Abstract
Creating miniature chip scale implementations of optical quantum information protocols is a dream for many in the quantum optics community. This is largely because of the promise of stability and scalability. Here we present a monolithically integratable chip architecture upon which is built a photonic device primitive called a Bragg reflection waveguide (BRW). Implemented in gallium arsenide, we show that, via the process of spontaneous parametric down conversion, the BRW is capable of directly producing polarization entangled photons without additional path difference compensation, spectral filtering or post-selection. After splitting the twin-photons immediately after they emerge from the chip, we perform a variety of correlation tests on the photon pairs and show non-classical behaviour in their polarization. Combined with the BRW's versatile architecture our results signify the BRW design as a serious contender on which to build large scale implementations of optical quantum processing devices.
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Introduction
The use of non-linear optical effects has lead to an era of high-level quantum experiments, where quantum entanglement between pairs of photons can be achieved with very high count rates, quality and flexibility. It has relied heavily on a photon pair producing process called spontaneous parametric down conversion (SPDC)1,2, where under conservation of energy and momentum, a “pump” photon spontaneously decays, leaving a pair of daughter photons in its place. SPDC is now easily achieved using lasers and the same materials and principles involved in the more classical processes of sum frequency and second harmonic generation.
More challenging has been the creation of entangled photon pairs in a degree of freedom, in our case polarization, that is uncorrelated with other aspects of the pair producing process3. The challenge is indirectly tied to the very same principles and materials that facilitate the creation of photon pairs in the first place. Birefringence, which makes phase matching the pump and daughter photons an easy task, also tends to provide distinguishing information that hinders the production of entanglement. Despite this natural limitation, bulk-crystal photon sources have created entanglement via clever interference techniques and often include additional compensating optics4. While some outstanding results have been achieved5, too often the interferometers and compensation procedures are unstable, requiring daily maintenance, strict environmental conditions, or complicated automation. It is generally thought that, to achieve larger scale demonstrations of optical quantum information protocols, the techniques developed to date should be integrated in some sense6,7 – a so called optical bench on a chip.
Semiconductors are an obvious platform for integration, but the material physics are vastly different from what is found in traditional SPDC based resources of quantum information. Recently publicized as a strong source of photon pairs8 the gallium arsenide (GaAs) based Bragg reflection waveguide (BRW) was shown to have a distinct advantage over other semiconductor sources, due largely to its monolithic architecture – its layered design underpinning many photonic devices. Using the same techniques as employed in bulk-crystal sources9, it has recently been shown that the BRW can deliver polarization entangled photons through the use of post-selection. Here we show a significant advantage by demonstrating the intrinsic capability of the BRW to directly produce polarization entangled photon pairs, without any additional interferometry, spectral filtering, compensation or post-selection. Combined with the fact that the structure can be its own pump laser10, our results set the stage for the BRW to be a self-contained room temperature resource of entanglement occupying no more than a few square millimeters of chip real-estate.
Built on a GaAs substrate, the BRW consists entirely of layers of GaAs containing different amounts of aluminum. A subset of the layers function as Bragg reflectors, one lying below and one on top of a core region where light can be guided. A schematic is shown in Fig. 1(a). In addition to optical modes guided via the process of total internal reflection (TIR), the reflectors confine modes of light to the core region through interference. Aptly named, the dispersion characteristics of Bragg modes are mostly independent from those of the more traditional TIR modes. This degree of freedom allows the designer to use Bragg interference to create structures where the daughter TIR modes of SPDC are perfectly phase matched to the pump Bragg modes11 – a technique called modal phase matching.
