Efficient quantum dot single photon extraction into an optical fiber using a nanophotonic directional coupler
M. Davanco, M.T. Rakher, W. Wegscheider, D. Schuh, A. Badolato, K. Srinivasan
aa r X i v : . [ phy s i c s . op ti c s ] S e p Efficient quantum dot single photon extraction into an optical fiber using ananophotonic directional coupler
M. Davan¸co,
1, 2, ∗ M. T. Rakher, W. Wegscheider, D. Schuh, A. Badolato, and K. Srinivasan Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA Institute for Experimental and Applied Physics,University of Regensburg, D-93053 Regensburg, Germany Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
We demonstrate a spectrally broadband and efficient technique for collecting emission from a singleInAs quantum dot directly into a standard single mode optical fiber. In this approach, an opticalfiber taper waveguide is placed in contact with a suspended GaAs nanophotonic waveguide withembedded quantum dots, forming a broadband directional coupler with standard optical fiber inputand output. Efficient photoluminescence collection over a wavelength range of tens of nanometersis demonstrated, and a maximum collection efficiency of 6 % (corresponding single photon rate of3.0 MHz) into a single mode optical fiber is estimated for a single quantum dot exciton.
Single epitaxially grown quantum dots (QDs) can serveas bright, stable sources of single photons for applicationsin quantum information processing [1]. A key limitationof QDs embedded in high refractive index semiconduc-tors is the relatively small fraction of the total QD emis-sion ( ≈ Q ),small mode volume resonator such as a micropillar cav-ity [4, 5] is one approach to improving photon extrac-tion, where ideally one benefits from both a faster radia-tive rate (Purcell enhancement) and a far-field emissionpattern that can be efficiently collected. High extrac-tion efficiencies have indeed been demonstrated with thisapproach [6]. One challenging aspect of using a high- Q microcavity is the necessity for spectral overlap be-tween a narrow cavity mode and the QD emission line,though tunable geometries [7] can overcome this chal-lenge. Alternatively, spectrally broadband approaches(usually without Purcell enhancement) avoid precise tun-ing and are needed for efficient spectroscopy of multiplespectrally distinct QD transitions and/or emission frommultiple QDs, and have recently been pursued using solidimmersion lenses [8, 9] and in vertically oriented taperednanowire geometries [10]. Here, we demonstrate a guidedwave nanophotonic structure for efficient extraction ofPL from a single InAs QD directly into an optical fiber,with an operation bandwidth of tens of nm, and an over-all single mode fiber collection efficiency of ≈ ∗ Electronic address: [email protected]
FIG. 1: (a) Nanophotonic directional coupler for single pho-ton extraction from a single embedded QD. (b) SEM image ofa fabricated GaAs channel WG. (c) Optical microscope imageof the FTW/channel WG directional coupler. form for waveguide-based photonic circuits involving sin-gle QDs and efficient coupling to optical fibers.Our structure is a hybrid directional coupler formedby a suspended GaAs channel waveguide (WG) contain-ing InAs QDs and a micron diameter optical fiber taperwaveguide (FTW) (Fig. 1(a)). The FTW is an opticalfiber whose diameter is adiabatically reduced to a wave-length scale minimum, providing access to an evanescentfield for guided wave coupling while maintaining singlemode fiber ends and low loss. The GaAs WG (Fig. 1(b))has a cross-sectional diameter of ≈
100 nm, enablingphase matching to the FTW and efficient power trans-fer between the two WGs [11]. This structure supports T r a n s m i ss i o n P h o t o n s ( x H z ) T r a n s m i ss i o n P h o t o n s ( x H z ) T r a n s m i ss i o n P h o t o n s ( x H z )
