Two-photon interference from a bright single photon source at telecom wavelengths

Long-distance quantum communication relies on the ability to efficiently generate and prepare single photons at telecom wavelengths. In many applications these photons must also be indistinguishable such that they exhibit interference on a beamsplitter, which implements effective photon-photon interactions. However, deterministic generation of indistinguishable single photons with high brightness remains a challenging problem. We demonstrate two-photon interference at telecom wavelengths using an InAs/InP quantum dot in a nanophotonic cavity. The cavity enhances the quantum dot emission, resulting in a nearly Gaussian transverse mode profile with high out-coupling efficiency exceeding 36% after multi-photon correction. We also observe Purcell enhanced spontaneous emission rate up to 4. Using this source, we generate linearly polarized, high purity single photons at 1.3 micron wavelength and demonstrate the indistinguishable nature of the emission using a two-photon interference measurement, which exhibits indistinguishable visibilities of 18% without post-selection and 67% with post-selection. Our results provide a promising approach to generate bright, deterministic single photons at telecom wavelength for applications in quantum networking and quantum communication.

Single photon sources are important building blocks for optical quantum information processing [1][2][3][4]. They are essential to generate photonic quantum bits (qubits) that can travel long distances over optical fibers and interconnect distant quantum network nodes [5][6][7]. Efficient on-demand single photon sources also enable quantum computation schemes based on either linear [3,4] or nonlinear [8] optical elements.
Many applications in quantum communication require deterministic single-photon sources that emit at telecom wavelengths. Parametric down-conversion sources can operate in this wavelength range [9,10] but provide only heralded single-photon states and cannot be easily extended to ondemand operation. In contrast, single quantum emitters provide the potential for creating ondemand single-photon sources [11,12]. Quantum dots in III-V semiconductors are particularly promising quantum emitters that generate single photons with high indistinguishability at nearinfrared wavelengths [13][14][15][16][17][18], and are also compatible with electrical injection [19,20] and integration with nanophotonic structures [21][22][23][24]. A number of works have extended the emission of III-V quantum dots to telecom wavelengths by optimizing materials and growth parameters [25][26][27][28][29][30][31]. However, an on-demand source of indistinguishable single photons remains an outstanding challenge at telecom wavelength.
In this work, we demonstrate two-photon interference from a bright single photon source at telecom wavelengths. We use a single InAs/InP quantum dot in a photonic crystal cavity to attain bright and highly polarized single-photon emission at telecom wavelengths. Rather than using the fundamental mode of the cavity, we utilize a higher-order mode that exhibits better directionality and emits a transverse mode that can efficiently couple to fibers. Cavity-coupled single quantum dots exhibit significantly enhanced brightness with their high out-coupling efficiency. We also observe a Purcell enhancement of up to 4 for the spontaneous emission rate. From these cavitycoupled dots, we demonstrate the indistinguishability by performing Hong-Ou-Mandel-type interference measurements [32], which exhibits a clear two-photon interference effect. These results show that InAs/InP quantum dots coupled to photonic crystals can serve as bright indistinguishable single-photon sources for applications in long-distance quantum communication. Figure 1(a) shows a scanning electron microscope image of a typical photonic crystal cavity structure used in this work. The cavity design is based on an L3 defect cavity [33] with a lattice parameter (denoted as a) of 370 nm, a hole radius of 0.27 a, and a slab thickness of 280 nm. To optimize the Q value of the fundamental cavity mode, we shift the three holes adjacent to the cavity outward by 0.26 a, 0.16 a, and 0.16 a, respectively.
To fabricate the device, we began with a wafer consisting of a 280 nm thick InP layer grown on top of a 2 µm-thick AlInAs sacrificial layer using molecular beam epitaxy. The center of the InP layer contained a thin layer of InAs quantum dots with densities of approximately 10 µm -2 . We have previously reported the details of the quantum dot growth procedure and material characterization [34]. We used plasma-enhanced chemical vapor deposition to deposit a 100-nmthick silicon nitride thin film that served as an etching mask. We then patterned the mask using electron beam lithography and fluorine-based reactive ion etching, and transferred the pattern from the etch mask to the InP membrane using chlorine-based reactive ion etching. Finally, we removed the sacrificial layer by selective wet etching to form an air-suspended photonic crystal membrane.
We used a confocal microscope system as shown in Fig. 1(b) to optically characterize the device.
