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Abstract
Interference between single photons is key for many quantum optics experiments and applications in quantum technologies, such as quantum communication or computation. It is advantageous to operate the systems at telecommunication wavelengths and to integrate the setups for these applications in order to improve stability, compactness and scalability. A new promising material platform for integrated quantum optics is lithium niobate on insulator (LNOI). Here, we realise Hong-Ou-Mandel (HOM) interference between telecom photons from an engineered parametric down-conversion source in an LNOI directional coupler. The coupler has been designed and fabricated in house and provides close to perfect balanced beam splitting. We obtain a raw HOM visibility of (93.5 ± 0.7) %, limited mainly by the source performance and in good agreement with off-chip measurements. This lays the foundation for more sophisticated quantum experiments in LNOI.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Linear optical networks are the basis of quantum technologies. Many important applications of quantum technologies such as quantum key distribution [1] and boson sampling [2] were demonstrated using linear optics. At the heart of these linear networks lie optical beam splitters (BS) and phase shifters, since it was shown that with these two components any unitary matrix operation can be implemented [3].
A particular interest has been devoted to the study and realisation of integrated optical circuits, since they offer high stability, the possibility of compact devices and high efficiencies, and thus enable scalability in contrast to their free space or bulk counterparts. The history of integrated linear networks is summarised in many review articles see, e.g., [4].
A new promising material for the implementation of future quantum circuits is lithium niobate on insulator (LNOI) since it combines a high integration density, as known from silicon photonics, with its unique functionalities of electro-optical modulation and a second order nonlinearity [5]. It consists of a thin-film of lithium niobate (LN) (300 nm to 1000 nm) bonded on a SiO$_2$ layer. The light is guided in the LN thin-film and thus it inherits the diverse property portfolio of LN, e.g., its wide transparency window, its large second order non-linearity and electro-optical coefficients [6]. Due to its structure with a SiO$_2$ layer underneath and the low dimension of the LN thin-film a strong confinement for rib waveguides can be realised, giving rise not only to the high integration density, but also to a highly improved effective non-linearity and the possibility of dispersion engineering.
LNOI has already been employed for the realisation of a variety of devices, such as electro-optic modulators [7–9], directional couplers [10–15], as well as for second harmonic generation [16–18] and spontaneous parametric down-conversion [19–21]. The importance of this platform for quantum photonics is also summarised in different papers, such as [22,23] or [24]. All of these functionalities combined with the possibility to achieve very low loss waveguides [25] illustrate the high potential of LNOI for future photonic quantum technologies. A key building block of quantum networks is two-photon Hong-Ou-Mandel (HOM) interference.
Here, we demonstrate HOM interference of photons at telecommunication wavelengths from a parametric down-conversion source in an LNOI directional coupler. We observe an interference visibility of ($93.5\pm 0.7$) $\%$, limited by the source performance and similar to an off-chip measurement. This constitutes an important building block for realising optical quantum networks on LNOI and paves the way towards future applications.
This paper is structured as follows. In Section 2, we briefly discuss the basics of HOM interference. Section 3 details the theory and the modeling of the LNOI directional coupler and we describe the fabrication process in Section 4. In Sections 5 and 6 we present the characterisation of the coupler and the HOM measurements, respectively. Section 7 concludes the paper.
2. Fundamentals
HOM interference describes the bunching of two indistinguishable photons at a balanced, non-polarising beam splitter (BS) where both photons enter from one input port each, but leave them together in one of the outputs. Typically, the degree of distinguishability between the two photons is continuously changed from completely distinguishable to fully indistinguishable, by introducing a time delay between the photons. Monitoring the number of coincidence events between the output ports of the BS as function of delay then yields the famous HOM dip [26]. The visibility of this dip is calculated with the maximum (distinguishable photons) $c_\text {dist}$ and minimum (indistinguishable photons) $c_\text {indist}$ coincidence rate as
The visibility is ideally 100 $\%$ but typically limited by the imbalance of the BS and the indistinguishability of the impinging photons. Here, we compare the dip visibility, which we obtain with our LNOI device, against the visibility, which we observe with an off-chip reference measurement. This allows us to gauge the impact of the LNOI directional coupler on the photon indistinguishability and hence the applicability of LNOI in integrated optical quantum networks.