024 024 wavelength ( µ m) wavelength (nm) wavelength (nm) (d) (e) (f) W ch = 193 ± 11 nm W ch = 211 ± 10 nm W ch = 252 ± 11 nm T r a n s m i ss i o n TM-like TE-like (b)
340 ± 3.3 nm287 ± 4.7 nm266 ± 4.6 nm240 ± 4.4 nm
220 240 260 280 300 320 340 3601.11.21.31.41.51.61.7
Waveguide Width (nm) w a v e l e n g t h ( µ m ) TM-like phase-matching (c)
TE-like phase-matching wavelength ( µ m) wavelength ( µ m) −1 0 1−1012 x ( µ m) y ( µ m ) −1 0 1 −1012 0.20.40.60.8 x ( µ m) y ( µ m ) TE-like, I TE-like, II −1 0 1−1012 x ( µ m) y ( µ m ) −1 0 1−1012 x ( µ m) y ( µ m ) TM-like, I TM-like, II (a) |E| |E| |E| |E| FIG. 2: (a) Electric field amplitudesquared for the TE-like (top) andTM-like (bottom) supermode pairs ofthe directional coupler. (b) TE-likeand TM-like transmission spectra forsuspended channel WGs of varyingwidths, probed with a ≈ µ m FTWat room temperature. (c) Evolu-tion of transmission minima withWG widths for the two polarizationsin (a). Dashed lines are calculatedphase-matching wavelengths for thefiber and WG. (d)-(f): Low temper-ature ( ≈ W ch . single guided modes with strong transverse confinement,into which QD radiation is almost completely coupled.Efficient QD coupling to WG modes phase-matched tothe single FTW mode thus leads to efficient extractionof QD emission into the fiber. Detailed simulations havepredicted a single QD fluorescence collection efficiency ashigh as ≈
35 % into an optical fiber ( ≈
70 % includingboth fiber ends), with an operation bandwidth of tens ofnm [11].We first assessed the directional coupler without QDs,to confirm the basic light transfer mechanism betweenFTW and channel WG. A first set of suspended WGswith no QDs was fabricated on a 250 nm thick GaAswafer for passive directional coupler characterization [12].An ≈ µ m diameter FTW was brought into contact withindividual channel WGs, forming directional couplers asillustrated in Fig. 1(c). Transmission spectra were ob-tained by launching broadband polarized light from atungsten halogen lamp into the FTW input and ana-lyzing output light with an optical spectrum analyzer.The FTW and channel WG each support a single guidedmode of TE-like (x-oriented electric field) and TM-like(y-oriented electric field) polarizations. The resulting di-rectional coupler supports a pair of hybrid supermodesfor each polarization (Fig. 2(a)) [11]. The transmis-sion spectrum for a given polarization is determined bythe beating of the corresponding coupler supermodes,and exhibits minima when power is transferred from theFTW to the channel WG but not back into the FTWdue to termination of the channel [12].Several 8 µ m long WGs with widths between 240 nmand 340 nm were measured. The transmission spectra(Fig. 2(b)) for the two main coupler polarizations dis-played broad, >
40 nm wide minima which typicallyreached >
90 % extinction, evidencing efficient powertransfer between the FTW and suspended WGs. Af-ter optical characterization, WG widths were measured with a scanning electron microscope. Figure 2(c) showsminimum transmission wavelengths as a function of WGwidth, along with the phase-matching wavelengths calcu-lated with a vector finite element method [11]. The min-ima closely follow the calculated phase-matching wave-lengths. The higher rate with which the TE-like phase-matching wavelength shifts with WG width is expectedfrom these modes’ higher intensity at the WG side-walls. The agreement between theoretical and experi-mental curves indicates that the expected efficient direc-tional coupler operation is indeed achieved.We next attempted to validate efficient PL extractionfrom a second set of devices fabricated on a high QDdensity portion of the same wafer, where the QD en-semble s-shell emission peak was at ≈ ≈ µ m diam-eter FTW in a cryostat at < η = 6 .
05 % ± .
061 % [12]. We point out thatthe transmission of the collection portion of the FTWis ≈
84 %, so collection into the FTW (our first col-lection optic) is 7 .
250 % ± .
