields in the air holes, which allows forhigh-efficiency coupling [14].
The cavities are designed by finite-difference time-domain(FDTD) simulations [25]. We place 39 rectangular holes inan air-bridge nanobeam structure (see Supplemental Material
Fig. S1 [26]), and the periodicity is increased at the cavity
center in a parabolic manner over 16 periods [14]. The mode
profile is presented in Fig. 1(b), where the large fields in the airholes can be seen. The cavity has a resonant wavelength λ =1460 nm and its quality factor and mode volume are calculated
to be 4 × 105 and 0.025 × λ3 , respectively.
Because CNTs suffer from strong quenching effect upon
contact with the substrate [27,28], we place spacer layers tosuspend the tubes a few hundred nanometers above the cavity.
The thickness of the spacers is critical in our device design
since the evanescent fields of the cavity mode decreases exponentially above the cavity [Figs. 1(c) to 1(e)]. Due to theultrasmall mode volume of the cavity, a Purcell factor of 5.8 isstill available even a few hundred nm above the cavity surface[Fig. 1(d), dashed line].
Based on the simulation results, we choose a spacer layer
thickness of 250 nm to place CNTs at z = 380 nm for our
devices and fabricate the cavities from a silicon-on-insulator
wafer. The nanobeams are designed to be 800-nm wide andthe hole width is fixed at 500 nm, where we chose the parameters to correct for fabrication errors. The lattice constant a isvaried from 320 nm to 511 nm to cover a wide wavelength
range from 1100 to 1600 nm for coupling to a variety of nanotube chiralities and the hole length is scaled to be 0.4a. We
begin by defining cavities and alignment marks by electron
beam lithography, and the 260-nm-thick top Si layer is etchedby inductively coupled plasma etcher. Another electron beam
writing patterns the spacer regions, where Si is sputtered andsubsequently lifted off. The 1-μm-thick buried oxide layer
is then etched by hydrofluoric acid to form the air-bridge
structure. We perform a final electron beam writing to define
catalyst windows, and the completed chip is diced into 4-mm
square chips. We finally synthesize the nanotubes by alcohol
chemical vapor deposition [28]. A scanning electron micrograph of a device is shown in Fig. 2(a).
The devices are characterized with a home-built confocal
microscope system [17,28]. Samples are mounted on a motorized three-dimensional feedback stage, allowing us to perform
automated measurements over a large number of devices. A
wavelength-tunable Ti:sapphire laser is used as an excitation
source, and the beam is focused by an objective lens witha numerical aperture of 0.85 and a focal length of 1.8 mm.
Emission is collected with the same objective lens and coupled to a grating spectrometer with a liquid-nitrogen-cooled
InGaAs photodiode array through a confocal pinhole corresponding to an aperture with 2.7-μm diameter at the sample
image plane. Laser reflection is simultaneously collected andis monitored by a silicon photodiode to construct reflectivity
images. Continuous-wave excitation is used unless otherwise
noted and all measurements are performed at room temperature in a dry nitrogen environment.
As the chirality and the location of the nanotubes are randomly distributed, some effort is required to find tubes thathave good spatial and spectral overlap with the cavity modes.
To overcome the low yield of devices with optical coupling,

L022011-2

EVIDENCE FOR NEAR-UNITY RADIATIVE QUANTUM …

PHYSICAL REVIEW RESEARCH 4, L022011 (2022)

FIG. 2. (a) Scanning electron micrograph of a fabricated device.
A CNT is suspended across the width of the trench near the center ofthe image. The scale bar is 1 μm. (b) Typical PL spectrum of a device
showing optical coupling to the cavity. The dots are data and the grayline is the bi-Lorentzian fit. The blue and red curves correspond tothe cavity and the CNT peak components, respectively. We interpretthe asymmetry of the peak shape as a dip caused by the interferenceof the optics or the interference with the reflection from the bottomof the nanobeam substrate. (c,d) PL images for the (c) cavity and(d) CNT emission, obtained by mapping out the peak areas for eachpeak. (e) Reflectivity image taken simultaneously with (c) and (d).
The scale bar in (c) is 1 μm and is shared between panels (c)–(e).
For (b)–(e), the excitation laser wavelength is 793 nm and the laser
polarization is parallel to the nanotube axis. (f) PL excitation map
for the same device, taken with the laser polarization perpendicular
to the nanobeam axis. Chirality is assigned to (9,8) using tabulated
data [28]. Inset: Excitation polarization dependence of PL at 1378 nm
with a spectral integration window of 5 nm. The dots are data andthe line is a fit by cosine squared. (b)–(f) are taken with an excitation
power of 20 μW.