Perfect HOM interference is only observed with a perfectly balanced BS. Unavoidable fabrication intolerances will, however, lead to deviations from a 50:50 splitting. The impact of these on the HOM visibility can be summarised as [27]
where $\eta$ is the reflectivity of the BS. To fabricate a 50:50 directional coupler, we first carried out numerical simulations to estimate the coupling behaviour. These are discussed in the next section.3. Simulations of waveguide and directional coupler structures
The aim of our simulations is to find a suitable waveguide and directional coupler geometry that meets our needs such as single modeness, short coupling length, a gap width that is compatible with our fabrication capabilities, and a large bandwidth. For the numerical evaluation, we briefly recap the operation principle of a directional coupler.
A directional coupler consists of two waveguides that are brought close to one another for a given length, $L_I$, with a small gap given by $G$ (see Fig. 1(a)).
Fig. 1. Images of directional coupler. The first image shows a schematic of a directional coupler with the important parameters. The second picture is a scanning electron micrsocope (SEM) image of the device.
Along the length $L_I$ the coupling takes place via the evanescent fields of the two waveguides. Mathematically, this is explained by coupled mode theory which yields that the incoupled power oscillates sinusoidally between the two waveguides [28]. The coupling depends on the wavelength, the waveguide geometry, the interaction length and the gap and is summarised by the coupling coefficient. A user-chosen splitting ratio can be realised by adapting $L_I$ appropriately.
We first investigated the single modeness of a single waveguide using the eigenmode solver MODE of Lumerical [29]. For that, we fixed the thin-film thickness to 600 nm and used X-cut LNOI. The sidewall angle of the waveguide is set to $60~{^{\circ }}$ mirroring our fabrication process. Furthermore, the top width is adjusted to 1 µm and we applied a cladding layer of 150 nm SiO$_2$. For these parameters we simulated different etching depths to find a single mode waveguide geometry and chose 150 nm as an etching depth. In Fig. 2(a) a single waveguide with the discussed geometry is shown. We can see the fundamental mode guided in the LN thin-film, the SiO$_2$ substrate underneath the LN and the SiO$_2$ cladding layer.
Fig. 2. Simulations of waveguide structures in LNOI. The three images show the model of a single waveguide and of the directional coupler. The image of the single waveguide shows the electric field intensity and the images of the directional coupler show the real part of the z-component of the electric field. The parameters of the waveguide that can be changed are the thin-film thickness, the etching depth, the top width, the angle and the thickness of the cladding layer and for the directional coupler the gap can be varied. For more information, see text.
Afterwards, we simulated the coupling behaviour of a directional coupler and we introduced a second waveguide to our model defining the center to center distance between the two waveguides as a new parameter called gap $G$. The calculated symmetric and anti-symmetric mode are shown in Fig. 2(b) and Fig. 2(c). The resolution of the laser lithography used for defining the structures placed a lower limit on our gap width, which set a minimum coupling length for us. A gap width of 2.3 µm yielded a coupling length of 137 µm, leading to small device footprint well suited for high-density integration.
For characterising the bandwidth of the coupler we show in Fig. 3 the normalised splitting ratio as a function of the wavelength which we calculate using again the eigenmode solver of Lumerical and calculating the coupling length for different wavelengths. In a range of $\pm$ 10 nm the splitting ratio only varies by less than 1 $\%$ which shows that the coupler is wavelength independent for a broad range. Since the bandwidth of the single photons used for the HOM experiment is 1.8 nm at a wavelength of 1542.22 nm, we found a stable geometry with a large enough bandwidth for our experiment. In the next step, we fabricated this geometry to test the coupling behaviour.
Fig. 3. The graph shows the normalised splitting ratio as a function of the wavelength. The splitting ratio lies within 1 $\%$ of the desired 50:50 value for wavelengths between 1540 nm and 1560 nm.
4. Fabrication of directional couplers
For the analysis of our directional couplers, we produced a sample with multiple waveguide groups consisting of a directional coupler and a straight waveguide to estimate the propagation losses. The spacing of the input and output waveguides is 60 µm and a cosine bending with a length of 300 µm is used for all couplers. We changed the interaction length $L_I$ of the couplers from 30 µm to 580 µm to be able to determine the coupling length as explained in the next section.
We fabricate the waveguides via a physical dry etching process utilizing SiO$_2$ structured by a lift-off process as an etching mask. To realise the etching mask, we spin coat photo resist onto a LNOI sample (NanoLN), which is subsequently structured with a laser lithography system (Heidelberg Instruments DWL 66+). After developing, 150 nm of SiO$_2$ is deposited on the sample via sputtering (Prevac Sputtering system 518) and is structured by a lift-off process. Afterwards, the structured SiO$_2$ is used as an etching mask to transfer the structure in the lithium niobate thin-film layer. We use a dry etching process with a pure Argon plasma (Oxford Instruments PlasmalabSystem100). In a last step, the end-facets of the sample are chemo-mechanically polished. For this purpose, a SiO$_2$ cladding layer is evaporated to protect the sample during polishing. The sample has a length of 7 mm.
