1. Introduction

In quantum physics two objects are said to be indistinguishable, if their quantum mechanical states are entirely identical. In case of photons, indistinguishability can be used to reveal the bosonic nature of light: The fundamental Hong-Ou-Mandel experiment has demonstrated that two indistinguishable photons impinging on a beamsplitter from different input arms, always leave through the same output [1]. This effect is understood as interference of two identical photons. It has been used in many concepts of quantum information processing [2,3] and quantum communication [4–6] ever since, as it offers a tool for effective photon-photon interaction and the creation of photon entanglement [7]. In order to establish quantum information applications, bright on-demand single photon sources with high single photon purity and Fourier-limited spectral and temporal properties are necessary [8]. In this respect, semiconductor quantum dots (QD) have proven to be a promising system. Many schemes for coherent control of exciton states in quantum dots [9,10] and the use of their fluorescence photons for indistinguishability experiments with high interference contrasts [11–17] have been shown so far. However, as many other single photon sources, most quantum dots emit fluorescence photons at visible (VIS) or near-infrared (NIR) wavelengths. Therefore, the photons suffer high losses in optical fibers, which effectively limits their performance in long-haul quantum networks [18]. Interesting perspectives are introduced by QDs that directly emit within the low-loss telecom O- or C-band [19–23]. Despite that progress, the quality in terms of brightness and indistinguishability of QDs emitting at the VIS or NIR region is unmatched, so far [17].

An alternative approach is to employ quantum frequency down-conversion (QFDC) in order to transfer the short wavelength of single photons to the preferable telecom regime [24]. The underlying process of QFDC relies on the nonlinear interaction of the participating light fields, i.e. a low conversion efficiency is inherent to this technique. As the efficiency scales with the light intensity, down-conversion has been brought to a beneficial regime by shaping the nonlinear materials into waveguides [25] and using a strong pump field to stimulate the process. Furthermore, the purity of the converted single photon state is sensitive to background photons created during the conversion process. Common sources of background photons have been identified to be parametric fluorescence [26] and Raman scattering of the pump [27] and have been minimized by putting the pump wavelength to the far long-wave side of the single photon field along with additional narrow-band filtering of the down-converted photons. By that, experiments became feasible, which clearly demonstrated that QFDC can be performed efficiently and is conserving first and second order coherence of single photons [28], matter-photon entanglement [29,30] as well as indistinguishability [31]. Therefore, QFDC can be seen as a versatile tool to transfer all desirable single-photon properties provided by QDs to the telecom regime. Moreover, the advantages of QFDC are desirable for a variety of applications in the context of quantum networks, e.g. connecting different physical systems by conversion to a common bus wavelength, and have been used to interface quantum memories with the telecom regime [32,33].

However, the performance of quantum information protocols often depends non-linearly on the photon input rate. In this respect it is a necessity for QFDC to operate at the highest possible efficiencies in order to make it a competitive technique. Down-conversion of single photons with simultaneously reaching a high conversion efficiency and conserving the entire quantum mechanical state has not been shown so far. To fill this gap, the present paper focuses on the down-conversion of indistinguishable single photons emitted by a p-shell excited InAs/GaAs QD at λ_nir = 904 nm. The scheme uses a λ_p = 2155 nm cw pump laser in order to stimulate the process, thus down-converting the photons to the telecom C-Band at λ_tel = 1557 nm, according to ${\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}_{\text{nir}}-{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}_{\mathrm{p}}={\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}_{\text{tel}}$. We demonstrate that our scheme combines high conversion efficiencies and the conservation of important single photon properties, while the process is shown to be essentially noise-free, thus offering an excellent platform to create an efficient source of indistinguishable photons at the telecom regime.

2. Experimental setup

Our experimental setup is depicted in Fig. 1. It mainly consists of a confocal microscope, a frequency conversion setup containing a MgO doped, periodically poled lithium niobate waveguide (MgO:PPLN) and detectors along with appropriate spectral filtering. In order to test indistinguishability, we additionally insert two Mach-Zehnder interferometers (MZI) into the excitation and detection beam paths, respectively, each of which introducing a time delay of 4 ns between both interferometer arms.

