Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization.

Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong-Ou-Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

Spectral Hong-Ou-Mandel Effect between a Heralded Single-Photon State and a Thermal Field: Multiphoton Contamination and the Nonclassicality Threshold.

The Hong-Ou-Mandel (HOM) effect is crucial for quantum information processing, and its visibility determines the system's quantum-classical characteristics. In an experimental and theoretical study of the spectral HOM effect between a thermal field and a heralded single-photon state, we demonstrate that the HOM visibility varies dependent on the relative photon statistics of the interacting fields. Our findings reveal that multiphoton components in a heralded state get engaged in quantum interference with a thermal field, resulting in improved visibilities at certain mean photon numbers. We derive a theoretical relationship for the HOM visibility as a function of the mean photon number of the thermal field and the thermal part of the heralded state. We show that the nonclassicality degree of a heralded state is reflected in its HOM visibility with a thermal field; our results establish a lower bound of 41.42% for the peak visibility, indicating the minimum assignable degree of nonclassicality to the heralded state. This research enhances our understanding of the HOM effect and its application to high-speed remote secret key sharing, addressing security concerns due to multiphoton contamination in heralded states.

Single-Photon Level Dispersive Fourier Transform: Ultrasensitive Characterization of Noise-Driven Nonlinear Dynamics.

Dispersive Fourier transform is a characterization technique that allows directly extracting an optical spectrum from a time domain signal, thus providing access to real-time characterization of the signal spectrum. However, these techniques suffer from sensitivity and dynamic range limitations, hampering their use for special applications in, e.g., high-contrast characterizations and sensing. Here, we report on a novel approach to dispersive Fourier transform-based characterization using single-photon detectors. In particular, we experimentally develop this approach by leveraging mutual information analysis for signal processing and hold a performance comparison with standard dispersive Fourier transform detection and statistical tools. We apply the comparison to the analysis of noise-driven nonlinear dynamics arising from well-known modulation instability processes. We demonstrate that with this dispersive Fourier transform approach, mutual information metrics allow for successfully gaining insight into the fluctuations associated with modulation instability-induced spectral broadening, providing qualitatively similar signatures compared to ultrafast photodetector-based dispersive Fourier transform but with improved signal quality and spectral resolution (down to 53 pm). The technique presents an intrinsically unlimited dynamic range and is extremely sensitive, with a sensitivity reaching below the femtowatt (typically 4 orders of magnitude better than ultrafast dispersive Fourier transform detection). We show that this method can not only be implemented to gain insight into noise-driven (spontaneous) frequency conversion processes but also be leveraged to characterize incoherent dynamics seeded by weak coherent optical fields.

Shaping the spectral correlation of bi-photon quantum frequency combs by multi-frequency excitation of an SOI integrated nonlinear resonator.

We reveal the generation of a broadband (> 1.9 THz) bi-photon quantum frequency comb (QFC) in a silicon-on-insulator (SOI) Fabry-Pérot micro-cavity and the control of its spectral correlation properties. Correlated photon pairs are generated through three spontaneous four-wave mixing (SFWM) processes by using a co-polarized bi-chromatic coherent input with power P1 and P2 on adjacent resonances of the nonlinear cavity. Adjusting the spectral power ratio r = P1/(P1 + P2) allows control over the influence of each process leading to an enhancement of the overall photon pair generation rate (PGR) µ(r) by a maximal factor of µ(r = 0.5)/µ(r = 0) ≈ 1.5, compared to the overall PGR provided by a single-pump configuration with the same power budget. We demonstrate that the efficiency aND of the non-degenerate excitation SFWM process (NDP) doubles the efficiency a1 ≈ a2 of the degenerate excitation SFWM processes (DP), showing a good agreement with the provided model.

AlGaAs-on-insulator waveguide for highly efficient photon-pair generation via spontaneous four-wave mixing.