Modal phase matching based on Bragg reflection has important ramifications for integrated optical quantum devices that employ SPDC. Not only does the BRW allow for the production of photon pairs in non-birefringent semiconductors like GaAs8, but the detrimental effects of any residual birefringence on the production of polarization entangled photons are minimal and design related. In fact, the GaAs based BRW can be engineered such that the optical properties of orthogonally polarized TIR modes are identical. Specifically, inherent polarization entanglement becomes possible for frequency non-degenerate co-linear type-II modal phase matching where daughter photons are generated at different frequencies but guaranteed to have orthogonal polarization. Because there is little to no birefringence, the daughter photons can emerge orthogonally polarized via two different decay “channels”: In one channel, there is a probability amplitude AHV (ω1, ω2) where the higher (lower) frequency photon is horizontally (vertically) polarized. Alternatively, there is a probability amplitude AV H (ω1, ω2) where the higher (lower) frequency photon is vertically (horizontally) polarized. There is no need for compensation of any kind and since the photons within a pair always have different frequencies, each pair can be easily split into distinct spatial arms, which we call signal and idler, by using a dichroic beam splitter (DBS). The expected state is polarization entangled and written as:
where H(V) symbolizes horizontal(vertical) polarization, ω1 and ω2 represent the angular frequency of the photon and γ accounts for a relative phase which can be controlled by placing and tilting a birefringent element such as a quarter wave plate (QWP) in one of either the signal or idler arm. Note that the sum, AHV (ω1, ω2) + AV H (ω1, ω2), is proportional to the joint spectral amplitude of the photon pairs generated by the BRW and that the index interchange in the second term of Eq. 1 arises from the DBS transformation, which collapses the entire spectral output of the BRW to either the signal or idler arm. For a more in depth analysis of the generated quantum states in the presence of a DBS, please refer to the Supplementary Information.
Results
Two-photon polarization entanglement quality is inexorably linked to the absence of any information that might determine the polarization of either photon before it is measured. In our case, it is pre-dominantly limited by the amount of spectral overlap between AHV (ω1, ω2) and AV H (ω2, ω1). For this reason we measured the spectrum of both H and V polarized photons produced by the BRW for a range of pump wavelengths (λp = 776–778 nm). Details of this measurement can be found in the Methods section. The results, depicted in Fig. 2, show clear similarities between the two orthogonally polarized spectra. Importantly, they point to an inherent ambiguity in determining the polarization of any one photon by acquiring knowledge of its wavelength. Our observations imply that, for our experimental setup, a pump frequency setting of λp ≈ 777.9 nm is optimal for producing frequency non-degenerate polarization entangled photons.
It is worth emphasizing that such spectral evidence of two different decay channels is in contradistinction to the spectra of typical type-II SPDC where, when pumping away from degeneracy, only a single decay channel is observed. In those sources, the underlying crystal lattice asymmetry yields significant birefringence that prevents a second decay channel from being simultaneously phase matched. Here however, the absence of lattice asymmetry in GaAs (no birefringence) means that fundamentally, where an H-V signal-idler pair can have the correct phase matching, so can a V-H pair. From a polarization entanglement perspective, this is an extremely desirable phase matching scenario. The BRW design is therefore advantageous because it not only solves the historically challenging problem of phase matching in non birefringent media, but the possibility of entanglement emerges as a naturally occurring byproduct.
In order to test the capabilities of the BRW to produce frequency non-degenerate polarization entanglement we subsequently performed two standard tests. The first measured entanglement visibilities, verifying that we indeed observe a coherence between the photon pairs. The second involved a detailed examination of the polarization state by way of quantum state tomography. Details are provided in the Methods section.
