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The propagation and scattering of electromagnetic waves in magnetized plasmas in a state where a global mode has been established or is in turbulence, are of theoretical and experimental interest in thermonuclear fusion research. Interpreting experimental results, as well as predicting plasma behavior requires the numerical solutions of the underlying physics, that is, the numerical solution of Maxwell equations under various initial conditions and, under the circumstances, complex boundary conditions. Casting, the underlying equations in a coordinate free form that exploits the symmetries and the conserved quantities in a form that can easily encompass a variety of initial and boundary conditions is of tantamount importance. Pursuing this task we utilize the advantages the Clifford Algebras can possibly provide. For simplicity we deal with a cold multi-species lossless magnetized plasma. The formulation renders a Dirac type evolution equation for am augmented state that consists of the electric and magnetic field bivectors as well as the polarizations and their associated currents for each species. This evolution equation can be dealt with a general spatial lattice disretization scheme. The evolution operator that dictates the temporal advancement of the state is Hermitian. This formulation is computationally simpler whatever the application could be. However, small wavelength capabilities (on the Debye length scale) for spatially large systems (magnetic confinement devices) is questionable even for conventional super-computers. However, the formulation provided in this work it is entirely suitable and it can be directly transferred in a quantum computer. It is shown that the simplified problem in the present work could be suitable for contemporary rudimentary quantum computers., Comment: 24 pages

Motivated by the contemporary advances in quantum implementation of non-unitary operations, we propose a new dilation method based on the biorthogonal representation of the non-unitary operator, mapping it to an isomorphic unitary matrix in the orthonormal computational basis. The proposed method excels in implementing non-unitary operators whose eigenvalues have absolute values exceeding one, when compared to other dilation and decomposition techniques. Unlike the Linear Combination of Unitaries (LCU) method, which becomes less efficient as the number of unitary summands grows, the proposed technique is optimal for small-dimensional non-unitary operators regardless of the number of unitary summands. Thus, it can complement the LCU method for implementing general non-unitary operators arising in positive only open quantum systems and pseudo-Hermitian systems., Comment: 8 Pages, 3 Figures

Compact photonic systems that offer high frequency stability and low noise are of increasing importance to applications in precision metrology, quantum computing, communication, and advanced sensing technologies. However, on-chip resonators comprised of dielectrics cannot match the frequency stability and noise characteristics of Fabry-Perot cavities, whose electromagnetic modes live almost entirely in vacuum. In this study, we present a novel strategy to interface micro-fabricated Fabry-Perot cavities with photonic integrated circuits to realize compact, high-performance integrated systems. Using this new integration approach, we demonstrate self-injection locking of an on-chip laser to a milimeter-scale vacuum-gap Fabry-Perot using a circuit interface that transforms the reflected cavity response to enable efficient feedback to the laser. This system achieves a phase noise of -97 dBc/Hz at 10 kHz offset frequency, a fractional frequency stability of 5*10-13 at 10 ms, a 150 Hz 1/pi integral linewidth, and a 35 mHz fundamental linewidth. We also present a complementary integration strategy that utilizes a vertical emission grating coupler and a back-reflection cancellation circuit to realize a fully co-integrated module that effectively redirects the reflected signals and isolates back-reflections with a 10 dB suppression ratio, readily adaptable for on-chip PDH locking. Together, these demonstrations significantly enhance the precision and functionality of RF photonic systems, paving the way for continued advancements in photonic applications.

Using the Madelung transformation on a generalized scalar Gross-Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete representation of this Gross-Pitaevski equation and the simulations are compared to those using classical fluid dynamic techniques., Comment: 4 pages, 1 figure

The remarkable frequency stability of resonant systems in the optical domain (optical cavities and atomic transitions) can be harnessed at frequency scales accessible by electronics using optical frequency division. This capability is revolutionizing technologies spanning time keeping to high-performance electrical signal sources. A version of the technique called 2-point optical frequency division (2P-OFD) is proving advantageous for application to high-performance signal sources. In 2P-OFD, an optical cavity anchors two spectral endpoints defined by lines of a frequency comb. The comb need not be self-referenced, which greatly simplifies the system architecture and reduces power requirements. Here, a 2P-OFD microwave signal source is demonstrated with record-low phase noise using a microcomb. Key to this advance is a spectral endpoint defined by a frequency agile single-mode dispersive wave that is emitted by the microcomb soliton. Moreover, the system frequency reference is a compact all-solid-state optical cavity with a record Q-factor. The results advance integrable microcomb-based signal sources into the performance realm of much larger microwave sources.