We cooled the sample to 4 K using a low vibration closed cycle cryostat and excited the sample with a 780 nm laser emitting in either continuous wave or pulsed modes. We performed both excitation and collection using confocal microscopy with an objective lens that has a numerical aperture of 0.7. We used a spectrometer with a liquid nitrogen cooled InGaAs array to measure the spectrum of the emission and to select the desired quantum dot line. We also used a halfwaveplate and a polarizing beamsplitter for polarization analysis of the collected emission. To perform time-resolved lifetime and photon correlation measurements, we used a 780 nm pulsed laser excitation source with a pulse width of 50 ps and a repetition rate of 40 MHz. For photon correlation measurements, we detected the photons using two fiber-coupled InGaAs single photon avalanche diodes.
We performed indistinguishability measurements of emitted photons using a Hong-Ou-Mandeltype two-photon interferometer. The interferometer was composed of two unbalanced fiber Mach-Zehnder interferometers. We coupled the pump laser to the first interferometer, composed of two fibers with a one meter path length difference to generate double pulses separated by 5 ns that excite the quantum dot. We then coupled the collected emission to the second interferometer which had the same path length difference to generate a two-photon interference effect. Schematic of measurement set-up. For single photon measurement by using a fiber-coupled Hanbury-Brown and Twiss (HBT) setup, the parts of delay A and B and beam splitter (dotted boxes in Fig. 1(b)) are removed from the setup. For two photon interference measurement by using a fiber-based Hong-Ou-Mandel (HOM) setup, two unbalanced Mach-Zehnder interferometers (dotted boxes) are inserted in both excitation and emission paths. OL, HWP, PBS, TCSPC, and SMF represent objective lens, half-wave plate, polarizing beam splitter, time-correlated single photon counter, and single mode fiber, respectively. Blue-colored SMF is a polarization maintained SMF.
We characterized the mode structure of the fabricated device using photoluminescence measurements. We excited the sample with a continuous wave laser at a high pump power of 30 µW in order to saturate all the quantum dots and measured the cavity emission spectrum, shown in Fig. 2(a). The spectrum exhibits several peaks corresponding to different cavity modes. The fundamental mode (denoted M1) occurs at a wavelength of 1380 nm and has a Q of 7,000. In addition to the mode, we observe several higher order modes (M2-M5) that have Q values of 4300, 380, 1000, and 2000, respectively. Figure 2 The high Q value of mode M1 enables strong interactions and a large Purcell effect [35,36].
However the collected emission from this mode is very weak due to the poor directionality of it's far-field pattern as shown in Fig. 2(c) [37]. The majority of the radiation emits at large angles that are outside the collection aperture of the objective lens (NA=0.7), denoted by the white circle, which leads to low collection efficiency. Furthermore, even when using a collection lens with a larger numerical aperture, the collected mode would have a transverse mode profile that is very difficult to couple to a single-mode fiber.
The higher-order modes of the photonic crystal cavity have far-field transverse mode profiles that overlap much better with the collection area of the lens [38,39]. Mode M3 in particular has a Gaussian-like transverse mode pattern that is well-suited for coupling to a single-mode fiber.
From the simulations we calculate that more than 80% of photons emitted from the top of the device lie within the acceptance angle of our collection lens, as compared to only 30 % for mode M1. We note that these numbers only consider the light radiated in the upward direction, and that additional losses occur due to emission of a fraction of the light below the sample. To observe single quantum dot emission we now reduced the laser excitation power to 100 nW in order to avoid saturation and power broadening. Figure 3(a) shows the photoluminescence spectrum at this pump power from a cavity region (black line) as well as a region away from the cavity (red line). The emission from the cavity region exhibits a clearly enhanced brightness as compared to the bulk. Near the resonance of mode M3, we observe a bright narrow line corresponding to a single quantum dot emission which we label as dot A. This quantum dot line has a spectrometer-resolution-limited linewidth of 50 μeV at 1320 nm, which matches the fiber To confirm the single-photon nature of the cavity-coupled dot A, we performed second-order correlation measurements using a Hanbury-Brown and Twiss intensity interferometer. We filtered the quantum dot emission using a spectrometer, and detected the filtered emission using a 50:50 fiber beamsplitter and two InGaAs single photon avalanche diodes. We excited the quantum dot by using a 780 nm pulsed laser with a repetition rate of 40 MHz, a pulse width of 50 ps., and an average power of 5 nW. Figure 3(b) shows the measured second-order correlation (g (2) (τ)), which exhibits a clear antibunching at τ =0. We fit the correlation curve to two-sided exponential functions convolved with a Gaussian function that accounts for the limited detector response time of 200 ps. We measured the detector dark counts and used this value as a background level (gray-colored region) of the fitted curve (See Supplement 1). From the fit we determine g (2) (0)=0.085±0.022, indicating the bright emission of dot A originates from a single quantum dot with highly suppressed twophoton emission. The value of g (2) (0) increases with excitation power, but it remains below 0.5 up to the maximum quantum dot intensity (See Supplement 3). Cavities can modify the local density of optical modes, which enhances the spontaneous emission rate of dots [35]. From numerical calculation we obtain a cavity mode volume (V) of 0.66(λ/n) 3 . Combining this value with the measured Q of 380 for mode M3, we determine a Purcell factor ( = The cavity-coupled dot shows a bi-exponential decay behavior (τfast = 650 ps and τslow = 1.8 ns). We attribute the slow decay component to occasional conversion to dark exciton states [40] and also to other uncoupled dots that potentially excite the cavity through non-resonant energy transfer [41,42].
