Many proposals for solid-state photonic implementations of quantum information processing utilize high-quality optical resonators to achieve strong coupling between guided fields and heterogeneously incorporated qubits. Given the practical difficulty of accurately placing quantum dots, vacancy centers, or other such atomlike emitters throughout a complex nanophotonic circuit, it would be natural to consider whether high-quality resonators could be used in conjunction with bulk optical nonlinearities to create optically coupled qubit degrees of freedom via lithographic patterning of a homogeneous medium. A recent limit theorem for quantum stochastic differential equations can be used to prove rigorously that this should be possible, in principle, using resonators incorporating a strongly Kerr-nonlinear, ${\ensuremath{\chi}}^{(2)}$-nonlinear, or two-photon-absorbing material with very low loss at the fundamental optical wavelength.
Many proposals for solid-state photonic implementations of quantum information processing utilize high-quality optical resonators to achieve strong coupling between guided fields and heterogeneously incorporated qubits. Given the practical difficulty of accurately placing quantum dots, vacancy centers, or other such atomlike emitters throughout a complex nanophotonic circuit, it would be natural to consider whether high-quality resonators could be used in conjunction with bulk optical nonlinearities to create optically coupled qubit degrees of freedom via lithographic patterning of a homogeneous medium. A recent limit theorem for quantum stochastic differential equations can be used to prove rigorously that this should be possible, in principle, using resonators incorporating a strongly Kerr-nonlinear, \ensuremathχ(2)-nonlinear, or two-photon-absorbing material with very low loss at the fundamental optical wavelength.
A single semiconductor quantum dot that is strongly coupled to a photonic crystal nanocavity yields optical nonlinearities at the single photon level. The promise of quantum information processing is driving developments in several different physical implementations. Photons are attractive as carriers of quantum information be-cause they can travel long distances without losing their infor-mation through interactions with their environment. However, their passive nature can be a problem in applications such as the construction of logic gates, where it is necessary for two or more photons to interact. This interaction requires a nonlinear optical medium. Particularly strong nonlinearities are achieved when photons drive an emitter near its resonance frequency, and this nonlinearity is even greater if the photon is confined near the emitter in an optical cavity.
Quantum optical nonlinearities have received growing interest for their key role in quantum information science, quantum simulations, and other quantum technologies. Unfortunately, most materials exhibit very weak optical nonlinearities, virtually non-existent at the single photon level. Nano-scale optical resonators can store light for a long period of time in cubic-wavelength scale volume, and thus present a unique opportunity to enhance the light-matter interaction. Additionally, breakthroughs in materials science allow us to engineer inherently strong nonlinear materials. In this talk, I will present our theoretical and experimental efforts in nonlinear nanophotonics, integrated with atomically thin 2D materials, specifically transition metal dichalcogenides and solution-processed quantum dots. By confining both light and matter in the wavelength scale, we aim to reach the nonlinear regime, where single photons start repelling each other. I will also elaborate on the possibility of scaling this platform to multiple single photon quantum nodes with the possibility of creating a correlated quantum fluid of light.
Quantum optical nonlinearities have received growing interest for their key role in quantum information science, quantum simulations, and other quantum technologies. Unfortunately, most materials exhibit very weak optical nonlinearities, virtually non-existent at the single photon level. Nano-scale optical resonators can store light for a long period of time in cubic-wavelength scale volume, and thus present a unique opportunity to enhance the light-matter interaction. Additionally, breakthroughs in materials science allow us to engineer inherently strong nonlinear materials. In this talk, I will present our theoretical and experimental efforts in nonlinear nanophotonics, integrated with atomically thin 2D materials, specifically transition metal dichalcogenides and solution-processed quantum dots. By confining both light and matter in the wavelength scale, we aim to reach the nonlinear regime, where single photons start repelling each other. I will also elaborate on the possibility of scaling this platform to multiple single photon quantum nodes with the possibility of creating a correlated quantum fluid of light.