Optical frequency division based on bulk or fiber optics provides unprecedented spectral purity for microwave oscillators. To extend the applications of this approach, the big challenges are to develop miniaturized optical frequency division oscillators without trading off phase noise performance. In this paper, we report a chip-scale electro-optical frequency division microwave oscillator with ultra-low phase noise performance. Dual laser sources are co-self-injection-locked to a single silicon nitride spiral resonator to provide a record high-stability, fully on-chip optical reference. An integrated electro-optical frequency comb based on a novel thin-film lithium niobate phase modulator chip is incorporated for the first time to perform optical-to-microwave frequency division. The resulting chip-scale photonic microwave oscillator achieves a phase noise level of -129 dBc/Hz at 10 kHz offset for 37.7 GHz carrier. The results represent a major advance in high performance, integrated photonic microwave oscillators for applications including signal processing, radar, timing, and coherent communications.

Electromagnetic waves are an inherent part of all plasmas -- laboratory fusion plasmas or astrophysical plasmas. The conventional methods for studying properties of electromagnetic waves rely on discretization of Maxwell equations suitable for implementing on classical, present day, computers. The traditional methodology is not efficient for quantum computing implementation -- a future computational source offering a tantalizing possibility of enormous speed up and a significant reduction in computational cost. This paper addresses two topics relevant to implementing Maxwell equations on a quantum computer. The first is on formulating a quantum Schrodinger representation of Maxwell equations for wave propagation in a cold, inhomogeneous, magnetized plasma. This representation admits unitary, energy preserving, evolution and conveniently lends itself to appropriate discretization for a quantum computer. Riding on the coattails of these results, the second topic is on developing a sequence of unitary operators which form the basis for a qubit lattice algorithm (QLA). The QLA, suitable for quantum computers, can be implemented and tested on existing classical computers for accuracy as well as scaling of computational time with the number of available processors. In order to illustrate the QLA for Maxwell equations, results are presented from a time evolving, full wave simulation of propagation and scattering of an electromagnetic wave packet by non-dispersive dielectric medium localized in space., Comment: 13 Pages, 4 Figures A complexity analysis on the quantum implementation of QLA has been added along with a relocation of the sub-sections for coherence purposes

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. The effect of the steepness of these derivatives on two dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer., Comment: 20 pages, 14 figures

Photonics offer numerous functionalities that can be used to realize astrophotonic instruments. The most spectacular example to date is the ESO Gravity instrument at the Very Large Telescope in Chile. Integrated astrophotonic devices stand to offer critical advantages for instrument development, including extreme miniaturization, as well as integration, superior thermal and mechanical stabilization owing to the small footprint, and high replicability offering cost savings. Numerous astrophotonic technologies have been developed to address shortcomings of conventional instruments to date, including for example the development of photonic lanterns, complex aperiodic fiber Bragg gratings, complex beam combiners to enable long baseline interferometry, and laser frequency combs for high precision spectral calibration of spectrometers. Despite these successes, the facility implementation of photonic solutions in astronomical instrumentation is currently limited because of (1) low throughputs from coupling to fibers, coupling fibers to chips, propagation and bend losses, device losses, etc, (2) difficulties with scaling to large channel count devices needed for large bandwidths and high resolutions, and (3) efficient integration of photonics with detectors, to name a few. In this roadmap, we identify 24 areas that need further development. We outline the challenges and advances needed across those areas covering design tools, simulation capabilities, fabrication processes, the need for entirely new components, integration and hybridization and the characterization of devices. To realize these advances the astrophotonics community will have to work cooperatively with industrial partners who have more advanced manufacturing capabilities. With the advances described herein, multi-functional instruments will be realized leading to novel observing capabilities for both ground and space platforms., Comment: 191 pages, 47 figures. This is the version of the article before peer review or editing, as submitted by an author to J. Phys. Photonics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://iopscience.iop.org/article/10.1088/2515-7647/ace869/meta