To verify that the reduced lifetime is a cavity effect, we performed lifetime measurements using 32 quantum dots from 20 different cavities. Figure 4(b) plots the measured lifetimes of all of these dots as a function of their detuning from the cavity mode M3. The distribution shows an enhanced spontaneous emission rate when the quantum dots are on resonance with mode M3, while the far detuned dots show a suppressed spontaneous emission rate, even lower than the averaged bulk dot rate, shown as a red dashed line. This behavior is consistent with a resonantly enhanced and suppressed Purcell effect [35]. We observe a lifetime as short as 400 ps for the fastest emitting quantum dot, corresponding to a Purcell enhancement of 4.4±0.5.
Together with spectral coupling, we consider spatial coupling, which multiplies a spatial mismatch term, | ( )| 2 /| | 2 , in the Purcell factor, where ( ) and denote the electric field at the position of dots and the maximum field intensity [43]. The Purcell factor drops by a factor of 10 when the dot is only about 150 nm away from the field maximum (Supplement 4). In addition, the polarization mismatch between dots and cavities further reduces the Purcell factor [44]. These imperfect spatial and polarization matches cause the discrepancy between the calculated and measured Purcell effect, and explains why some dots have negligible Purcell effect even at near zero spectral detuning in Fig. 4(b).
Figure 4(c) shows the emission intensity of dot A as a function of pump power using continuous wave laser excitation, along with a bulk quantum dot for comparison. We choose the bulk dot that has a similar wavelength to dot A and higher brightness than average bulk dots (see Supplement 2). Well below saturation, dot A emits 80 times brighter than the bulk quantum dot. We attribute this intensity difference to the fact that a large fraction of the emitted photons from the bulk dot reflect back into the substrate due to total internal reflection. We note that in this measurement, dot A emits at a count rate that would ordinarily saturate our single photon detectors that have a where max I is the maximum quantum dot emission intensity and P and Psat are the pump power and the saturation power, respectively. From this fit we calculate a maximum emission intensity of We measured the out-coupling efficiency by repeating the measurement of emission rate vs. pump power using a 50-ps pulsed laser with a repetition rate of 5 MHz. From this measurement we observed a maximum quantum dot intensity of 37±1 KHz, which corresponds to a photon detection probability of 0.74±0.02%. To estimate the collection efficiency through the first objective lens, we measured the transmission loss through each optical component. Our spectrometer has an efficiency of 42±2%, the coupling efficiency to the fiber is 48±4%, and we encounter additional losses due to lenses, mirrors, and beam splitters that further reduce the efficiency by 41±2%. These factors combine to give an overall efficiency of 8.3±0.9% for the collection system. We set the detector quantum efficiency to 20%, which further reduces the overall detection efficiency to 1.6±0.2%. Using these numbers we estimate that we collected 46±6% of quantum dot emission into the first objective lens (NA=0.7). If we consider non-zero g (2) (0) value, causing multi-photon events at high excitation power, we attain the multi-photon corrected efficiency of 36±5% [15] (see Supplement 3).