which is typically less than 0.1%, more than 300 000 devices
in total are prepared. Automated scanning is performed toefficiently collect PL spectra from a large number of devices,
constructing colormaps of PL intensity as a function of position and wavelength (see Supplemental Material Fig. S2[26]). The signature of optical coupling is the spectrally narrow peak corresponding to the cavity mode. We perform
two-dimensional peak detection to extract such data and thennonlinear curve fitting is used to determine the linewidths
for each peak. We select devices for detailed characterization
when the linewidth is below 5 nm, sufficiently narrower than
the typical linewidths of nanotubes.
Figure 2(b) shows a PL spectrum of a representative device, where a sharp peak corresponding to the cavity modecan be seen on top of a broader peak from CNT emission into

free space. The cavity peak is centered at 1378.1 nm (0.90 eV)
and has a linewidth of 0.5 nm (0.3 meV), whereas the CNT
peak has a center wavelength of 1378.4 nm (0.90 eV) witha linewidth of 14.1 nm (9.2 meV). The cavity linewidth islimited by the spectrometer resolution and a separate measurement was performed to evaluate the actual value and thequality factor (see Supplemental Material Fig. S3 [26]). The
cavity peak area Icav and the CNT peak area ICNT can beextracted using bi-Lorentzian fitting and a two-dimensional
PL scan is performed to map out the spatial extent of thetwo components [Figs. 2(c) and 2(d)]. A reflectivity image issimultaneously taken and is shown in Fig. 2(e), which shows
the location of the cavity. The profile of the cavity emission
is predominantly localized at the center of the device, as
expected from the electric field distribution of the cavity mode
[Fig. 2(c)]. In comparison, the nanotube peak component extends beyond the width of the nanobeam, showing emission
from the full length of the suspended nanotube [Fig. 2(d)].
We further characterize the device to ensure that the tube is
individual and clean. A PL excitation map is used to identify
the chirality, whereas the angle of the nanotube is obtained
from polarization dependence of PL [Fig. 2(f)]. Devices
showing multiple peaks or temporal instabilities are eliminated from further measurements, as they indicate bundlingor contamination [29,30]. After such rigorous characterization, the number of devices that can be used for determining
the quantum efficiency is less than 20 out of the 300 000
devices.
The Purcell factor is extracted from the PL spectrum taken
at the center of the device [Fig. 2(b)], using the PL intensitiesof the two peak components. Letting Ccav and CCNT be thecollection efficiencies of the cavity mode and the nanotube
emission, respectively,
F=

Icav /Ccav.
ICNT /CCNT(2)

The collection efficiencies therefore have a critical effecton the value of F and are obtained using the radiation patterns
from FDTD simulations (see Supplemental Material Sec. S4[26]). For Ccav , we place a resonant source at the cavity centerto compute the cavity radiation pattern [Fig. 3(a)]. Since thecavity mode primarily consists of zone boundary waveguidemodes [Fig. 3(b)], coupling to leaky modes above the lightline is small [31]. Most of the light that leaks out is directed
at a low angle along the nanobeam, likely because most of thecoupling occurs near the light line. As a result, only a small
fraction of cavity photons fits within the numerical apertureof the objective lens, giving Ccav = 0.15. We calculate thenanotube radiation pattern in a similar manner, but the offresonant excitation source is placed at the node of the mode
profile and is spectrally detuned by 26 nm. In contrast to thecavity radiation pattern, the nanotube radiation is reduced by
the photonic band gap at low angles, causing the emission to
be redirected upward and increasing the collection efficiency
to 40% [Fig. 3(c)]. In addition to the collection efficiency ofthe objective lens, we also include a correction factor in CCNT
to take into account the emission from the length of the tube
beyond the width of the nanobeam. The additional factor isgiven by the entire length of the tube normalized with respect
to the spatial width of the cavity mode. The entire tube length

L022011-3

MACHIYA, YAMASHITA, ISHII, AND KATO

PHYSICAL REVIEW RESEARCH 4, L022011 (2022)