After the sample was fabricated, the geometry was measured and we could extract the following parameters: the thin-film thickness was 605 nm, the etching depth was 130 nm, the top width of the waveguides was 1066 nm (see Fig. 1(b)). All other parameters are as simulated. These different parameters lead to a coupling length of around 120 µm.
5. Linear characterisation of waveguides and directional couplers
We measured the propagation losses of eight straight reference waveguides for the TE polarisation at a wavelength of 1550 nm using the so-called Fabry-Pérot method [30]. The light was coupled into and out of the LNOI waveguides with aspheric lenses. From these measurements, we estimate average propagation losses of ($4.85\pm 0.95$) dB/cm and note that these do not impede the quality of HOM interference. This is the case as the source is operated in a regime where higher order photon number contributions are negligible and thus a measured coincidence means that no loss has occurred. Losses thus could only affect the HOM interference quality in such a way, that the visibility is reduced if the rate of background coincidences in comparison to the signal is too high. Due to the low dark count rate of the used superconducting nanowire single photon detectors (SNSPDs) this background coincidences are negligible. However, the losses will reduce the signal rate and thus increase the measurement time.
Next, we investigated the coupling behaviour of the directional couplers for the TE polarisation. For that, we coupled laser light with a wavelength of 1550 nm (Santec TSL-550) into one input arm of the coupler and imaged the two output ports on a camera (Xenics Wildcat 640). In Fig. 4 two examples of measured output modes can be seen. In Fig. 4(a) all the light from one input port coupled to the opposite output port. In contrast, in Fig. 4(b) the incoupled light is split nearly 50:50. We then calculated for each output port the power ratio via this relation:
Here, $P_{1,2}$ is the power of the output mode 1 and 2, respectively. In Fig. 5 the power ratio is plotted against the interaction length of the directional coupler for incoupling into input $a$ and input $b$. It can be seen that for zero interaction length the splitting ratio is different from the expected zero and one value. Rather there is an offset for zero interacting length. This is due to the fact that coupling already occurs in the bending region, where the waveguides are brought into close proximity. Since we used the same bending for all couplers, this leads to a constant offset.
Fig. 4. Output modes of two directional coupler with different interaction length. (a) All light coupled from one waveguide to the other. (b) A nearly 50:50 splitting ratio is reached.
Fig. 5. Power ratio as a function of the interaction length. The measurement of the coupling behaviour shows that the light oscillates as expected between the two waveguides. Input a and b refer to the reflectivity and transmittivity of the directional coupler , respectively. The coupling length is (112.86$\pm$2.82) µm.
We extract the coupling length of the directional coupler from a sinusoidal fit, which yields lengths of ($114.85\pm 0.04$) µm and ($110.87\pm 0.04$) µm for inputs $a$ and $b$, respectively. The slight discrepancy can be caused by irregular width variations along the propagation direction. The average coupling length is ($112.86\pm 2.82$) µm, which is in excellent agreement with the expected 120 µm predicted from the model. It is also visible that not all splitting ratios add up to one. This could be due to asymmetric losses in the output waveguide which would lead to different splitting ratios.
For the HOM experiment a 50:50 coupler is needed. For this we choose the coupler that is nearest to this splitting ratio which is the one with the interaction length of 257 µm. Note that this implied that we use a higher-order coupling process (light couples to and fro once), which is expected to have a reduced spectral bandwidth compared to a 0-th order coupling.