We report on the generation of correlated photon pairs in AlGaAs-on-insulator (AlGaAs-OI) waveguides through nonlinear spontaneous four-wave-mixing (SFWM). Our measurements reveal an SFWM pair generation efficiency of ∼0.096×1012pairs/(sW2) at a wavelength of 1550 nm. This is one of the highest efficiencies achieved to date for integrated SFWM sources. A maximal coincidence-to-accidental ratio of ∼122 is measured. A spectral characterization of the device's pair emission at the quantum level demonstrates a broad generation bandwidth of 2.0 THz, which is important for frequency multiplexing applications. Our results indicate that AlGaAs-OI is an efficient material platform for integrated quantum photonics at telecom wavelengths.

Two-photon quantum interference and entanglement at 2.1 µm.

Quantum-enhanced optical systems operating within the 2- to 2.5-µm spectral region have the potential to revolutionize emerging applications in communications, sensing, and metrology. However, to date, sources of entangled photons have been realized mainly in the near-infrared 700- to 1550-nm spectral window. Here, using custom-designed lithium niobate crystals for spontaneous parametric down-conversion and tailored superconducting nanowire single-photon detectors, we demonstrate two-photon interference and polarization-entangled photon pairs at 2090 nm. These results open the 2- to 2.5-µm mid-infrared window for the development of optical quantum technologies such as quantum key distribution in next-generation mid-infrared fiber communication systems and future Earth-to-satellite communications.

Highly reconfigurable hybrid laser based on an integrated nonlinear waveguide.

The ability of laser systems to emit different adjustable temporal pulse profiles and patterns is desirable for a broad range of applications. While passive mode-locking techniques have been widely employed for the realization of ultrafast laser pulses with mainly Gaussian or hyperbolic secant temporal profiles, the generation of versatile pulse shapes in a controllable way and from a single laser system remains a challenge. Here we show that a nonlinear amplifying loop mirror (NALM) laser with a bandwidth-limiting filter (in a nearly dispersion-free arrangement) and a short integrated nonlinear waveguide enables the realization and distinct control of multiple mode-locked pulsing regimes (e.g., Gaussian pulses, square waves, fast sinusoidal-like oscillations) with repetition rates that are variable from the fundamental (7.63 MHz) through its 205th harmonic (1.56 GHz). These dynamics are described by a newly developed and compact theoretical model, which well agrees with our experimental results. It attributes the control of emission regimes to the change of the NALM response function that is achieved by the adjustable interplay between the NALM amplification and the nonlinearity. In contrast to previous square wave emissions, we experimentally observed that an Ikeda instability was responsible for square wave generation. The presented approach enables laser systems that can be universally applied to various applications, e.g., spectroscopy, ultrafast signal processing and generation of non-classical light states.

Universal N-Partite d-Level Pure-State Entanglement Witness Based on Realistic Measurement Settings.

Entanglement witnesses are operators that are crucial for confirming the generation of specific quantum systems, such as multipartite and high-dimensional states. For this reason, many witnesses have been theoretically derived which commonly focus on establishing tight bounds and exhibit mathematical compactness as well as symmetry properties similar to that of the quantum state. However, for increasingly complex quantum systems, established witnesses have lacked experimental achievability, as it has become progressively more challenging to design the corresponding experiments. Here, we present a universal approach to derive entanglement witnesses that are capable of detecting the presence of any targeted complex pure quantum system and that can be customized towards experimental restrictions or accessible measurement settings. Using this technique, we derive experimentally optimized witnesses that are able to detect multipartite d-level cluster states, and that require only two measurement settings. We present explicit examples for customizing the witness operators given different realistic experimental restrictions, including witnesses for high-dimensional entanglement that use only two-dimensional projection measurements. Our work enables us to confirm the presence of probed quantum states using methods that are compatible with practical experimental realizations in different quantum platforms.

Second-harmonic generation in AlGaAs-on-insulator waveguides.