 

Fig. 1 Experimental setup for excitation of the QD sample, frequency conversion and two-photon interference. (a) Excitation light at 884 nm is provided by a pulsed laser with a repetition rate of 80 MHz and 4 ps pulse width. The pulses are split up and recombined within a MZI in order to create double pulses with a spacing of 4 ns. Subsequently, the excitation light enters our confocal microscope through a microscope objective (MO) of 100× magnification and NA = 0.9. Microscope objective and sample reside within a liquid helium cryostat at a temperature of 10 K. The single fluorescence photons are directed through an etalon (ET), longpass filter (LP) and bandpass filter (BP) in order to separate fluorescence wavelength and background light such as scattered laser light. Eventually, a single mode fiber is installed in the confocal plane of the microscope for collecting and directing the single photons to further experiments and analysis. (b) The unconverted single photons enter a second MZI in order to compensate the time delay of 4 ns, which was introduced in (a). The two-photon interference takes place at the output BS of the MZI. Photons at both output arms of the MZI are detected by Si-APDs. (c) For the frequency conversion, the fluorescence photons are mixed with a pump field at 2155 nm at a dichroic mirror (DM) and coupled to the MgO:PPLN-waveguide trough an aspheric lens (AL). The converted photons at 1557 nm are spectrally cleaned up at a bandpass filter with central wavelength of 1550 nm and in a fiber-based setup consisting of a circulator (Circ.) and fiber Bragg-grating (FBG). Finally, the converted photons enter a fiber-based MZI. In analogy to (b) the photons undergo two-photon interference at the output fiber beam splitter (FBS) and are detected by SSPDs.

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As source of single photons we use a sample of self-assembled InAs/GaAs QDs embedded inside an AlAs/GaAs distributed Bragg reflector cavity grown by metal organic chemical vapor phase epitaxy. The sample is located in a cryostat at a temperature of 10 K. For quasi-resonant excitation [34], the QD was illuminated with a pulsed Ti:Sa-laser tuned to 884 nm (pulse width 4.3 ps, repetition rate 80 MHz). Fluorescence photons at 904 nm are passing through an etalon (Finesse ℱ ≈ 25, free spectral range 341 GHz), a 900 nm longpass filter and a 905 nm bandpass filter (joint transmission of ~ 42 %) in order to remove residual excitation light, unwanted background fluorescence and quantum dot emission other than the single excitation line. After spectral filtering the photons are detected with a rate of about 38 800 counts per second (cps) by silicon avalanche photodiodes (Si-APDs, quantum efficiency 33 %).

In a second step, the single photons are converted to 1557 nm. In order to stimulate the frequency conversion process a strong cw pump laser at 2155 nm is coupled into the MgO:PPLN-waveguide along with the fluorescence photons. Due to its narrow acceptance bandwidth of 126 GHz, the conversion process transduces photons just within a small range around the center wavelength of the fluorescence photons to the telecom regime (cf. remarks on signal-to-background ratio below) [28]. Thus, for the conversion experiments the longpass and bandpass filter as well as the etalon for the NIR light are redundant and can be removed. Accordingly the conversion setup has a photon input rate of around 279 kHz. Noise introduced by the conversion process itself is removed using a 1550 nm bandpass filter and a fiber Bragg-grating with a FWHM of 121 GHz bandwidth. The highest conversion efficiency was observed at a pumping power of P = 293 mW inside the waveguide resulting in around 8 800 cps detected by the superconducting single photon detectors (SSPDs, quantum efficiency 10 %). The external conversion efficiency is defined as the fraction of photons entering the conversion setup that become converted and not lost on the optical path to the detector input. Taking the quantum efficiency of the SSPD into account, the detected count rate leads to an external conversion efficiency of (31.1±0.2) %. As an upper bound for the internal photon-to-photon conversion efficiency inside the waveguide, the depletion of the 904 nm photons was separately measured to be 92 %. The discrepancy between internal and external efficiencies is in good agreement with the expected over-all photon loss on the optical path between the input fiber of the frequency conversion setup and the SSPDs. Limitations on the internal conversion efficiency can be attributed to a non-perfect mode overlap of fluorescence photons with the pump field and general imperfections of waveguide geometry as well as periodic poling. Independent of the 2155 nm pump power, our setup yielded 350 background events per second, which solely resulted from detector dark counts, i.e. any background photons that might be created by noise-processes during the conversion itself are removed by the subsequent spectral filtering. Therefore, our down-conversion scheme is entirely noise-free and any detected noise or background events can be attributed to the QD or detection system.