072 %. The most likelyreason for smaller collection efficiencies than predicted isnon-optimal positioning of the QD in the GaAs WG, assupported by simulations presented in the supplementarymaterial [12].The 957.7 nm transition was located outside the op-erating wavelength band of the tunable bandpass filteravailable for spectral isolation, preventing further char-acterization of this device. A second WG was avail-able, however, that displayed an isolated transition at ≈
963 nm, shown in Fig. 3(b), located within the couplertransmission dip (inset). The evolution of the 963 nmpeak collected PL rate into the single mode fiber asa function of pump power is shown in Fig. 3(c). For P in <
100 nW, integrated PL counts increase linearlywith pump power. A fit to the data assuming an idealsingle exciton QD line (Fig. 3(c)) [12] matches the datafor P in <
100 nW, but overestimates the PL rate for P in >
100 nW. For the highest measured PL inten-sity, the integrated counts correspond to η ≈ P in ≪ P sat ≈
133 nW, where the QD can be assumed tobehave ideally, however, η ≈ g (2) ( τ ), for pulsed excitation at P in ≈
75 nW (Fig. 3(e)). g (2) (0) = 0 . ± .
02 [12], indicating sin-gle QD emission that is dominantly comprised of singlephotons. The nonzero g (2) (0) is likely due to insufficientfiltering, which allows uncorrelated photons and possibleemission from other QDs to be detected. In particular,the spectrum of the detected light (inset in Fig. 3(f))contains two broad sidelobes in addition to the 963 nmexcitonic line. These may correspond to emission fromother QDs with broadened lines, owing to proximity toWG sidewalls [13]. A bi-exponential decay of the ex-citonic line (Fig. 3(f)) with fast and slow lifetimes of1 .
48 ns ± .
08 ns and 4 . ± . g (2) ( τ )(Fig. 3(e)), where the coincidence counts between peaksdo not return all the way to zero. The fast decay con-stant approaches the lifetime of a typical InAs QD (thelack of radiative rate enhancement is predicted in simula-tions [11]), while the long decay evidences QD coupling tononradiative states that may lead to a reduced quantumefficiency and collection efficiency estimates.In summary, we have demonstrated a fiber-coupled,QD single photon source based on a planar, guided wavenanophotonic coupler. We use this spectrally broadbandapproach to demonstrate an in-fiber, single QD PL collec-tion efficiency of 6 %. Future work is aimed at improvedefficiency through precise QD location [14, 15] within thedevice and understanding sources of non-ideal QD behav-ior. Acknowledgments
This work was partly supported by the NIST-CNST/UMD-NanoCenter Cooperative Agreement. Wethank R. Hoyt, C. S. Hellberg, Alexandre M.P.A. Silva,and Hugo Hern´andez-Figueroa for useful discussions. [1] A. J. Shields, Nature Photonics , 215 (2007), 0704.0403.[2] H. Benisty, H. D. Neve, and C. Weisbuch, IEEE J. Quan.Elec. , 1612 (1998).[3] W. L. Barnes, G. Bj¨ork, J. G´erard, P. Jonsson, J. A. E.Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D , 197 (2002).[4] G. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev.Lett. , 3903 (2001).[5] M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S.Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. , 233602 (2002).[6] S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren,P. M. Petroff, and D. Bouwmeester, Nature Photonics ,704 (2007).[7] A. Muller, E. B. Flagg, M. Metcalfe, J. Lawall, and G. S.Solomon, Appl. Phys. Lett. , 173101 (2009).[8] V. Zwiller and G. Bjork, J. Appl. Phys. , 660 (2002).