In dispersive media, dissipation appears in the Schr\"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. A first order Suzuki-Trotter approximation for the evolution operator enables us to isolate the non-unitary operators (associated with dissipation) from the unitary operators (associated with lossless media). The unitary operators can be implemented through qubit lattice algorithm (QLA) on $n$ qubits. However, the non-unitary-dissipative part poses a challenge on how it should be implemented on a quantum computer. In this paper, two probabilistic dilation algorithms are considered for handling the dissipative operators. The first algorithm is based on treating the classical dissipation as a linear amplitude damping-type completely positive trace preserving (CPTP) quantum channel where the combined system-environment must undergo unitary evolution in the dilated space. The unspecified environment can be modeled by just one ancillary qubit, resulting in an implementation scaling of $\textit{O}(2^{n-1}n^2)$ elementary gates for the dilated unitary evolution operator. The second algorithm approximates the non-unitary operators by the Linear Combination of Unitaries (LCU). We obtain an optimized representation of the non-unitary part, which requires $\textit{O}(2^{n})$ elementary gates. Applying the LCU method for a simple dielectric medium with homogeneous dissipation rate, the implementation scaling can be further reduced into $\textit{O}[poly(n)]$ basic gates. For the particular case of weak dissipation we show that our proposed post-selective dilation algorithms can efficiently delve into the transient evolution dynamics of dissipative systems by calculating the respective implementation circuit depth. A connection of our results with the non-linear-in-normalization-only (NINO) quantum channels is also presented., Comment: 10 pages, 2 Figures. New material has been added pertinent to non-linear PTP quantum channels and a detailed elaboration on the different algorithmic steps with an emphasis on the role of post-selection and the physical implications

Numerous modern technologies are reliant on the low-phase noise and exquisite timing stability of microwave signals. Substantial progress has been made in the field of microwave photonics, whereby low noise microwave signals are generated by the down-conversion of ultra-stable optical references using a frequency comb. Such systems, however, are constructed with bulk or fiber optics and are difficult to further reduce in size and power consumption. Our work addresses this challenge by leveraging advances in integrated photonics to demonstrate low-noise microwave generation via two-point optical frequency division. Narrow linewidth self-injection locked integrated lasers are stabilized to a miniature Fabry-P\'{e}rot cavity, and the frequency gap between the lasers is divided with an efficient dark-soliton frequency comb. The stabilized output of the microcomb is photodetected to produce a microwave signal at 20 GHz with phase noise of -96 dBc/Hz at 100 Hz offset frequency that decreases to -135 dBc/Hz at 10 kHz offset--values which are unprecedented for an integrated photonic system. All photonic components can be heterogeneously integrated on a single chip, providing a significant advance for the application of photonics to high-precision navigation, communication and timing systems.

A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to solve this representation of Maxwell equations. QLA consists of an interleaved unitary sequence of collision operators (that entangle on lattice-site qubits) and streaming operators (that move this entanglement throughout the lattice). External potential operators are introduced to handle gradients in the refractive indices, and these operators are typically non-unitary, but sparse matrices. By also interleaving the external potential operators with the unitary collide-stream operators one achieves a QLA which conserves energy to high accuracy. Some two dimensional simulations results are presented for the scattering of a one-dimensional (1D) pulse off a localized anisotropic dielectric object., Comment: 16 pages, 22 figures

By self-injection-locking a 1560 nm distributed feedback semiconductor laser to a high-$Q$ silicon nitride resonator, a high-coherence 780 nm second harmonic signal is generated via the photogalvanic-induced second-order nonlinearity. A record-low frequency noise floor of 4 Hz$^2$/Hz is achieved for the 780 nm emission. The approach can be generalized for signal generation over a wide range of visible and near-visible bands.

$\bf{Abstract}$: A qubit lattice algorithm (QLA), which consists of a set of interleaved unitary collision-streaming operators, is developed for electromagnetic wave propagation in tensor dielectric media. External potential operators are required to handle gradients in the refractive indices, and these operators are typically non-unitary. A similar problem arises in the QLA for the Korteweg-de Vries equation, as the potential operator that models the KdV nonlinear term is also non-unitary. Several QLAs are presented here that avoid the need of this non-unitary potential operator by perturbing the collision operator. These QLAs are fully unitary., Comment: 10 pages, 0 figures

Thermal silica is a common dielectric used in all silicon-photonic circuits. And bound hydroxyl ions (Si-OH) can provide a significant component of optical loss in this material on account of the wet nature of the thermal oxidation process. A convenient way to quantify this loss relative to other mechanisms is through OH-absorption at 1380 nm. Here, using ultra-high-Q thermal-silica wedge microresonators, the OH absorption loss peak is measured and distinguished from the scattering loss base line over a wavelength range from 680 nm to 1550 nm. Record-high on-chip resonator Q factors are observed for near-visible and visible wavelengths, and the absorption limited Q factor is as high as 8 billion in the telecom band. OH ion content level around 2.4 ppm (weight) is inferred from both Q measurements and by Secondary Ion Mass Spectroscopy (SIMS) depth profiling., Comment: 4 pages, 3 figures