3. Results

To characterize the QFDC process several fundamental properties of the single photons prior to and after the down-conversion step were measured: The coherence time of the single photons was determined with the help of a separate Michelson interferometer and turned out to be T_2,nir = (116±3) ps before and T_2,tel = (114±2) ps after down-conversion. For p-shell excited quantum dots, this coherence time is slightly lower than expected, which can be related to dephasing by charge-carrier induced electrostatic fluctuations of the QD environment even under p-shell resonant excitation [35]. The spectral line width of the pump laser light of 670 kHz corresponds to a coherence time of T_2,p = 474 ns ≫ T_2,nir, thus its impact on T_2,tel can be neglected. Accordingly, we found T_2,nir = T_2,tel within the measurement error. Furthermore we measured the temporal width T₁ of the single photons, which is mainly determined by the exciton lifetime of the quantum dot. For this purpose, a time correlated single photon counting experiment was performed employing the clock output of the excitation laser as trigger signal. With this we found T_1,nir = (970±1) ps for the unconverted and T_1,tel = (887±3) ps for the converted photons. By comparing temporal width T₁ and coherence time T₂, it can be seen that the emitted photons are not Fourier-limited, which restrains the maximally possible HOM interference visibility to V_lim = T₂/(2T₁) = 0.06 for converted and unconverted photons [36, 37]. As the Michelson interferometer used for the T₂ measurements integrates photon rates on a time scale of several milliseconds, V_lim should be understood as a lower bound for the HOM visibility [37,38].

Next we investigated the photon statistics by measuring the second order coherence function g⁽²⁾ (τ) using a Hanbury-Brown-Twiss (HBT) interferometer. The results are presented in Fig. 2. Extracting the antibunching values from the raw data yields ${ }^{\text{nir}}{g}_{\mathrm{E}}^{(2)}(0)=0.171$ and ${ }^{\text{tel}}{g}_{\mathrm{E}}^{(2)}(0)=0.290$ for unconverted and converted photons, respectively (cf. Table 1). In either case the randomly distributed detector dark counts add a constant background of uncorrelated events to the g⁽²⁾ measurements. After subtracting this contribution, we get corrected values of ${ }^{\text{nir}}{g}_{\mathrm{E},\text{corr}}^{(2)}(0)=0.153$ and ${ }^{\text{tel}}{g}_{\mathrm{E},\text{corr}}^{(2)}(0)=0.117$. The remaining deviation from zero stems from fluorescence photons emitted by a spectrally broad background of the QD-sample. To quantify this, the number of emitted background-fluorescence photons per QD-photon was determined by integrating separately the background and the QD emission line within the transmission-window of our filters as depicted in Fig. 3. The ratio of these two numbers (QD photons over background-fluorescence photons) is commonly referred to as signal-to-background ratio (SBR) and yields 11.5 in case of unconverted photons. To calculate the SBR for the converted photons accordingly, a spectrum of unfiltered QD photons (Fig. 3(b), green curve) was multiplied with a relative conversion efficiency function (black curve) to obtain the spectrum of photons that eventually become converted (red curve). This function accounts for the drop of conversion efficiency due to an increasing phase mismatch for wavelengths differing from the chosen operating point. It was modelled according to [40], taking into account the waveguide geometry and quasi-phase-matching pitch specified by the manufacturer as well as the wavelength- and temperature-dependency of the refractive index of MgO:LN given in [41]. The applicability of this model for our system was separately validated with measured data showing the spectral distribution of telecom photons that originate from a spontaneous parametric down-conversion process of 905 nm photons. The resulting curve in Fig. 3(b) shows the anticipated sinc²-shape with a FWHM of 126 GHz. Integration within the FBG transmission-window now leads to an SBR of 17.2. The obtained SBRs can be directly related to an expected g⁽²⁾ value via [42]

 

Fig. 2 Measurement of second order coherence function g⁽²⁾ (τ) (a) before and (b) after the down-conversion. The values of ${ }^{\text{nir}}{g}_{\mathrm{E},\text{corr}}^{(2)}(0)=0.153$ and ${ }^{\text{tel}}{g}_{\mathrm{E},\text{corr}}^{(2)}(0)=0.117$ reveal a clear signature of antibunching. The scattered dots represent normalized measured data, whereas the solid lines with shaded area correspond to Monte-Carlo simulations.

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Table 1. Summary of g⁽²⁾ values for converted and unconverted photons. Values are given for measurements and Monte-Carlo simulations with and without detector noise contribution. Additionally the SBR limit derived from the spectra is shown (see Fig. 3).

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Fig. 3 (a) QD emission spectrum with bandpass and etalon filtering. A signal-to-background ratio of QD photon emission related to background fluorescence emission of 11.5 can be extracted by integration within the bandpass filter window. (b) Multiplying the unfiltered QD emission spectrum (green) with the spectral, relative conversion efficiency (black) yields the spectrum of photons that become converted. Integration within the FBG filter window yields an SBR of 17.2.