[9] A. N. Vamivakas, M. Atat¨ure, J. Dreiser, S. T. Yilmaz,A. Badolato, A. K. Swan, B. B. Goldberg, A. Imamoˇglu, and M. S. ¨Unl¨u, Nano Letters , 2892 (2007).[10] J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffren-nou, N. Gregersen, C. Sauvan, P. Lalanne, and J. G´erard,Nature Photonics , 174 (2010).[11] M. Davan¸co and K. Srinivasan, Opt. Lett. , 2542(2009).[12] See Supporting Information for additional experimental,simulation, and nanofabrication details.[13] C. F. Wang, A. Badolato, I. Wilson-Rae, P. M. Petroff,E. Hu, J. Urayama, and A. Imamoglu, Appl. Phys. Lett. , 3423 (2004).[14] K. Hennessy, A. Badolato, M. Winger, D. Gerace,M. Atature, S. Guide, S. Falt, E. Hu, and A. Imamoglu,Nature (London) , 896 (2007).[15] S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M.Irvine, P. M. Petroff, and D. Bouwmeester, Appl. Phys.Lett. , 111115 (2009). (a) ph o t o n s / s input power (nW) η = c o ll . e ff . ( % ) (c)(d) −100 −50 0 50 10000.51.0 g ( ) ( τ ) -2 -1 t (ns) c o un t s / s (f)
960 962 964 96600.20.40.60.81.0 wavelength (nm)
950 1050 1150110100 wavelength (nm) t r an s m i ss i on ( % )
950 955 960 96500.20.40.60.81.01.2 wavelength (nm) ph o t o n s / s x 10 (e) (b) ph o t o n s / s
955 960 965 970 975 9800123456789 x 10 wavelength (nm) ph o t o n s / s
10 10 input power (nW) ph o t o n s / s FIG. 3: (a)Fiber-collected single QDPL for the brightest device. Inset:photon rate for 957.7 nm line againstpump power. (b) Fiber-collected sin-gle QD PL for second WG. Inset: di-rectional coupler transmission spec-trum, showing position of QD line.(c) Collected PL rate versus excita-tion power for 963 nm line in (b). Er-ror bars are 95 % fit confidence inter-vals. Dashed line: linear fit to databelow saturation. Continuous line:fit to theory. (d) Fiber collectionefficiency obtained from (c), assum-ing ideal QD behavior. (e) Second-order correlation g (2) ( τ ) and (f) life-time for the excitonic line in (b), af-ter a 1 nm bandpass filter (inset spec-trum). Green line: bi-exponential fit. SUPPORTING INFORMATION
Finite difference time domain simulations
Finite difference time domain simulations were used to study the relationship between coupler transmission and PLspectra. The simulated structure consisted of a 1 µ m diameter FTW of infinite extent and a 190 nm thick, 160 nmwide, 4 µ m long GaAs channel waveguide. The computational domain was terminated with perfectly matched layersto simulate open boundaries. Transmission spectrum
To determine the simulated transmission spectrum, a fundamental mode was launched into the FTW, at a 3 µ mdistance from the channel waveguide, and steady-state fields after the channel waveguide termination (for transmission)and before the mode launch position (for reflection), were recorded at various wavelengths. These fields were thenconvolved with the FTW mode and normalized to the injected power, to yield transmission and reflection spectra.Fig. 1(a) shows transmission and reflection spectra for the structure with the above dimensions, and (b)-(d) showelectric field profiles, recorded at the x = 0 plane, for FTW mode excitation at z = − µ m at three differentwavelengths. A broad transmission dip, and corresponding reflection peak, are observed in Fig. 1(a) at λ = 1072 nm,where FTW and channel waveguide are phase-matched. In the corresponding field profile, Fig. 1(c), it is evidentthat efficient power transfer occurs from the FTW into the waveguide, along the 4 µ m extent of the latter. Due towaveguide termination at z = 2 µ m, however, transfer back into the optical fiber is interrupted. Power guided inthe channel is, instead, strongly scattered at the waveguide facet, and, as evidenced by the standing-wave pattern at z <