The recent advent of optical metasurfaces, ultra-thin structures composed of nanoresonators facilitating strong light concentration [1–3], opens the path towards efficient \nfrequency conversion [4–7] in a material thousand times thinner than a human hair [8]. \nThere is a remarkable capacity to individually shape each nanoresonator of the metasurface to spatially and spectrally control the conversion process with unprecedented \nnanoscale resolution, facilitating an ultimate flexibility to selectively convert, focus, \nand image different colours with a single metasurface. The strong enhancement of the \nnonlinear processes in dielectric nanoresonators is largely due to the absence of material \nabsorption and the excitation of Mie-type bulk resonances [2]. The highest conversion \nefficiency to date has been achieved employing III-V semiconductor nanostructures, \nsuch as AlGaAs which is a non-centrosymmetric material with high quadratic nonlinear \nsusceptibility. In particular, second-harmonic generation efficiencies up to 10−4 have \nbeen recently demonstrated [8–12], six orders of magnitude higher than in plasmonics. \nSuch capabilities can make an immense fundamental and practical impact, including \nthe quantum state generation in nonlinear metasurfaces as we discuss in this chapter. \nThe quantum state of correlated photon-pairs is the essential building block for photon entanglement [13, 14], which underpins many quantum applications, including secure networks, enhanced measurement and lithography, and quantum information processing [15]. One of the most versatile techniques for the generation of correlated photons is the process of spontaneous parametric down-conversion (SPDC) [16, 17], see \nFig. 1. It allows for an arbitrary choice of energy and momentum correlations between \nthe generated photons, robust operation at room temperature, as well as for spatial and \ntemporal coherence between simultaneously pumped multiple SPDC sources. Alternative approaches based on atom-like single photon emitters, such as solid-state fluorescent atomic defects [18], quantum dots [19, 20], and 2D host materials [21, 22], have \nreached a high degree of frequency indistinguishability, purity and brightness [19, 20]. \nHowever, this comes with the expense of operation at cryogenic temperatures and lack \nof spatial coherence between multiple quantum emitters. These features might limit \npossible applications and reduce the potential for device scalability. Furthermore, the \nsmall size of the atomic sources often requires complex schemes aimed at coupling to \noptical nanoantennas and improving the photon extraction efficiency [21]. \nThe miniaturization of SPDC quantum-light sources to micro and nanoscale dimensions is a continuing quest, as it enables denser integration of functional quantum \ndevices. Traditionally, bulky cm-sized crystals were utilized for SPDC, entailing the \ndifficulty of aligning multiple optical elements after the SPDC crystal, while offering \nrelatively low photon-pair rates [17]. As a first step of miniaturization, SPDC was \nrealized in low-index-contrast waveguides, which allowed confining light down to several square micrometers transversely to the propagation direction, significantly enhancing the conversion efficiency [23]. However, this approach still requires centimetres \nof propagation length, which makes the on-chip integration with other elements challenging [24]. The introduction of high-index contrast waveguides and ring resonators \nallowed for shrinking the sizes necessary for SPDC to millimetres [25], and to tens \nof micrometers [26]. However, further miniaturisation down to the metasurfaces composed of nanoresonators requires conceptually different approaches.
We study theoretically the interaction between two photons in a nonlinear cavity. The photons are absorbed into the cavity by an effective tuning of its input-output coupling via external control of a coupling to a second, strongly output-coupled cavity mode. Such ``dynamically coupled'' cavities, which can be implemented using bulk ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ nonlinearities, enable incoming photon wave packets to be absorbed into the cavity with high fidelity when the duration of the control is similar to that of the wave packets. Further, this configuration can be used to avoid limitations in the photon-photon interaction time set by the delay-bandwidth product of passive cavities and enables the elimination of wave-packet distortions caused by dispersive cavity transmission and reflection. We consider three kinds of nonlinearities, two arising from ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ materials and one due to an interaction with a two-level emitter. To analyze the input and output of few-photon wave packets, we use a Schr\"odinger-picture formalism in which traveling-wave fields are discretized into infinitesimal time bins. We suggest that dynamically coupled cavities provide a very useful tool for improving the performance of quantum devices relying on cavity-enhanced light-matter interactions such as single-photon sources and atomlike quantum memories with photon interfaces. As an example, we present simulation results showing that high-fidelity two-qubit entangling gates may be constructed using any of the considered nonlinear interactions.
A central goal in photonic quantum information processing is the ability to perform high-fidelity logic gates between multiple optical qubits. Here, we present our recent theoretical work on using optical nonlinearities to implement controlled-phase gates between two optical qubits. Our approach is based on using dynamically coupled cavities to convert photons travelling in a waveguide into highly confined cavity modes. This conversion enables very strong interactions between photons in quasi-monochromatic modes, which enables high fidelity gates. We will discuss gate protocols based on second- and third order nonlinear materials as well as interactions with two-level emitters.