Soliton microcombs are helping to advance the miniaturization of a range of comb systems. These combs mode lock through the formation of short temporal pulses in anomalous dispersion resonators. Here, a new microcomb is demonstrated that mode locks through the formation of pulse pairs in normal-dispersion coupled-ring resonators. Unlike conventional microcombs, pulses in this system cannot exist alone, and instead must phase lock in pairs to form a bright soliton comb. Also, the pulses can form at recurring spectral windows and the pulses in each pair feature different optical spectra. This pairwise mode-locking modality extends to higher dimensions and we demonstrate 3-ring systems in which 3 pulses mode lock through alternating pairwise pulse coupling. The results are demonstrated using the new CMOS-foundry platform that has not previously produced bright solitons on account of its inherent normal dispersion. The ability to generate multi-color pulse pairs over multiple rings is an important new feature for microcombs. It can extend the concept of all-optical soliton buffers and memories to multiple storage rings that multiplex pulses with respect to soliton color and that are spatially addressable. The results also suggest a new platform for the study of quantum combs and topological photonics.

Normal group velocity dispersion (GVD) microcombs offer high comb line power and high pumping efficiency compared to bright pulse microcombs. The recent demonstration of normal GVD microcombs using CMOS-foundry-produced microresonators is an important step towards scalable production. However, the chromatic dispersion of CMOS devices is large and impairs generation of broadband microcombs. Here, we report the development of a microresonator in which GVD is reduced due to a couple-ring resonator configuration. Operating in the turnkey self-injection-locking mode, the resonator is hybridly integrated with a semiconductor laser pump to produce high-power-efficiency combs spanning a bandwidth of 9.9 nm (1.22 THz) centered at 1560 nm, corresponding to 62 comb lines. Fast, linear optical sampling of the comb waveform is used to observe the rich set of near-zero GVD comb behaviors, including soliton molecules, switching waves (platicons) and their hybrids. Tuning of the 20 GHz repetition rate by electrical actuation enables servo locking to a microwave reference, which simultaneously stabilizes the comb repetition rate, offset frequency and temporal waveform. This hybridly integrated system could be used in coherent communications or for ultra-stable microwave signal generation by two-point optical frequency division., Comment: 8 pages, 4 figures

While photonic integrated circuits (PICs) are being widely used in applications such as telecommunications and datacenter interconnects, PICs capable of replacing bulk optics and fibers in high-precision, highly-coherent applications will require ultra-low-noise laser sources to be integrated with other photonic components in a compact and robustly aligned format -- that is, on a single chip. Such PICs could offer superior scalability for complex functionalities and volume production, as well as improved stability and reliability over time. However, there are two major issues preventing the realization of such envisioned PICs: the high phase noise of semiconductor lasers, and the difficulty of integrating optical isolators directly on chip. PICs are still considered as inferior solutions in optical systems such as microwave synthesizers, optical gyroscopes and atomic clocks, despite their advantages in size, weight, power consumption and cost (SWaPC). Here, we challenge this convention by introducing three-dimensional (3D) integration in silicon photonics that results in ultra-low-noise, isolator-free PICs. Through multiple monolithic and heterogeneous processing sequences, direct on-chip integration of III-V gain and ultra-low-loss (ULL) silicon nitride (SiN) waveguides with optical loss around 0.5 dB/m are demonstrated. Consequently, the demonstrated PIC enters a new regime, such that an integrated ultra-high-Q cavity reduces the laser noise close to that of fiber lasers. Moreover, the cavity acts as an effective block for any downstream on-chip or off-chip reflection-induced destabilization, thus eliminating the need for optical isolators. We further showcase isolator-free, widely-tunable, low-noise, heterodyne microwave generation using two ultra-low-noise lasers on the same silicon chip.

Chip-integrated optical frequency combs are attractive optical sources in comb applications requiring high-repetition-rate, low power consumption, or compact size. Spontaneous soliton formation via Kerr parametric oscillation is a promising generation principle in these frequency combs, and has been demonstrated in several material platforms over the past decade. Of these materials, AlGaAs has one of the largest Kerr nonlinearity coefficients allowing low pump threshold comb generation. However, bright soliton generation using this material has only been possible at cryogenic temperature because of the large thermo-optic effect at room temperature, which hinders stable access to the soliton regime. Here, we report self-stabilized single soliton generation in AlGaAs microresonators at room temperature by utilizing a rising soliton step in large free-spectral-range resonators. With sub-milliWatt optical pump power, 1 THz repetition-rate soliton generation is demonstrated. Perfect soliton crystal formation and soliton breather states are also observed. Besides the advantages of large optical nonlinearity, the devices are natural candidates for integration with III-V pump lasers., Comment: 7 pages, 3 figure