0, partially reflected back into the fiber. At wavelengths away from the phase-matching condition, Fig. 1 (b) and(d), power launched into the fiber is transferred, without significant losses, past the GaAs guide, and transmissiontends to 100 %, reflection to 0. Comparing the calculated transmission spectrum of Fig. 1 to the measured curves inFig. 2 in the main text, we see that the measured data matches prediction well in terms of their general shape and inparticular, their depth and bandwidth. −2 0 2 4−2−1012 y ( µ m ) z ( µ m) −2 0 2 4−2−1012 y ( µ m ) z ( µ m) −2 0 2 4−2−1012 y ( µ m ) z ( µ m) t r a n s m i ss i o n r e fl e c " o n (a)(b) (c) (d) λ = 966 nm λ = 1072 nm λ = 1260 nm900 950 1000 1050 1100 1150 1200 1250 1300 FTW GaAs WG FTW GaAs WG FTW GaAs WG
FIG. 1: (a) Transmission (blue filled circles) and reflection (green open circles) spectra for simulated directional coupler formedby 1 µ m diameter FTW and a 190 nm thick, 160 nm wide, 4 µ m long suspended GaAs WG. (b)-(d) Steady-state, amplitudesquared electric field at the x = 0 plane for fiber mode excitation at z = − µ m at three different wavelengths. The couplerextends along the ˆ z direction, and the 4 µ m long suspended GaAs WG is centered at z = 0. PL spectrum
To determine simulated PL spectra, the structure was excited with a broadband electric dipole source, and thesteady-state electromagnetic field at z = 2 µ m was recorded for various wavelengths. These fields were convolvedwith the isolated FTW mode field as in ref. 1 to yield the fiber-coupled power. The total radiated power was alsorecorded, and was used to obtain the total collection efficiency. Figure 2 shows collection efficiency for dipoles locatedat varying positions z along the coupler length, with z = 0 at the center. Maximized collection collection is observedat wavelengths near 1050 nm, corresponding to the transmission dip in Fig. 1, for z = −
500 nm. While efficientpower transfer from the WG to the fiber occurs due to phase-matching, the coupler length must be long enough forsufficient transfer to occur, as evidenced by the considerably lower collection efficiencies obtained for the additionaldipole positions simulated. For example, at z = 1500 nm, the efficiency dips considerably below 10 % within thecoupler operation band at λ ≈ x -axis asdefined in Fig. 1(a) in the main text. There, it was shown that if the dipole alignment was aligned along the ˆ z -axis,the predicted PL extraction dropped by about a factor of 7. Thus, along with the QD’s position, its dipole orientationmay also reduce the measured collection efficiencies relative to the maximum possible values.
950 1000 1050 1100 1150 1200 wavelength (nm) F i b e r P o w e r / P s o u r c e z = -500 nm z = -1500 nm z = 500 nm z = 1500 nm FIG. 2: Predicted single QD photoluminescence collection efficiency into the optical fiber mode for the coupler from Fig. 1. Thecurves were obtained by simulating a horizontally oriented electric dipole at the center of the channel waveguide cross-section( x = 0, y = 0), and at various positions z along the longitudinal direction, ˆ z ( z = 0 is at the center of the coupler, as in Fig. 1). Experimental DetailsFabrication
Wafers were grown by molecular beam epitaxy, with an epistructure consisting of a GaAs waveguide layer on top ofa 1 µ m thick, Al x Ga − x As ( x > .