FIG. 3. (a) Calculated far-field radiation pattern of the fundamental cavity mode. (b) Schematic showing the photonic band
diagram of one-dimensional photonic crystal. The red colored region of the air band represents the zone-boundary waveguide mode.
(c) Calculated far-field radiation pattern of the uncoupled nanotube
emission. For (a) and (c), photon flux density is plotted as a functionof polar and azimuthal angles in spherical coordinates. The radial
axis represents the polar angle. The green circle represents the numerical aperture of the objective lens.

is calculated geometrically by the tube angle with respect tothe nanobeam axis [Fig. 2(f), inset], and the width of the cavity
mode is taken to be 540 nm. Combining both contributions,
we obtain CCNT = 1.6. This analysis results in Purcell factor
F = 0.84 ± 0.23 for this device, a reasonable value considering the lateral displacement of ∼0.6 μm [Figs. 2(c) to 2(e)]from the cavity field maxima and the simulation in Figs. 1(c)to 1(e).
In order to estimate the quantum efficiency, we now need toevaluate the acceleration factor by performing time-resolved
PL measurements. The same PL microscopy setup is used
but the devices are excited with ∼100-fs laser pulses with arepetition rate of 76 MHz and an average power of 100 nW.
After spectral rejection of the excitation laser, we couple theemission to a single-mode optical fiber which limits detection
to a 1.8-μm diameter spot at the sample. A fiber-coupled
superconducting single-photon detector with a timing jitterof 32 ps is used to detect the photons and the decay curves
are constructed by time-correlated single-photon counting.
Time-resolved PL data taken from the device shown in Fig. 2
is plotted as a blue curve in Fig. 4(a). We observe fast andslow decay components with lifetimes τ f and τs , respectively[32]. By comparing the decay curve to that of a nanotube infree space having a similar length [red curve in Fig. 4(a)],we already see that τ f corresponding to the bright exciton
lifetime is considerably shorter, while τs reflecting the dark
exciton dynamics is comparable. This is expected as the bright
exciton decay is accelerated by the Purcell effect, whereas thedark excitons do not interact with photons and therefore their
lifetime would not be changed by the cavity. We note that thecontrasting behavior of bright and dark exciton lifetimes rulesout extrinsic quenching effects as the cause for bright exciton

FIG. 4. (a) Decay curves for the Purcell-enhanced nanotube
emission from the same device as in Fig. 2 (blue) and a 2.0-μm-long(9,8) nanotube in free space (red). The gray curve is the instrument
response function. The excitation powers are 100 nW and 5 nW for
nanotubes in the cavity and in free space, respectively. (b), (c) Length
dependence of (b) τs and (c) τ f in free space. The red dots are data
and the lines are fits using the exciton diffusion model [32]. The blue
dashed line in (b) shows the dark exciton lifetime in the cavity, fromwhich we extract the effective nanotube length. The blue trianglein (c) shows the Purcell-accelerated bright exciton lifetime. The
laser wavelength and polarization are adjusted to maximize the PL
intensity. Wavelength-dependent instrument response is obtained bymeasuring broadband supercontinuum pulses through a spectrometerwith a spectral window of ∼1 nm.

lifetime shortening. Such effects including quenching causedby contact with the substrate should shorten both bright anddark exciton lifetimes, as in the case for end quenching[32].
We fit the decay curve of the cavity-coupled emission[Fig. 4(a), blue curve] to obtain τ f and τs . A biexponentialfunction convoluted with the instrument response function isused to extract τ f = 34.8 ± 0.3 ps, and a single exponential fit
to the data in the time range beyond 10τ f yields τs = 586 ±5 ps. The change in τ f for the nanotube coupled to the cavity
compared with a nanotube in free space is needed to obtainthe value of A, but care must be taken since τ f is dependent on
the nanotube length L [32]. We take advantage of the fact thatthe dark exciton dynamics is unaffected by the cavity and use
the length dependence of τs obtained from the exciton diffusion model [32] to determine the nanotube length at which τ f
is compared.
Figures 4(b) and 4(c) show the length dependence of τsand τ f , respectively, for air-suspended (9,8) nanotubes infree space [32]. Both the bright and dark exciton lifetimes
increase with the nanotube length due to reduced end quenching in longer nanotubes. By looking up the nanotube lengthfor τs = 586 ps [Fig. 4(b), dashed line], L = 2.5 ± 0.1 μm
is obtained. The acceleration factor is then evaluated using the corresponding bright exciton lifetime in free space[Fig. 4(c)] and we find A = 1.82 ± 0.09. The error for theacceleration factor is computed from the 1σ confidence intervals of the fits and the standard deviation of the lifetime
data in free space. Having determined both F and A for thisdevice, the radiative quantm efficiency of bright excitons is
calculated to be 0.98 ± 0.29 using Eq. (1). We may have