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For an independent cross-check, we performed Monte-Carlo simulations to reproduce the g⁽²⁾-measurements. They were implemented by emulating a large number of excitation cycles, whereas each cycle contains exactly one QD fluorescence photon. Within each repetition, a set of decisions is made with the help of appropriately distributed random numbers that generate click-lists for both detectors. Eventually, both click-lists are correlated to obtain the final result. These decisions (and according probability distributions) are:

The duration of one excitation cycle equals the repetition time of the excitation laser and was separately measured to be T_rep = 12.47 ns. All necessary values to describe the relevant probability distributions were known by independent measurements and are given above. Therefore no additional fit to the measured data was necessary. The simulated curves are shown in Fig. 2 as shaded areas. Here we obtain ${ }^{\text{nir}}{g}_{\mathrm{S}}^{(2)}\left(0\right)=0.172$ and ${ }^{\text{tel}}{g}_{\mathrm{S}}^{(2)}\left(0\right)=0.278$ for simulations including detector noise as well as ${ }^{\text{nir}}{g}_{\mathrm{S},\text{corr}}^{\left(2\right)}\left(0\right)=0.154$ and ${ }^{\text{tel}}{g}_{\mathrm{S},\text{corr}}^{\left(2\right)}\left(0\right)=0.109$ excluding detector noise. These findings clearly support our preceding analysis and underline the fact that the small acceptance bandwidth of the QFDC-process along with the narrowband filtering of the FBG improves the signal-to-background ratio of the single photons during the down-conversion. The spread between measured and simulated values as well as the SBR-limit is just 0.001 for unconverted photons, reflecting the good agreement of all approaches. For converted photons, however, the values spread over a range of 0.012. This is a direct result of the lower photon rate in the telecom regime, which was not compensated by an accordingly higher integration time. Consequently, the data are subject to a higher statistical error leading to a slight disagreement with the simulated values and SBR-limit.

To test the indistinguishability of independently emitted photons, we established a setup as proposed in [11]. For the unconverted photons, the first MZI shown in Fig. 1(a) created an excitation sequence of double pulses separated by 3.98 ns, which was repeated every 12.47 ns. Accordingly, the emitted single fluorescence photons followed the same temporal pattern. The second MZI was set to exactly compensate the initially introduced 3.98 ns, leaving three pulses with an intensity ratio of 1:2:1 at both output ports of the MZI as shown in Fig. 1(b). Cross-correlating the detection events of both output arms yields clusters of 5 peaks. The clusters are separated again by the inverse repetition rate of the excitation source, while the relative delays within a cluster are −7.96, −3.98, 0, 3.98, 7.96 ns. If the correlated detection events belong to distinct excitation cycles, the single cluster peaks exhibit intensity ratios of 1:4:6:4:1, and 1:2:2:2:1, if they originate from the same excitation cycle. In our scheme, neighbouring clusters strongly overlap, yielding a complicated over-all structure. This overlap is commonly avoided by choosing a smaller MZI arm imbalance [11,31]. Due to the large temporal width of the single photon pulses (≈ 1 ns), this would lead to a strong merging of all peaks within one cluster and was therefore not implemented for our MZI design. Despite that, the central peak at a time delay of zero does not suffer from any overlap, i.e. any signature of two-photon-interference can directly be extracted from it. For the converted photons both excitation and detection MZI instead featured a pulse spacing of 8.03 ns. This change of the setup arrangement was not motivated by any physical considerations. It resulted from a mistake in our MZI design, which stayed concealed during the experiments due to technical bounds of the interferometer length measurement. However, the same explanation as before can be applied to the resulting pattern of the correlation measurement. The only difference is that the time passing between the emission of both photons is increased from 3.98 ns for unconverted photons to 8.03 ns for converted photons.