7) sacrificial layer. Suspended GaAs WGs (Fig. 1(b) in the main text) containingself-assembled InAs QDs were fabricated using standard, submicron III-V processing techniques. Two different waferswere used, with waveguide layer thicknesses of 250 nm and 190 nm, and in the center of the waveguide a single layerof InAs QDs with a variable density gradient (from > µ m − to 0 µ m − , along the (01¯1) wafer direction) wasgrown, allowing for the creation of devices with varying QD densities.Device fabrication was as follows. Electron-beam lithography with ZEP520-A resist was used to define waveguidepatterns on top of a 200 nm SiN x layer deposited on the epiwafer via plasma-enhanced chemical vapor deposition(PECVD). The patterns were transferred to the SiN x through reactive ion etching (RIE) with a CHF /Ar mixture.Following resist removal, the waveguide patterns were transferred to GaAs through inductively coupled plasma (ICP)etching, with a Cl /Ar mixture. Finally, the sacrificial layer and remaining SiN mask were removed with a >
10 s, 49% HF dip. In many devices, the SiN x mask layer was omitted and direct transfer from the electron-beam mask to theGaAs was performed using the same ICP etch. No significant change in device quality or performance was observedin going from a straight electron-beam mask to a SiN x mask.For device interrogation within the cryostat, it was often most convenient to isolate the waveguide devices to amesa that was ≈ µ m above the rest of the sample’s surface. This was done through contact photolithography anda H O :H PO :CH OH (10:1:1 by volume) solution at 50 ◦ C for 30 min.The material containing dots with s-shell emission near 940 nm was annealed in a rapid thermal annealer at ≈ ◦ Cfor 30 s prior to fabrication. This was done to blue-shift the QD s-shell emission, which originally occurred at ≈ O and removing the formed oxide layer with a 1 molar solution of citric acid (C H O ). Transmission spectrum measurement
As illustrated in Fig. 1 in the main text, a FTW of ≈ µ m diameter was brought into contact with individualwaveguides, forming directional coupler structures that are interrogated using the experimental setup depicted inFig. 3. Light from a quartz-tungsten-halogen lamp was coupled into a single-mode optical fiber and passed throughan in-line polarizer and polarization controller, and then launched into the FTW input. An optical spectrum analyzer(OSA) was used to obtain transmission spectra, from 1100 nm to 1600 nm, for the formed directional couplers. Toobtain spectra for the two main polarizations, the polarization controller was used to minimize transmission at somewavelength range after the WGs were first put in contact. This range was assumed to be that for which power transferfrom the suspended WG to the fiber was maximized, for one of the two main polarizations. A spectrum was recorded,the fiber lifted and a background spectrum was then taken. The fiber was next brought back in contact with theGaAs guide, and a second spectrum was taken to verify that the transmission minima, and thus the polarization,was unchanged. The polarization controller was next used to maximize the transmission at the minimum wavelengthrange, and a second transmission spectrum was taken, assumed to be for the second main polarization. Finally, thefiber was lifted and a second background spectrum was recorded. LHe
LHe cryostat
780 nm pulsed laser diode
TRIG
TBPF
50 : 50splitter
SPAD
TCSPC: g (2) ( τ ) SPAD FPC VOA
780 nm CW Laser Diode
SMF SMF
830 nm CW Laser Diode
Tungsten lamp polarizer zoom barrel white lightsource S i CC D c a m e r a Si CCDcamera
TCSPC: PL(t) LPF
Spectrometer
CCD
LPF
FPC
OSA
SPAD
FIG. 3: Experimental setup for cryogenic transmission and photoluminescence measurements. VOA: variable optical attenuator;SMF: single mode optical fiber OSA: optical spectrum analyzer; LPF: long wavelength pass filter; TBPF: tunable bandpassfilter; FPC: fiber polarization controller; SPAD: single photon avalanche detector; TCSPC: time correlated single photoncounter; CCD: charge-coupled device; LHe: liquid helium; TRIG: trigger.
The minimum transmission wavelengths plotted on Fig. 2(b) in the main text correspond to measured globaltransmission minima. Detection noise leads to uncertainties in the determination of an actual minimum transmissionwavelength. This is represented by error bars in the figure, which correspond to intervals over which the transmittedpower fluctuates below 1.05 times the minimum transmission.To determine the waveguide widths, top view scanning electron microscope images of the devices were taken, and anedge detection technique was employed to determine sidewall profiles along the waveguide length. For each waveguide,averages and standard deviations were obtained for the locations of the two waveguide sidewalls, which were thenused to calculate waveguide widths and corresponding deviations due to sidewall roughness. The standard deviationsare plotted as error bars in the graph of minimum transmission wavelength versus waveguide width on Fig. 2(b) inthe main text.
