Author: Ronen Shekel
In a previous post, we talked about how periodic poling provides quasi-phase-matching, its various benefits, and the control it provides over different SPDC parameters.
SPDC light is used for numerous applications, such as quantum imaging, quantum communications, and quantum computing. As these applications mature, it becomes increasingly important to have better and stronger control over the properties of the generated quantum states, such as their purity and fidelity. For instance, for some quantum computation or communication applications one would like to generate specific entangled states, such as Bell states or cluster states [1]. However, for a heralded single-photon application, one would like the SPDC process to result in a separable state, since heralding a photon out of an entangled pair will result in a single photon in a mixed state.
A promising approach for achieving such control is to create more sophisticated crystals by further tailoring their poling and realizing aperiodic poling and custom duty cycles. For example, one could create a chirping grating, where the poling interval is linearly varied between the entrance and end facets of the crystal. Such a method has been employed for the generation of an ultrabroad-spectrum in SPDC light [2], achieving a record-breaking narrow Hong-Ou-Mandel (HOM) dip.
Another example of engineering poling is given in [3, 4]. In the usual case, the nonlinearity that the pump pulse experiences is turned on suddenly as the pump enters the crystal and turned off just as suddenly as the pump exits the crystal. This results in sinc side lobes in the joint spectrum amplitude (JSA) of the generated states. What it means is that part of the SPDC photon pairs are generated at a combination of different wavelengths, resulting in different quantum states. Since for high visibility quantum interference and superposition we need photons which are well defined in their physical properties, we need to find an engineering method which will concentrate the generated SPDC photon pairs into one well defined quantum state. Here, it is shown that a special type of domain engineering allows an apodization of the spectrum, the removal of the sinc sidelobes (Fig. 1).
As evident by the large HOM dip visibility, the states generated from this apodised crystal are highly pure and indistinguishable. Such purity and indistinguishability are of utmost importance for advanced photonic technologies, which rely on a high number of successive two-photon interference events.
Having control on the crystal spectral properties is of special interest when generating high-dimensional quantum states and novel entanglement possibilities [6] . Such states are gaining growing interest in recent years due to their higher information capacity and their improved resilience to noise [5]. They come in two flavors: spectral entanglement and spatial entanglement. As opposed to polarization encoding, both cases allow the encoding of high-dimensional information, enabling each photon to carry more information. Encoding in the spectrum enjoys the fact that such states experience virtually no decoherence. Encoding in the spatial domain is attractive because it is easy to control and manipulate using the mature technology of spatial light modulators. In both cases, aperiodic polling, together with optimizing the pump beam that stimulates the SPDC process, has been shown to allow greater control over the generated states.
In [6], a variety of spectrally encoded states, such as Bell states and two-qutrit states, have been generated using domain engineering, along with the modulation of a broadband pulsed pump. Using this method, there is no need to filter the (very few) SPDC photons after the generation process, since shaping the pump and crystal already enables the generation of the desired joint spectrum directly. Specifically, the pump modulation was done via a simple technique, using only passive optical elements such as birefringent wedges and waveplates. In general, the pump spectrum could be shaped even more flexibly using diffraction gratings and spatial light modulators [7].
A similar two-dimensional approach is shown in [8], but in the spatial domain. A detailed physical model, together with a machine learning framework, finds optimal 3-dimensional crystal structures as well as tailored pump shapes that generate arbitrary spatially encoded states. In [9] this has been shown experimentally, generating a spatial Bell state in the Hermite-Gauss basis, by engineering the nonlinear crystal.
Raicol is a world leader in both periodic and aperiodic poling of nonlinear crystals, and provides aperiodically poled KTP crystals (APKTP) that increase the spectral purity and indistinguishability of the emitted photon pairs at telecom wavelengths. We also provide tailored solutions for crystals with aperiodic poling. Please contact us to discuss your application and how we can help you use state-of-the-art crystals to achieve your goals.
[1] Briegel, Hans J., et al. “Measurement-based quantum computation.” Nature Physics 5.1 (2009): 19-26.
[2] Nasr, M.B., Carrasco, S., Saleh, B.E., Sergienko, A.V., Teich, M.C., Torres, J.P., Torner, L., Hum, D.S. and Fejer, M.M., 2008. Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion. Physical review letters, 100(18), p.183601.
[3] Graffitti, F., Barrow, P., Proietti, M., Kundys, D. and Fedrizzi, A., 2018. Independent high-purity photons created in domain-engineered crystals. Optica, 5(5), pp.514-517.
[4] Dosseva, Annamaria, Łukasz Cincio, and Agata M. Brańczyk. “Shaping the joint spectrum of down-converted photons through optimized custom poling.” Physical Review A 93.1 (2016): 013801.
[5] Ecker, Sebastian, Frédéric Bouchard, Lukas Bulla, Florian Brandt, Oskar Kohout, Fabian Steinlechner, Robert Fickler et al. “Overcoming noise in entanglement distribution.” Physical Review X 9, no. 4 (2019): 041042.
[6] Shukhin, Anatoly, Inbar Hurvitz, Sivan Trajtenberg-Mills, Ady Arie, and Hagai Eisenberg. “Two-dimensional control of a biphoton joint spectrum.” Optics Express 32, no. 6 (2024): 10158-10174.
[7] Ansari, Vahid, et al. “Heralded generation of high-purity ultrashort single photons in programmable temporal shapes.” Optics express 26.3 (2018): 2764-2774.
[8] Rozenberg, Eyal, Aviv Karnieli, Ofir Yesharim, Joshua Foley-Comer, Sivan Trajtenberg-Mills, Daniel Freedman, Alex M. Bronstein, and Ady Arie. “Inverse design of spontaneous parametric downconversion for generation of high-dimensional qudits.” Optica 9, no. 6 (2022): 602-615.
[9] Yesharim, Ofir, Shaul Pearl, Joshua Foley-Comer, Irit Juwiler, and Ady Arie. “Direct generation of spatially entangled qudits using quantum nonlinear optical holography.” Science Advances 9, no. 8 (2023): eade7968.
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