The dominant loss mechanism that limits the efficiency is due to the photons emitted in the down direction away from the objective lens. From numerical simulations we calculate that 62% of the light is emitted in the upward direction including back reflection from a bottom InP layer, and a fraction of 80% lies within the numerical aperture of the lens for mode M3. Also, the coupling efficiency for the cavity-coupled dot A is ≈ 1 − = 0.77, where τuc and τc are the lifetimes for the uncoupled (off resonant) and the coupled (on resonant) dots [35,43]. These numbers give the collection efficiency of ~39%, which well explains the measured collection efficiency. This collection efficiency is higher than that from the previously reported optical horn structures that emit bright single photons at telecom wavelength [29] and therefore, could provide bright deterministic single photon sources for long-distant quantum key distribution [7,45]. Many quantum information applications require indistinguishable photons that exhibit twophoton interference [1][2][3]. To investigate the indistinguishability of the source we performed a Hong-Ou-Mandel two-photon interference experiment ( Fig. 1(b)). Figure 5(a) shows the twophoton interference result of dot A with parallel polarization. The correlation histogram consists of a series of 5 peaks, which we label 1-5. The 5 ns peak separation of these peaks corresponds to the path length differences between the two arms of the Mach-Zehnder interferometers ( Fig. 1(b)). For an ideal indistinguishable source, peak 3 which is centered around zero time delay should completely disappear due to two-photon interference, leading to an intensity ratio of 1:2:0:2:1. But for realistic sources a residual peak still exists due to imperfect temporal overlap, polarization mismatch of two-photon wavepackets, and also due to dephasing and timing/spectral jitter of the source [46,47]. This results in the indistinguishable visibility V = 0.18±0.01. Dephasing and timing jitter cause this low visibility [47] and has a clear effect on the correlation curve which manifests itself as a sharp dip around zero delay for parallel-polarized photons.
With temporal post-selection method we calculate g ∥ (2) (0) = 0.17 ± 0.01 by normalizing the parallel-polarized autocorrelation at zero delay by the averaged peak value of peaks 2 and 4. This dephasing [48], where τ1 and τdeph is the spontaneous emission rate and the dephasing time of the quantum dot, υ is the visibility of two-photon interference. τdeph has a following relationship, = 150 ±29 ps. We note that υ is within the margin of error for perfect visibility (υ =1), which suggests that the non-vanishing component of the measured data at zero time delay is primarily due to the finite time resolution of the detector. The blue-dashed line in Fig. 5(b) is the simulated curve for the indistinguishability we would obtain using ideal detectors with perfect time response.
Although the post-selection approach leads to higher indistinguishability, it expenses the brightness of single photons (Supplement 6). To overcome the low visibility without postselection, and to produce high purity, on-demand indistinguishable single photons, we should reduce the dephasing rate and timing jitter [46]. Recently a number of works have demonstrated the highly indistinguishable single photon sources using quasi-resonant [14,39,49] or s-shell resonant excitations [16][17][18]50] at near infrared wavelengths. Also applying electric bias can reduce the environment noise from the charges [18]. In addition to high brightness and indistinguishability, a well-defined polarization state of the quantum dot emission is also important in many quantum information process applications [3,51,52]. In particular, two-photon interference occurs when two photon wavepackets have the same polarization as well as wavelength, spatial, and temporal matching. Non-polarized singe photon emitters would require an additional linear polarizer to post-select one polarization state, resulting 50% loss of photons.
To characterize the polarization property of the cavity-coupled dots, we performed photoluminescence measurements. Fig. 6(a) shows the measured spectrum. In this sample we fortuitously found two bright quantum dots resonant with mode M3 denoted as dot 1 and dot 2, and two other bright dots resonant with mode M4 denoted as dot 3 and dot 4. Figure 6(b) shows the cavity emissions as a function of polarization at high pump power that saturates the quantum dots. The cavity modes show highly polarized emission. The polarization behavior agrees well with the expected polarization behavior shown in Fig. 2(b), where the polarization direction of modes M3 and M4 are orthogonal to modes M1 and M5. We do not clearly observe mode M2 in this figure due to its low intensity.
To confirm the polarization properties of quantum dots 1-4, we performed the same measurement at pump power well below the quantum dot saturation level. Figure 6(c) shows the results. The cavity-coupled dots 1-4 show highly polarized emission along the same direction as the cavity mode that they are coupled to. We have demonstrated two-photon interference from the cavity-coupled InAs/InP quantum dots that emit bright, highly polarized single photons at telecom wavelengths. These properties are essential for a broad range of applications in long-distance quantum communication. By utilizing low-Q modes that are highly directional, we attained multi-photon corrected collection efficiencies as high as 36%, which is the highest value we are aware for telecom wavelength quantum dot single-photon sources. These low-Q modes provide the additional advantage that they are relatively broad band and do not require highly precise matching of the quantum dot resonance to the cavity, and also induce Purcell effect in a broad range. The efficiency of our device could be further improved by introducing a distributed Bragg reflector mirror to re-direct the emission from the bottom of the cavity [53], which could potentially enable collection efficiencies as high as 80%. Furthermore, superconducting nanowire based single photon detectors with detection efficiencies over 90% are now available at telecom wavelength, which would enable even higher detection rates [54]. We could improve the indistinguishability using quasi-resonant [14,39,49] or resonant excitation schemes [16][17][18]50], which have already been demonstrated to improve indistinguishability at near infrared wavelengths. We note that InAs/InP quantum dots could potentially emit single photons at 1.5 μm [27,30], so our device and approach could be readily extended to this wavelength range for generating single photons at the c-band. Ultimately, our results show that InAs/InP quantum dots are promising candidates for producing indistinguishable photons for long distance quantum information applications [55,56].