Determination of collection efficiency
Collected photon rates were determined from PL spectra, after calibration of Si CCD count rates against the knownoptical power of a (fiber-coupled) continuous wave laser source, tuned to the QD emission wavelength. Integratedcounts in the spectrum of a 100 fW laser signal led to a conversion factor of 130 photons/CCD count. We pointout that this conversion factor, which includes the spectrometer in-coupling efficiency, grating efficiency, and CCDdetection efficiency and gain, falls within the expected range, considering manufacturer-provided specifications. TheSi CCD quantum efficiency is <
10 % at 960 nm, the CCD gain was set to 3 photoelectrons/CCD count, and thegrating efficiency is around 50 %.When measuring PL, a long-wavelength pass filter at 850 nm was introduced before the spectrometer slit, witha nominal transmission of 80 %. With this, the collected photon rate into the single mode fiber was calculated as R ph. = R det. · / .
8. To determine the emitted photon rate, the QDs were pumped into saturation and assumed tohave 100 % radiative efficiency. Under these conditions, the emission rate is that of the pump source, 50 MHz. Thecollection efficiency into the single mode fiber, η , is then given as η = R ph. / × .Considering an ideal single exciton QD line, the collected photon rate R ph is given by the product of the collectionefficiency η , the pulse repetition rate R rep. = 50 MHz and the average exciton occupancy per pulse: R ph = η · R rep / (1 + P in /P sat ), where P in is the average pump power and P sat is the pump saturation power. This model fitsthe data of Fig. 3(c) reasonably well for P in <
100 nW, with P sat = 133 . ± . P in >
100 nW, however, it overestimates the output PL rate, and for P in >
580 nW, a marked decline in PLintensity is observed, suggesting that the emission rate starts to decrease before QD saturation is achieved. g (2) ( τ ) measurements A fiber-based Hanbury-Brown and Twiss configuration was used to obtain the second-order correlation curve shownin Fig. 3(e) in the main text. The excitation was pulsed and below saturation ( P in ≈
75 nW). The setup consistedof two Si single photon avalanche detectors (SPADs) connected to the output ports of a 3dB optical fiber splitter,and a time-correlated single photon counting instrument, which performed histogramming of the photon arrival timedifferences. The SPAD detection efficiency was determined to be 26 % ± ± ± ± g (2) (0) value quoted in the text, we integrated the peaks in Fig. 3(e) in the main text over increasingintervals up to half the repetition period, and calculated averages. The mean and standard deviation values for thezero time peak (which corresponds to g (2) (0)) were then normalized by an average of all other integrated (averaged)peak values.To estimate the percentage of background emission in the analyzed signal, we derived an expression for g (2) ( τ )for the case of detection of QD emission together with perfectly uncorrelated background light. The second ordercorrelation function for the total detected light is g (2) ( τ ) = h I ( t ) I ( t + τ ) i ¯ I , (1)where I ( t ) = I QD ( t )+ I bg ( t ) is the total detected intensity, I QD and I bg are the quantum dot emission and backgroundintensities respectively, and ¯ I = h I ( t ) i . Assuming h I QD ( t ) I bg ( t + τ ) i = h I bg ( t + τ ) I QD ( t ) i = ¯ I QD ¯ I bg , (2)we get g (2) ( τ ) = (cid:0) ¯ I − ¯ I QD (cid:1) + ¯ I QD · g (2) QD ( τ )¯ I , (3)with g (2) QD ( τ ) = h I QD ( t ) I QD ( t + τ ) i . From this expression, the zero-time second-order correlation for the QD alone is g (2) QD (0) = 1 + (cid:18) RR (cid:19) · [ g (2) (0) − , (4)where g (2) (0) is the measured quantity, and R = I QD /I bg is the ratio of QD light intensity I QD over background lightintensity I bg at the detector (i.e., R is the signal-to-background ratio). Since I QD + I bg = I , we get I bg I total = 11 + R . (5)Assuming perfectly antibunched single QD emission, R was obtained by setting g (2) QD (0) = 0, and the background ratioover the total was computed from 5.Assuming that the detected signal is composed of perfectly antibunched light from the single QD emission peak at963 nm and uncorrelated background photons, we determine that 16 % of the total detected photons would correspondto background emission. In this case, since the area under the sharp excitonic line in the spectrum of the main text’sFig. 3(e) inset is ≈
51 % of the total, the broad features would have to be produced in part by the same QD. A morelikely situation is that the detected signal also includes emission from additional (broadened) QDs.