Entanglement visibility measurements illuminate the type of nonclassical polarization correlations that are expected. Pair count rates were recorded as follows: A basis or reference frame was chosen by the polarization analyzer in the signal arm while the idler arm made many polarization measurements in continuous fashion. For a polarization entangled state, pair count rates are expected to behave sinusoidally in more than one basis as the idler arm's polarization analyzer changes. For the “HV” basis, visibilities are shown in Fig. 3(a). Fig. 3(b) displays many visibilities for the anti-diagonal basis and exemplifies our ability to control the phase term γ of Eq. 1. As alluded to earlier, birefringence was introduced in the idler arm via the insertion of an additional QWP. By tilting the QWP, the distance the idler photon traveled inside the birefringent material was altered, introducing an additional polarization dependent phase. This changed the polarization correlations between the signal and idler photon. For a maximally entangled pure state (e.g. ), the expected behaviour is the conversion of a sinusoid with perfect visibility (minima = 0) to an inverted sinusoid and back again, going through a period of flat uncorrelated behaviour when γ = π/2. That the pair count rates do not approach the noise floor in the experiment for all basis choices is mainly a result of the imperfect overlap between the spectra shown in Fig. 2. Additional arguments for the reduced visibilities are put forth in the discussion. Nonetheless, the existence of significant interference for all basis choices is consistent with the predictions of Eq. (1) and solidifies the observation of polarization entanglement emerging directly from the BRW.
To fully quantify the correlations of the photon pair generated by the BRW, quantum state estimation was performed via tomographic measurements12 and the resulting density matrix was reconstructed using the maximum likelihood method13. The Methods section explains the measurements in more detail. The result is shown in Fig. 4. Off-diagonal elements are clearly visible, evidence of the non-classical nature of the biphoton state. From the density matrix, various indicators of the entanglement quality can be computed. The concurrence, an entanglement monotone14,15, is found to be 0.52, while the fidelity15 with the expected maximally entangled state is computed to be 0.83. These measures provide further proof that the BRW is capable of inherently producing polarization entanglement.
Discussion
The BRW examined here was not intentionally fabricated to produce entangled photons. Designed to optimize pair production and upconversion efficiency16, the spectral overlap is not ideal and degrades the intrinsic entanglement generation capability. An interesting asymmetry observed in this work is the level of the minima measured in the H/V basis. The origins of this small but appreciable H/H background are likely due to residual pump fluorescence and/or polarization hybridization in the V-polarized down converted mode. Nonetheless, these effects are not fundamental limitations, but arise from the current design and fabrication method. Future samples that are optimized to produce entanglement17 promise to avoid this behaviour.
Despite the many material benefits that GaAs offers (order of magnitude stronger than typical crystals, large transparency window, monolithicity, integratability etc.), it has remained a prized but elusive non-linear material. Entirely due to its challenging phase matching requirements, GaAs based photon sources have been overshadowed in the quantum community by materials such as, lithium niobate, pottasium titanyl phosphate and barium borate which are easier to phase match. Indeed, in juxtaposition, efforts have been aimed at integrating these materials18,19,20. As an alternative to GaAs, high quality integrated quantum photonic circuitry has been developed in silica7,21, but as an entangled photon source, its optical non-linearity is weaker22 and still has its challenges to become a fully integrated platform viable for quantum processes.
For GaAs, techniques have been developed to solve the phase matching problem such as form-birefringence23; out of plane pumping24; or quasi-phase matching by traditional periodic crystal inversion25. Further, out of plane pumping has the benefit of producing counter-propagating entangled photons26. But while these designs are promising, most are not truly monolithic and are at greater risk of becoming encumbered with the complications of integration with other photonic components.
In contrast, the BRW design has now shown to be capable of solving all of the above concerns. It is favourable for becoming its own pump laser10, it is efficient at producing pairs8 and here we demonstrate a very distinct “quantum” opportunity. Gained by a clever modal phase matching technique that exploits mature nanofabrication technology, the GaAs based BRW can produce useful polarization entangled photons directly and without the need for any post selection, compensation or interferometry. Ironically, its success is tied to the difficulty in phase matching – GaAs's lack of birefringence turns out to be a virtue for the production of on chip entanglement. Combined with the many aforementioned benefits that GaAs has to offer, these latest results show that the BRW platform should be seriously considered among the integrated quantum photonics community as one of the most promising platforms on which to build integrated optical quantum information processing devices.