Second-harmonic generation is demonstrated in AlGaAs-on-insulator waveguides at telecom wavelengths. Using this material platform, a maximum internal normalized efficiency of 1202±55% W-1 cm-2 is achieved for a 100 fs pulsed excitation wavelength at 1560 nm. This finding is important towards enabling new chip-scale devices for sensing, metrology, and quantum optics.

Customizing supercontinuum generation via on-chip adaptive temporal pulse-splitting.

Modern optical systems increasingly rely on complex physical processes that require accessible control to meet target performance characteristics. In particular, advanced light sources, sought for, for example, imaging and metrology, are based on nonlinear optical dynamics whose output properties must often finely match application requirements. However, in these systems, the availability of control parameters (e.g., the optical field shape, as well as propagation medium properties) and the means to adjust them in a versatile manner are usually limited. Moreover, numerically finding the optimal parameter set for such complex dynamics is typically computationally intractable. Here, we use an actively controlled photonic chip to prepare and manipulate patterns of femtosecond optical pulses that give access to an enhanced parameter space in the framework of supercontinuum generation. Taking advantage of machine learning concepts, we exploit this tunable access and experimentally demonstrate the customization of nonlinear interactions for tailoring supercontinuum properties.

Generation and Coherent Control of Pulsed Quantum Frequency Combs.

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

Multichannel phase-sensitive amplification in a low-loss CMOS-compatible spiral waveguide.

We investigate single-channel and multichannel phase-sensitive amplification (PSA) in a highly nonlinear, CMOS-compatible spiral waveguide with ultralow linear and negligible nonlinear losses. We achieve a net gain of 10.4 dB and an extinction ratio of 24.6 dB for single-channel operation, as well as a 5 dB gain and a 15 dB extinction ratio spanning over a bandwidth of 24 nm for multiple-channel operation. In addition, we derive a simple analytic solution that enables calculating the maximum phase-sensitive gain in any Kerr medium featuring linear and nonlinear losses. These results not only give a clear guideline for designing PSA-based amplifiers but also show that it is possible to implement both optical regeneration and amplification in a single on-chip device.

Practical system for the generation of pulsed quantum frequency combs.

The on-chip generation of large and complex optical quantum states will enable low-cost and accessible advances for quantum technologies, such as secure communications and quantum computation. Integrated frequency combs are on-chip light sources with a broad spectrum of evenly-spaced frequency modes, commonly generated by four-wave mixing in optically-excited nonlinear micro-cavities, whose recent use for quantum state generation has provided a solution for scalable and multi-mode quantum light sources. Pulsed quantum frequency combs are of particular interest, since they allow the generation of single-frequency-mode photons, required for scaling state complexity towards, e.g., multi-photon states, and for quantum information applications. However, generation schemes for such pulsed combs have, to date, relied on micro-cavity excitation via lasers external to the sources, being neither versatile nor power-efficient, and impractical for scalable realizations of quantum technologies. Here, we introduce an actively-modulated, nested-cavity configuration that exploits the resonance pass-band characteristic of the micro-cavity to enable a mode-locked and energy-efficient excitation. We demonstrate that the scheme allows the generation of high-purity photons at large coincidence-to-accidental ratios (CAR). Furthermore, by increasing the repetition rate of the excitation field via harmonic mode-locking (i.e. driving the cavity modulation at harmonics of the fundamental repetition rate), we managed to increase the pair production rates (i.e. source efficiency), while maintaining a high CAR and photon purity. Our approach represents a significant step towards the realization of fully on-chip, stable, and versatile sources of pulsed quantum frequency combs, crucial for the development of accessible quantum technologies.

On-chip generation of high-dimensional entangled quantum states and their coherent control.

Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.

Experimental Generation of Riemann Waves in Optics: A Route to Shock Wave Control.