L022011-4

EVIDENCE FOR NEAR-UNITY RADIATIVE QUANTUM …

PHYSICAL REVIEW RESEARCH 4, L022011 (2022)

FIG. 5. The acceleration factor as a function of the Purcell factor.
The dots are data and the error bars show the 1σ confidence interval.
The blue line indicates η = 1 as given by Eq. (1). Chiralities of thenanotubes in the measured devices are (9,7), (9,8), (10,8), and (11,6),
whose τ f are between 54.6 ps to 64.2 ps in free space. Since theshortest τ f resolvable by the fitting process is approximately 13 ps,
the upper bound of the measurable acceleration factor ranges from
4.2 to 4.9. Inset is the histogram of the radiative quantum efficiences.

overestimated the confidence intervals as η > 1 would be unphysical, which points to the limits of the assumptions in ourmodel.
The high quantum efficiency is reproducibly observed ina number of devices. We repeated the same measurements
in additional devices with varying Purcell factors, and theresults are summarized in Supplemental Material S5 [26]. The
acceleration factor is plotted as a function of the Purcell factor
in Fig. 5, where variations and errors in the measured quantum
efficiencies can be seen. The orange shaded area corresponds
to the region beyond the shortest resolvable lifetimes. Data
points closer to the top-left corner indicate higher quantum
efficiency and we observe that the blue line representing unity
quantum efficiency passes through a number of data points
within the error bars. The inset of Fig. 5 is the histogram ofthe obtained radiative quantum efficiencies, and 6 out of 15
nanotubes exhibit η > 0.7. It is not surprising that there are
devices showing lower efficiencies since shorter nanotubes
have higher nonradiative decay rates (see Supplemental
Material Fig. S4 [26]). We may therefore interpret the highest
efficiencies observed as being the intrinsic property of thebright excitons in CNTs. Even when considering the error
bars of the data points, it is fair to state that their quantum
efficiencies are near unity in free space.
The radiative quantum efficiency is directly related to the
PL yield, which is defined as a fraction of emitted photons
to absorbed photons. The PL yield is not necessarily equal
to the radiative quantum efficiency of the bright excitons, as
most of the absorbed photons end up in dark excitonic states.
There exist 16 exciton states since both the valence and the
conduction bands are four-fold degenerate, out of which only

one state is bright and all the other states are dark due to spin,
momentum, and parity selection rules [33–35]. The initial
population of all 16 states should be equal if free carriers
are generated as in the case of E22 excitation [36] and a PL
yield of 6.25% would result for unity quantum efficiency ofbright excitons if there are no further population redistribution. Experimentally, a similar value of ∼7% was reported for
air-suspended nanotubes at E22 excitation [24]. Conversionof the dark excitons to the bright excitons [32] can further
increase the PL yields.
We note that air-suspended nanotubes exhibit higher PL
yields compared to solution-based nanotubes. There aremainly two reasons for the difference [37]. First, the surfactant molecules can create charge traps that create quenchingsites. Second, solution-based tubes are often shorter than those
directly synthesized on substrates because of the sonication
process and the excitons are more susceptible to quenchingat the tube ends. The additional nonradiative decay processes
result in lower yields.
It should be possible to enhance the PL yield by choosing
excitation methods with higher initial population of bright excitons. Resonant excitation can be used to selectively populate
the bright states, and in principle unity PL yield would beachieved. If the rejection of the excitation laser becomes anexperimental issue, an alternative is to utilize phonon sidebands [38] and E11 excited states [39]. By limiting excitation
into the spin singlet manifold, the PL yield is expected to
improve by a factor of 4. A more sophisticated scheme will
be needed for electrical excitation, such as spin-polarized [40]or energy-selective [41] injection.
Lastly, we would like to comment on the radiative lifetimeof excitons in CNTs [34,35,42]. When the radiative quantum
efficiency is unity, bright exciton decay time is equivalent
to the radiative lifetime. We can therefore consider the reported bright exciton decay times of air-suspended nanotubes
ranging from 60 ps to 90 ps [32] to be their effective radiative lifetime at room temperature. In comparison, theoretical
calculations [34,35] yielded effective radiative lifetimes tobe on the order of 10 ns at room temperature for micellewrapped nanotubes, although the dielectric environment is
considerably different from those in the air-suspended structures. The experimentally observed bright exciton decay times
also show a clear family pattern [32], which has not beenaddressed theoretically. Updated calculations are needed foran accurate description of radiative lifetimes in air-suspended
nanotubes.
In conclusion, we quantitatively estimated the radiative
quantum efficiency of bright excitons in air-suspended CNTs.
The fraction of the radiative recombination is extracted
by utilizing quantum electrodynamical effects in air-mode
nanobeam cavities. Combining the Purcell factor characterized from the PL spectra and the acceleration factor obtained
from the time-resolved measurements, we find that the radiative quantum efficiency of bright excitons is near unity atroom temperature. Our results reveal the intrinsic property ofbright excitons in CNTs and demonstrate their true potential
for nanoscale photonics. With high-efficiency light emission
and single-photon generation capabilities, CNTs may bringbreakthroughs in subwavelength silicon photonics and integrated quantum optics.