6. Hong-Ou-Mandel interference experiment
For our final quantum experiment of the HOM interference, we realised a novel set-up as depicted in Fig. 6. The setup consists of two main parts. The first one is the source of the single photons generated by a spontaneous parametric down-conversion (PDC) process in a ppKTP waveguide, and the second part is the LNOI BS. Note that this PDC source is a well-established device in our group (see [31,32]), the concrete setup and state preparation of the photons has been reported in [33]. Here, an engineered type-II PDC process generates two indistinguishable pure photons with orthogonal polarisations at a wavelength of 1542.22 nm. The pulsed pump laser has a wavelength of 772.5 nm with a bandwidth of $\approx$ 0.3 nm. We place a broadband spectral filter with a FWHM of 1.8 nm after the ppKTP sample to remove the sinc sidelobes from the joint spectral amplitude function to guarantee spectral decorrelation between and therefore separability of the generated photons. We set the mean photon number of the generated PDC to a regime below 0.01 pairs per pulse to reduce the generation of higher photon components which would reduce the visibility. After the ppKTP sample the two photons are separated with a polarising BS and sent to delay lines. After the delay line each photon is coupled into a polarisation maintaining fiber and those fibers route to the BS setup where we couple the two photons from fibers to free space. The polarisation of the photon from Input 1 is set with a half-wave and quarter-wave plate to TE polarisation ensure indistinguishability. Two mirrors are used to guide the photon to the sample. For Input 2 instead of two mirrors, one mirror and a adjustable prism are used. The prism is used to bring the photons close to each other, because a single aspheric lens is used for the incoupling. After the BS, we collect the photons with another lens and couple them to two standard SMF-28 single mode fibers. These fibers are connected to two SNSPDs with a 70 ns dead time and efficiencies >95 $\%$ which are connected to a time tagger. The efficiency from the beam splitter setup is around 3 $\%$. This value consists of the losses of the chip and the incoupling losses to and from the chip which are below 50 $\%$ for each input and output and the detector efficiency. To measure the HOM dip, we scan the delay line in 1 µm steps for 250 µm. We perform several scans and add up the coincidences, to ensure that long term intensity fluctuations are not affecting the HOM dip. We extract the visibility with a Gaussian fit $c(t) = 1-d \cdot \exp (a\cdot t^2)$ and relating $c_\text {dist} = 1$ and $c_\text {dist} - c_\text {indist} = d$ from Eq. (1). This yields a visibility of ($93.5\pm 0.7$) $\%$ (see Fig. 7), where we did not subtract any background counts. Please note that the data shown in Fig. 7 has been normalised such that the baseline of the Gaussian fit is equal to 1 for better visualisation.
Finally, we calculate the expected maximum visibility. From our experiment (see Fig. 5), we get two different splitting ratios for the coupler with 257 $\mathrm{\mu}$m coupling length, namely 52.1$\%$ and 57.14$\%$ (which corresponds to a transmittivity of 42.86$\%$ for Input b). From these two ratios we extract an average splitting ratio of (54.6$\pm$3.8) $\%$, slightly off from perfect balanced splitting. By using this splitting ratio as a reflectivity in Eq. (2), the HOM visibility is limited to (98.32$\pm$2.8) $\%$. In order to test the source we replaced the LNOI BS with a tunable fibre BS and find a HOM visibility of (98.01$\pm$0.24) $\%$ [33] showing that the HOM interference is not limited by the source in our experiment. Taking into account the visibility of our source and the imperfect splitting ratio of the LNOI coupler, we obtain a expected visibility of (96.36$\pm$2.8) $\%$. However, comparing this to our measured visibility of (93.5$\pm$0.7) $\%$, we have a deviation of 3 $\%$. This could be due to effects that occur in high confined waveguide structures such as hybrid modes which have already been witnessed in LNOI [34]. These hybrid modes can have an influence on the polarisation of the photons which would alter the splitting ratio of the devices and thus reduce the visibility of the dip. However, this effect is challenging to quantify. Note that even though we did not reach the maximal visibility, the measured visibility agrees with the expected one within the uncertainty range. This demonstrates that the material platform does not adversely affect HOM interference.
Fig. 6. Setup for the quantum experiment. The setup consists of two main parts. The first part is the preparation of the single photons and the second part consists of the LNOI BS.
Fig. 7. Measured Hong-Ou-Mandel interference of the signal and idler photons interfered at the LNOI directional coupler. The Gaussian fit $1-0.935\cdot \text {exp}(-0.143 \cdot t^2)$ yields a visibility of ($93.5\pm 0.7$) $\%$.
7. Conclusion
In this paper, we demonstrated HOM interference with telecom photons on LNOI, the missing piece for establishing LNOI as quantum-ready platform for integration. For this, we fabricated a directional coupler based on numerical simulations. After that, we estimated the losses and the coupling behaviour. Finally, we performed a HOM experiment with single photons generated via a PDC process in ppKTP. With a measured visibility of (93.5$\pm$0.7) $\%$ we can conclude that LNOI is a favourable platform for integrated quantum optics. Connecting several of these directional couplers to a sophisticated network and combining it with already shown single photon sources and electro-optical modulators in LNOI opens the possibility for a quantum processor in LNOI.
Funding
Deutsche Forschungsgemeinschaft (Projektnummer 231447078, SFB-Geschäftszeichen TRR142/3-2022, Projekt C11); Max Planck School of Photonics.
Acknowledgment
Laura Padberg and Silia Babel are part of the Max Planck School of Photonics supported by the German Federal Ministry of Education and Research (BMBF), the Max Planck Society, and the Fraunhofer Society.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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