Photoluminescence excitation spectroscopy
In addition to photoluminescence spectroscopy, our fiber-based technique can be used for photoluminescence ex-citation (PLE) spectroscopy of single quantum dots, even in samples with a high density of emitters. In such a
FPC VOA
10 : 90splitter cryostat QD FTW PD T-980
10 nm BF @ 960 nm spectrometer
Si CCD spectrum acq. trigger10 nm BF @ 990 nm
ComputerControl s c a n t r i gg e r FIG. 4: Photoluminescence excitation spectroscopy setup measurement, the QD is excited quasi-resonantly in the p-shell, by a continuous wave, tunable external cavity diodelaser (ECDL), and the s-shell PL is recorded as the excitation wavelength is scanned. This type of measurement hasbeen used in the past to reveal carrier scattering mechanisms leading to s-shell photon emission [4, 5].We next describe a single QD PLE measurement performed on a high QD density sample, with s-shell emission near1000 nm, as shown in the inset of Fig. 5 (a). In our experimental setup, Fig. 4, the QD was excited with continuouswave light from a 963 nm to 995 nm ECDL via the FTW. The emitted s-shell PL, collected back into the input fiber(i.e., flowing in the direction opposite to that of the excitation light), was diverted towards a grating spectrometerthrough a 10:90 directional fiber coupler. This was done to reduce the intensity of excitation light at the spectrometerentrance, which would otherwise have overwhelmed the PL signal. The laser wavelength was set to be scanned over aportion of the QD ensemble p-shell range, with a rate of 10 pm/s. During the scan, photoluminescence spectra witha 1 s integration time were continuously recorded. Figure 5(a) shows fiber collected s-shell emission for an excitationwavelength λ in = 963 . λ = 990 . λ in varying between 961.5 nm and 965 nm is shown Fig. 5(b), with a spectral resolution better than30 pm. The excitation spectrum displays sharp peaks related to the carrier dynamics leading to s-shell emission [4, 5].To confirm that the selected PL line is indeed produced by single dot, photon correlation measurements are per-formed with a Hanbury-Brown and Twiss setup, for λ in = 963 . g (2) (0) ≈ .
5) shown in Fig. 5(c) confirms that thep-shell excitation through the coupler can indeed select a single QD from within the dense ensemble. The nonzeroantibunching is most likely due to the limited measurement resolution (256 ps) and insufficient bandpass filtering,especially considering the high QD density of the sample. Bunching peaks surrounding the antibunching dip are alsoobserved (Fig. 5(d)), with a decay time of a few hundreds of nanoseconds, and are possibly related to the formationof charged QD states [6]. [1] M. Davan¸co and K. Srinivasan, Opt. Express , 10542 (2009).[2] M. Davan¸co and K. Srinivasan, Opt. Lett. , 2542 (2009).[3] K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, Appl. Phys. Lett. , 021108 (2005).[4] Y. Toda, O. Moriwaki, M. Nishioka, and Y. Arakawa, Phys. Rev. Lett. , 4114 (1999).[5] T. Warming, E. Siebert, A. Schliwa, E. Stock, R. Zimmermann, and D. Bimberg, Phys. Rev. B , 125316 (2009).[6] C. Santori, D. Fattal, J. Vuckovic, , G. S. Solomon, E. Waks, and Y. Yamamoto, Phys. Rev. B , 205324 (2004). FIG. 5: (a) Fiber-collected PL spectrum for CW quasi-resonant excitation at λ = 963 . λ = 990 . λ = 990 ..