The authors acknowledge funding from NSERC (CGS, QuantumWorks, Discovery, USRA), Ontario Ministry of Research and Innovation (ERA program and research infrastructure program), CIFAR, Industry Canada, CFI and CMC Microsystems. P. Kolenderski acknowledges support from the Mobility Plus project financed by the Polish Ministry of Science and Higher Education.
Methods
Device description and experimental setup
The 3.8 μm wide, 2.2 mm long ridge BRW was fabricated via metal-organic chemical vapour deposition. Details of the epitaxy can be found in Ref.27, where it is referred to as BRW1. The waveguide was placed into an objectively coupled “end-fire rig”8 and pumped with horizontally polarized light at a wavelength λp and power, P. The light was focussed onto the front facet and directed into the core region of the BRW. Output light emerging from the core at the back facet was filtered to remove the pump before being collected for measurement.
For the single photon spectrum measurements, P was approximately 20–30 mW. The output was transmitted through a polarizing beam splitter (PBS) separating the light into distinct H and V ports. Individually, both output ports were sent into a Czerny-Turner type monochromator equipped with a novel, high timing resolution, free space InGaAs/InP single photon avalanche diode28. Spectra for both polarizations were obtained for the range of CW-pump central frequencies from λp = 776–778 nm in increments of about 0.1–0.2 nm.
To characterize polarization entanglement, P was set to approximately 1.2 mW and the PBS was replaced by a DBS with a central wavelength λ ≈ 1560 nm and a width of ≈ 10 nm. The pump wavelength was set to λ = 777.9 nm, which produced photon pairs via SPDC with wavelengths near λ = 1537 (signal) nm and λ = 1575 nm (idler). Lower energy (λi > 1560 nm) idler photons were transmitted, while higher energy (λs < 1560 nm) signal photons were reflected. A polarization analyzer, consisting of a QWP, a half wave plate (HWP) and a linear sheet polarizer, was placed in each of the signal and idler arms. An additional QWP, which could be tilted, was placed in the idler arm to control the relative phase γ between HV and VH pairs. Each arm collected photons into a multi-mode fiber connected to a single photon detector (id201, idQuantique). The signal arm detector was internally triggered at 1 MHz, open for 20 ns and set for 10% quantum efficiency. Count rates were approximately 7000 ± 500 counts per second (cps). The idler arm – gated by counts recorded in the signal arm – was set at 15% efficiency and the gate time was set to 5 ns. Optical and electronic delays were adjusted so that the arrival of the idler photon coincided with the electronic gate signal. Thus, idler count rates were effectively pair count rates and were anywhere from 7–100 cps.
For the tomographic reconstruction of the state, an over-complete set of 36 polarization measurements were performed; setting the polarization analyzers for every combination of H,V,anti-diagonal, diagonal, left-circular and right-circular. Each measurement had a duration of 2 minutes. Background count rates were obtained by changing the electronic delay in the idler arm to ensure the observation of random background events.
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Contributions
A.S.H., D.P. and P.A. designed, supplied and characterized the sample. R.T.H., P.K., G.W. and T.J. led the experimental design. R.T.H. performed the experiment. R.T.H. and P.K. performed data analysis. R.T.H. wrote the main manuscript text. R.T.H. and P.K. performed and wrote the analysis. R.T.H., P.K., G.W. and T.J. advised and interpreted the data. L.H., S.V. and J.S. assisted with interpretation and data analysis. C.S., A.D.F. and A.T. supplied detection equipment. All authors reviewed the manuscript.
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Supplementary Information
Entanglement Analysis and SPDC Efficiency
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Horn, R., Kolenderski, P., Kang, D. et al. Inherent polarization entanglement generated from a monolithic semiconductor chip. Sci Rep 3, 2314 (2013). https://doi.org/10.1038/srep02314
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DOI: https://doi.org/10.1038/srep02314
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