L022011-5

MACHIYA, YAMASHITA, ISHII, AND KATO

PHYSICAL REVIEW RESEARCH 4, L022011 (2022)

This work is supported by MIC (SCOPE 191503001),
JSPS (KAKENHI JP20H02558, JP20J00817, JP20K15199,
JP19J10319), MEXT (Nanotechnology Platform JPMXP09F19UT0072), and RIKEN (Incentive Research
Project). H.M. and D.Y. are supported by JSPS (Research
Fellowship for Young Scientists). H.M. acknowledges

support from RIKEN (Junior Research Associate Program).
We thank H. Kumazaki and T. Tanabe for the transmission
measurements. FDTD calculations are performed using
the HOKUSAI BigWaterfall supercomputer at RIKEN. We
acknowledge the Advanced Manufacturing Support Team at
RIKEN for technical assistance.

[1] E. F. Schubert and J. K. Kim, Solid-state light sources getting
smart, Science 308, 1274 (2005).
[2] P. W. Milonni and J. H. Eberly, Laser Physics (John Wiley &Sons, New York, 2010), pp. 735–792.
[3] W. M. Steen and J. Mazumder, Laser Material Processing(Springer, London, 2010).
[4] H.-W. Chen, J.-H. Lee, B.-Y. Lin, S. Chen, and S.-T. Wu, Liquid
crystal display and organic light-emitting diode display: Present
status and future perspectives, Light Sci. Appl. 7, 17168 (2018).
[5] C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest,
Nearly 100% internal phosphorescence efficiency in an organic
light-emitting device, J. Appl. Phys. 90, 5048 (2001).
[6] S. Lamansky, P. Djurovich, D. Murphy, F. Abdel-Razzaq,
H.-E. Lee, C. Adachi, P. E. Burrows, S. R. Forrest, and M. E.
Thompson, Highly phosphorescent bis-cyclometalated iridium
complexes: Synthesis, photophysical characterization, and use
in organic light emitting diodes, J. Am. Chem. Soc. 123, 4304
(2001).
[7] N. M. Gabor, Z. Zhong, K. Bosnick, J. Park, and P. L. McEuen,
Extremely efficient multiple electron-hole pair generation incarbon nanotube photodiodes, Science 325, 1367 (2009).
[8] D. R. McCulley, M. J. Senger, A. Bertoni, V. Perebeinos, andE. D. Minot, Extremely efficient photocurrent generation incarbon nanotube photodiodes enabled by a strong axial electricfield, Nano Lett. 20, 433 (2020).
[9] N. Higashide, M. Yoshida, T. Uda, A. Ishii, and Y. K. Kato, Cold
exciton electroluminescence from air-suspended carbon nanotube split-gate devices, Appl. Phys. Lett. 110, 191101 (2017).
[10] A. Graf, M. Held, Y. Zakharko, L. Tropf, M. C. Gather, and J.
Zaumseil, Electrical pumping and tuning of exciton-polaritonsin carbon nanotube microcavities, Nat. Mater. 16, 911 (2017).
[11] X. Ma, N. F. Hartmann, J. K. S. Baldwin, S. K. Doorn, andH. Htoon, Room-temperature single-photon generation fromsolitary dopants of carbon nanotubes, Nat. Nanotechnol. 10,671 (2015).
[12] A. Ishii, T. Uda, and Y. K. Kato, Room-temperature singlephoton emission from micrometer-long air-suspended carbon
nanotubes, Phys. Rev. Appl. 8, 054039 (2017).
[13] X. He, H. Htoon, S. K. Doorn, W. H. P. Pernice, F. Pyatkov,
R. Krupke, A. Jeantet, Y. Chassagneux, and C. Voisin, Carbon
nanotubes as emerging quantum-light sources, Nat. Mater. 17,663 (2018).
[14] R. Miura, S. Imamura, R. Ohta, A. Ishii, X. Liu, T. Shimada, S.