The experimental data of the indistinguishability test are shown in Fig. 4(a) for unconverted and in Fig. 4(b) for converted photons. In an entirely classical and ideal scenario (no multi-photon interference, no noise, no bunching) the number of coincidence counts in the central peak A_c should be made of $p=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ and $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$ the number of coincidence counts of the directly neighbouring peaks A_n, corresponding to a delay of 3.98 ns and 8.03 ns, respectively (see eg. supplementary material of [14] for the short delay. Explanation for the long delay accordingly). As the number of coincidence counts of the central peak decreases linearly to zero with the HOM visibility $\tilde{V}$ increasing from zero to unity, it follows that $A_{\mathrm{c}}/A_{\mathrm{n}}=p\left(1-\tilde{V}\right)$. Here we find a reduced number of coincidences, which corresponds to a two-photon interference contrast of $\tilde{V}=36\%$ for unconverted and 12% for converted photons following that relation. These values are significantly decreased by the background from detector dark-counts and fluorescence photons. To extract the pure wave-packet overlap V, we again performed Monte-Carlo simulations in the same manner as described above with the same parameters for SBR, lifetime, repetition rate, detector dark count rate and timing jitter as before. Additionally, we now assumed two QD fluorescence photons per cycle spaced by the MZI arm imbalance corresponding to the excitation double-pulse sequence. The MZI interferometer in the detection beam path was included to the simulations by two reflection/transmission decisions for each photon according to the input and the output beam splitter, respectively. If two QD fluorescence photons hit the output BS at the same time, HOM interference can occur. The probability distribution in that case is a weighted average of the classical distribution 1/4:1/2:1/4 and the HOM interference distribution 1/2:0:1/2 for the three possible output states |2, 0〉, |1, 1〉 and |0, 2〉, whereas |n, m〉 describes the number of photons n, m in each output arm. The weighting factor was modelled to be the wave-packet overlap and was used as the only fitting parameter to our experimental data. A non-perfect mode overlap at the output BS and a non-symmetrical ratio $\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$T$}\right.$ of the BS reflection R and transmission T were not included in the simulations, as the MZI classical visibility was separately determined to be close to unity. The results can be seen in Fig. 4 as shaded areas and reveal V_nir = (48.6±0.1)% and V_tel = (26.3±0.2)%.

 

Fig. 4 Measurement of two-photon interference contrast (a) before and (b) after down-conversion. The measured data (black dots) are compared to Monte-Carlo simulations (shaded areas) yielding wave packet overlaps of 48.6 % and 26.3 % prior to and after the conversion step, respectively (for details refer to analysis given in the main text). The reduced overlap of the converted photons arises from a stronger spectral diffusion of the emission line due to the different MZI configuration (cf. inset). The dashed horizontal lines represent the expected peak height at zero delay for V = 0 under the given experimental conditions.

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The comparatively low wave-packet overlap for the unconverted photons is mainly a consequence of the excitation scheme used: The emission time of fluorescence photons following a quasi-resonant excitation step suffers from a timing-jitter due to the uncertainty on when exactly the exciton ground state becomes populated. Therefore, the wave-packet overlap of single photons at the HOM-beam splitter in the time domain is reduced. However, there is still an offset to typical values reported using quasi-resonant excitation [11,38,39]. Just as discussed above for the low coherence time, this might be a signature of an unstable electrostatic environment of the QD inducing spectral diffusion. An explanation for the significant drop of the wave-packet overlap for the converted photons can be found in the larger pulse separation of 8.03 ns according to [38]: Just Fourier-limited single photons behave ideally indistinguishable. Dephasing processes like spectral diffusion and phonon interaction corrupt the coherence time and therefore the HOM-interference visibility as well. Spectral diffusion in QD systems typically takes place in the range of a few nanoseconds [38,43] and therefore plays a crucial role on the time scale of MZI delays used here. To estimate the impact of spectral diffusion, we follow the formalism introduced in [38]: using the relations therein for radiative decay rate $\mathrm{\Gamma }=T_1^{-1}$ and the spectral diffusion rate in the limit for long integration times ${\mathrm{\Gamma }}_0^{\prime }=\mathrm{\Gamma }\left(1-T_2\mathrm{\Gamma }/2\right)$, the wave-packet overlap for a given pulse spacing δt is determined via the relation

4. Summary

To summarize our work, we demonstrated quantum frequency down conversion of single photons emitted by a quantum dot at 904 nm to the telecom C-band at 1557 nm. The conversion is highly efficient (> 30 %) and conserves crucial single photon properties such as first and second order coherence as well as indistinguishability. A small acceptance bandwidth of the conversion-process along with narrowband filtering at the telecom region further increases the signal-to-background ratio of the single photons. Importantly, the conversion process does not add any noise at the target wavelength. A direct comparison of our scheme to telecom QDs is not unambiguous. While some emitters [22] are brighter than our source, the indistinguishability achieved in the present work is slightly larger than reported in [23]. However, a telecom photon source created by a combination of our scheme with state-of-the-art NIR-QDs [17] would set a high standard. Moreover, the inherent tunability of the QFDC process can erase typical small wavelength mismatches between different QD samples. Thus, our scheme can be understood as a flexible, noise-free source of high purity single photons at telecom wavelengths, which is a key tool in establishing quantum communication and information applications based on remote building blocks inside a long haul network.

In future work, we plan to combine our down-conversion-scheme with strictly resonant excitation techniques [44] of quantum dots to obtain HOM-visibilities close to unity [17]. By extending the down-conversion to fluorescence photons emitted by two distinct quantum dots, we expect to prepare indistinguishable photons that have been distinguishable by their spectral properties before. This technique could play a crucial role in building quantum gates that are meant to process qubits stored in remote quantum dots.