Compared to conventional Si detectors, InGaAs detectors have a lower quantum efficiency of 20% and higher dark counts of ~200 Hz. We determined the background level in the correlation histograms in Fig.   3(b) and Fig. 5(a,b) as below.
The obtained correlation histogram (g (2) (τ)) is a product of two detector signals given by , where Nmi, Nsi, and Nbi indicate the measured signal, the quantum dot signal, and the background signal at detector i, respectively. Most background signal originates from the detector dark counts in our pulsed measurements.
Based on the fact that two detectors have a similar efficiency and Nm1 >> Nb2, the second term, 2(Nm1·Nb2), describes the background level in the measured histogram. To quantify the background level, we made detector 1 measure both the quantum dot and background signals while detector 2 only measure the detector dark counts by disconnecting the signal channel. We then calibrated the correlation data with time and took double this value.

Bulk quantum dot spectrum
In Fig. 4(c), we compared the intensity of the bulk dot and dot A. For this comparison, we chose one of bulk dots that has a similar wavelength to dot A and higher intensity than that of the average dots as shown in Fig. S1. 3. Power dependence of g (2) (0) We investigated the excitation power dependence of g (2) (0) value of dot A. Figure S2(a) shows the measured correlation histograms at various excitation powers. The figure shows that the g (2) (0) values remain low at low power but start to increase near the saturation power (Psat =12 nW). The increased g (2) (0) values at high excitation power originates from the increased background emission by other dots and the enhanced cavity emission by nonradiatively coupled to other dots [1,2]. To reduce the probability of multiple photon events, we should use low excitation powers, which could limit the brightness of single photon sources. We plot the g (2) (0) values and the measured collection efficiency as a function of power. Figure S2(b) shows the g (2) (0) value remains below 0.5 up to the maximum dot intensity. From non-zero g (2) (0) values, we correct the multi-photon events in the measured collection efficiency by multiplying the term, (1-g (2) (0)) 1/2 [3]. This reduces the collection efficiency from 46 % to 36 % at the maximum dot intensity. Plots of g (2) (0) values (black-solid dots), measured collection efficiency (red-solid dots), and multi-photon corrected collection efficiency (red-empty dots) as a function of excitation power.

Spatial coupling between cavities and dots
In our photonic crystal cavity with the measured Q of 380 and the simulated mode volume (V) of 0.66(λ/n) 3 for mode M3, we calculate the Purcell factor of 44 when we assume an ideal coupling between dots and cavities. However, the measured dots show one order of magnitude lower Purcell factors than the calculated value even at zero spectral detuning. This is mostly due to the spatial and polarization mismatches. To consider non-ideal spatial coupling, we multiply a spatial mismatch term, |E(r)| 2 /|E max | 2 in the Purcell factor, where E(r) and E max denote the electric field at the position of dots and the maximum field intensity. Figure 3(a-c) shows the simulated spatial map of |E(r)| 2 /|E max | 2 for mode M3 and their intensity profiles along x and y directions. Mode M3 has a two maximum peaks at the middle of cavity, denoted as P1 and P2. Figure 3(b,c) shows that the Purcell factor drops by a factor of 10 when the dot is about 150 nm (85 nm) away from the field maximum along x (y) direction. This small size of localized modes makes the spatial coupling difficult, and becomes a main cause of the reduced Purcell factor in the experiments [4][5][6][7].

Purcell effect on cavity-coupled dots
Purcell effect enables dots to emit single photons with an enhanced spontaneous emission rate, and therefore, it also increases the maximum brightness of the dots by increasing the saturation power level. To investigate the influence of the Purcell effect on the saturation power of dots, we chose two cavity-coupled dot 1 and dot 2 in Fig. S4(a), which have different lifetimes of 650 ps and 1.8 ns, respectively. Figure S4  6. Indistinguishability vs. brightness In Fig. 5(b), the cavity-coupled dot shows indistinguishable nature of single photons from two-photon interference. However, the strong dephasing limits the indistinguishable visibility of the dot and requires post-selection method to achieve high indistinguishability. Figure S5 shows that the indistinguishability increases as we reduce the time window for post-selection, while we lose the brightness of single photons.