Iwamoto, Y. Arakawa, and Y. K. Kato, Ultralow mode-volume
photonic crystal nanobeam cavities for high-efficiency coupling
to individual carbon nanotube emitters, Nat. Commun. 5, 5580
(2014).
[15] F. Pyatkov, V. Fütterling, S. Khasminskaya, B. S. Flavel, F.
Hennrich, M. M. Kappes, R. Krupke, and W. H. P. Pernice,Cavity-enhanced light emission from electrically driven carbon
nanotubes, Nat. Photonics 10, 420 (2016).
[16] A. Ishii, X. He, N. F. Hartmann, H. Machiya, H. Htoon, S. K.
Doorn, and Y. K. Kato, Enhanced single photon emission fromcarbon nanotube dopant states coupled to silicon microcavities,
Nano Lett. 18, 3873 (2018).
[17] H. Machiya, T. Uda, A. Ishii, and Y. K. Kato, Spectral tuningof optical coupling between air-mode nanobeam cavities andindividual carbon nanotubes, Appl. Phys. Lett. 112, 021101(2018).
[18] A. Noury, X. L. Roux, L. Vivien, and N. Izard, Enhanced lightemission from carbon nanotubes integrated in silicon microresonator, Nanotechnology 26, 345201 (2015).
[19] N. Higuchi, H. Niiyama, K. Nakagawa, and H. Maki, Efficient and narrow-linewidth photoluminescence devices basedon single-walled carbon nanotubes and silicon photonics, ACS
Appl. Nano Mater. 3, 7678 (2020).
[20] S. Khasminskaya, F. Pyatkov, K. Słowik, S. Ferrari, O. Kahl,
V. Kovalyuk, P. Rath, A. Vetter, F. Hennrich, M. M. Kappes,
G. Gol’tsman, A. Korneev, C. Rockstuhl, R. Krupke, and W. H.
Pernice, Fully integrated quantum photonic circuit with an electrically driven light source, Nat. Photonics 10, 727 (2016).
[21] E. M. Purcell, Spontaneous emission probabilities at radio frequencies, Phys. Rev. 69, 681 (1946).
[22] A. Jeantet, Y. Chassagneux, C. Raynaud, P. Roussignol, J. S.
Lauret, B. Besga, J. Estève, J. Reichel, and C. Voisin, Widely
Tunable Single-Photon Source from a Carbon Nanotube in the
Purcell Regime, Phys. Rev. Lett. 116, 247402 (2016).
[23] Y. Luo, E. D. Ahmadi, K. Shayan, Y. Ma, K. S. Mistry,
C. Zhang, J. Hone, J. L. Blackburn, and S. Strauf, Purcellenhanced quantum yield from carbon nanotube excitons
coupled to plasmonic nanocavities, Nat. Commun. 8, 1413
(2017).
[24] J. Lefebvre, D. G. Austing, J. Bond, and P. Finnie, Photoluminescence Imaging of Suspended Single-Walled Carbon
Nanotubes, Nano Lett. 6, 1603 (2006).
[25] A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel,
J. Joannopoulos, and S. G. Johnson, Meep: A flexible
free-software package for electromagnetic simulations by the
FDTD method, Comput. Phys. Commun. 181, 687 (2010).
[26] See Supplemental Material at http://link.aps.org/supplemental/
10.1103/PhysRevResearch.4.L022011 for a schematic showing
the parameters of nanobeam cavities, PL line scans along the
nanobeam cavities, the characterization of the cavity quality
factor, a discussion of the collection efficiencies, a summary
table of the Purcell and acceleration factors, and the length
dependence of the radiative quantum efficiency.
[27] I. Sarpkaya, Z. Zhang, W. Walden-Newman, X. Wang, J.
Hone, C. W. Wong, and S. Strauf, Prolonged spontaneous