We report the first observation of Riemann (simple) waves, which play a crucial role for understanding the dynamics of any shock-bearing system. This was achieved by properly tailoring the phase of an ultrashort light pulse injected into a highly nonlinear fiber. Optical Riemann waves are found to evolve in excellent quantitative agreement with the remarkably simple inviscid Burgers equation, whose applicability in physical systems is often challenged by viscous or dissipative effects. Our method allows us to further demonstrate a viable novel route to efficiently control the shock formation by the proper shaping of a laser pulse phase. Our results pave the way towards the experimental study, in a convenient benchtop setup, of complex physical phenomena otherwise difficult to access.

Generation of multiphoton entangled quantum states by means of integrated frequency combs.

Complex optical photon states with entanglement shared among several modes are critical to improving our fundamental understanding of quantum mechanics and have applications for quantum information processing, imaging, and microscopy. We demonstrate that optical integrated Kerr frequency combs can be used to generate several bi- and multiphoton entangled qubits, with direct applications for quantum communication and computation. Our method is compatible with contemporary fiber and quantum memory infrastructures and with chip-scale semiconductor technology, enabling compact, low-cost, and scalable implementations. The exploitation of integrated Kerr frequency combs, with their ability to generate multiple, customizable, and complex quantum states, can provide a scalable, practical, and compact platform for quantum technologies.

Cross-polarized photon-pair generation and bi-chromatically pumped optical parametric oscillation on a chip.

Nonlinear optical processes are one of the most important tools in modern optics with a broad spectrum of applications in, for example, frequency conversion, spectroscopy, signal processing and quantum optics. For practical and ultimately widespread implementation, on-chip devices compatible with electronic integrated circuit technology offer great advantages in terms of low cost, small footprint, high performance and low energy consumption. While many on-chip key components have been realized, to date polarization has not been fully exploited as a degree of freedom for integrated nonlinear devices. In particular, frequency conversion based on orthogonally polarized beams has not yet been demonstrated on chip. Here we show frequency mixing between orthogonal polarization modes in a compact integrated microring resonator and demonstrate a bi-chromatically pumped optical parametric oscillator. Operating the device above and below threshold, we directly generate orthogonally polarized beams, as well as photon pairs, respectively, that can find applications, for example, in optical communication and quantum optics.

Integrated frequency comb source of heralded single photons.

We report an integrated photon pair source based on a CMOS-compatible microring resonator that generates multiple, simultaneous, and independent photon pairs at different wavelengths in a frequency comb compatible with fiber communication wavelength division multiplexing channels (200 GHz channel separation) and with a linewidth that is compatible with quantum memories (110 MHz). It operates in a self-locked pump configuration, avoiding the need for active stabilization, making it extremely robust even at very low power levels.

Linearly polarized emission from random lasers with anisotropically amplifying media.

Simulations on three-dimensional random lasers were performed by finite-difference time-domain integration of Maxwell's equations combined with rate-equations providing gain. We investigated the frequency-dependent emission polarization of random lasers in the far-field of the sample and characterized the influence of anisotropic pumping in orthogonal polarizations. Under weak scattering, the polarization states of random lasing modes were random for isotropic pumping and linear under anisotropic pumping. These findings are in accordance with recent experimental observations. A crossover was observed towards very strong scattering, in which the scattering destroys the pump-induced polarization-anisotropy of the random lasing modes and randomizes (scrambles) the mode-polarization.

Integrated CARS source based on seeded four-wave mixing in silicon nitride.

We present a theoretical investigation of an integrated nonlinear light source for coherent anti-Stokes Raman scattering (CARS) based on silicon nitride waveguides. Wavelength tunable and temporally synchronized signal and idler pulses are obtained by using seeded four-wave mixing. We find that the calculated input pump power needed for nonlinear wavelength generation is more than one order of magnitude lower than in previously reported approaches based on optical fibers. The tuning range of the wavelength conversion was calculated to be 1418 nm to 1518 nm (idler) and 788 nm to 857 nm (signal), which corresponds to a coverage of vibrational transitions from 2350 cm-1 to 2810 cm-1. A maximum conversion efficiency of 19.1% at a peak pump power of 300 W is predicted.