L022011-6

EVIDENCE FOR NEAR-UNITY RADIATIVE QUANTUM …

PHYSICAL REVIEW RESEARCH 4, L022011 (2022)

emission and dephasing of localized excitons in air-bridged
carbon nanotubes, Nat. Commun. 4, 2152 (2013).
[28] A. Ishii, M. Yoshida, and Y. K. Kato, Exciton diffusion, end
quenching, and exciton-exciton annihilation in individual airsuspended carbon nanotubes, Phys. Rev. B 91, 125427 (2015).
[29] P. H. Tan, A. G. Rozhin, T. Hasan, P. Hu, V. Scardaci, W. I.
Milne, and A. C. Ferrari, Photoluminescence Spectroscopy ofCarbon Nanotube Bundles: Evidence for Exciton Energy Transfer, Phys. Rev. Lett. 99, 137402 (2007).
[30] K. Matsuda, Y. Kanemitsu, K. Irie, T. Saiki, T. Someya, S.
Miyauchi, and S. Maruyama, Photoluminescence intermittency
in an individual single-walled carbon nanotube at room temperature, Appl. Phys. Lett. 86, 123116 (2005).
[31] Q. Quan and M. Loncar, Deterministic design of wavelengthscale, ultra-high Q photonic crystal nanobeam cavities, Opt.
Express 19, 18529 (2011).
[32] A. Ishii, H. Machiya, and Y. K. Kato, High Efficiency Dark-ToBright Exciton Conversion in Carbon Nanotubes, Phys. Rev. X
9, 041048 (2019).
[33] Y. Miyauchi, Photoluminescence studies on exciton photophysics in carbon nanotubes, J. Mater. Chem. C 1, 6499 (2013).
[34] V. Perebeinos, J. Tersoff, and P. Avouris, Radiative Lifetime of
Excitons in Carbon Nanotubes, Nano Lett. 5, 2495 (2005).
[35] C. D. Spataru, S. Ismail-Beigi, R. B. Capaz, and S. G. Louie,
Theory and ab initio Calculation of Radiative Lifetime of

Excitons in Semiconducting Carbon Nanotubes, Phys. Rev.
Lett. 95, 247402 (2005).
[36] Y. Kumamoto, M. Yoshida, A. Ishii, A. Yokoyama, T. Shimada,and Y. K. Kato, Spontaneous Exciton Dissociation in Carbon
Nanotubes, Phys. Rev. Lett. 112, 117401 (2014).
[37] T. Hertel, S. Himmelein, T. Ackermann, D. Stich, and
J. Crochet, Diffusion Limited Photoluminescence Quantum
Yields in 1-D Semiconductors: Single-Wall Carbon Nanotubes,
ACS Nano 4, 7161 (2010).
[38] O. N. Torrens, M. Zheng, and J. M. Kikkawa, Energy of KMomentum Dark Excitons in Carbon Nanotubes by Optical
Spectroscopy, Phys. Rev. Lett. 101, 157401 (2008).
[39] J. Lefebvre and P. Finnie, Excited Excitonic States in SingleWalled Carbon Nanotubes, Nano Lett. 8, 1890 (2008).
[40] J. Wang, A. Chepelianskii, F. Gao, and N. C. Greenham, Control
of exciton spin statistics through spin polarization in organic
optoelectronic devices, Nat. Commun. 3, 1191 (2012).
[41] K. Kimura, K. Miwa, H. Imada, M. Imai-Imada, S. Kawahara,
J. Takeya, M. Kawai, M. Galperin, and Y. Kim, Selective triplet
exciton formation in a single molecule, Nature (London) 570,
210 (2019).
[42] Y. Miyauchi, H. Hirori, K. Matsuda, and Y. Kanemitsu, Radiative lifetimes and coherence lengths of one-dimensional
excitons in single-walled carbon nanotubes, Phys. Rev. B 80,
081410(R) (2009).

L022011-7