The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the scattering properties of the pulse mimics that found from the Fresnel jump conditions for a plane wave - except that the transmission to incident amplitudes are augmented by a factor of $\sqrt{n_2/n_1}$. As the boundary layer becomes thicker one finds deviations away from the Fresnel conditions and eventually one approaches WKB propagation. However there is found a small but unusual dip in part of the transmitted pulse that persists in time. The quantum lattice algorithm (QLA) used recovers the Maxwell equations to second order in a small parameter -- but QLA still recovers Maxwell equations when this parameter is unity. The expansion parameter is the speed of the pulse in medium $n_1$., Comment: 14 pages, 10 figures

A reformulation of Maxwell equations for an inhomogeneous, anisotropic, passive and non-dispersive medium results in a quantum-like Dirac equation that admits unitary time evolution. In contrast to other approaches, there is no a-priori introduction of the Riemann-Silberstein-Weber (RSW) vector but the Maxwell equations are considered in their standard fields, with given constitutive relations. From the electromagnetic conservation quantities a pseudo-Hermitian dynamics is found together with a Dyson map that recovers the full Hermicity of the dynamics in an extended Hilbert space that describes the physical notion of unitary evolution. As an example, a uniaxial tensor dielectric medium is considered, with the explicit Dyson map yielding an optimal representation in a set of generalized RSW vectors. In this newly discovered form, a Quantum Computing (QC) implementation for simulation of electromagnetic wave propagation in complex media can be made, with further extension into plasmas., Comment: 12 pages, 5 figures

Microwave signal generation with fast frequency tuning underlies many applications including sensing, imaging, ranging, time keeping, wireless communication, and high-speed electronics. Soliton microcombs are a promising new approach for photonic-based microwave signal synthesis. To date, however, tuning rate has been limited in microcombs (and in frequency combs generally). Here, we demonstrate the first microwave-rate soliton microcomb whose repetition rate can be tuned at a high speed. By integrating an electro-optic tuning/modulation element into a lithium niobate comb microresonator, a modulation bandwidth up to 75 MHz and a continuous frequency modulation rate up to 5.0 * 10^14 Hz/s are achieved, several orders-of-magnitude faster than existing microcomb technology. These features are especially useful for disciplining an optical VCO to a long-term reference such as an optical clock or for tight phase lock in dual-microcomb clocks or synthesizers. Moreover, the microwave signal rate can be set to any X - W band rate. Besides its positive impact on microwave photonics, fast repetition rate control is generally important in all applications of frequency combs.

High coherence visible and near-visible laser sources are centrally important to the operation of advanced position/navigation/timing systems as well as classical/quantum sensing systems. However, the complexity and size of these bench-top lasers is an impediment to their transitioning beyond the laboratory. Here, a system-on-a-chip that emits high-coherence visible and near-visible lightwaves is demonstrated. The devices rely upon a new approach wherein wavelength conversion and coherence increase by self-injection-locking are combined within in a single nonlinear resonator. This simplified approach is demonstrated in a hybridly-integrated device and provides a short-term linewidth around 10-30 kHz. On-chip, converted optical power over 2 mW is also obtained. Moreover, measurements show that heterogeneous integration can result in conversion efficiency higher than 25% with output power over 11 mW. Because the approach uses mature III-V pump lasers in combination with thin-film lithium niobate, it can be scaled for low-cost manufacturing of high-coherence visible emitters. Also, the coherence generation process can be transferred to other frequency conversion processes including optical parametric oscillation, sum/difference frequency generation, and third-harmonic generation.

A quantum lattice representation (QLA) is devised for the initial value problem of one-dimensional (1D) propagation of an electromagnetic disturbance in a scalar dielectric medium satisfying directly only the two curl equations of Maxwell. It si found that only 4 qubits/node are required. The collision, streaming, and potential operators are determined so as to recover the two curl equations to second order. Both polarizations are considered., Comment: 11 pages, 10 figures

A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A matrix formulation of the Maxwell equations, using the Riemann-Silberstein-Weber vectors, forms a basis for the QLA and a possible unitary representation. The electromagnetic fields are discretized using a 16-qubit representation at each grid point. The discretized QLA equations reproduce Maxwell equations to second order in an appropriate expansion parameter $\epsilon$. The properties of scattered waves depend on the scale length of the transition layer separating the vacuum from the core of the dielectric. The time evolution of the fields gives interesting physical insight into scattering when propagating fields are excited within the dielectric medium. Furthermore, simulations show that the QLA recovers Maxwell equations even when $\epsilon \sim 1$., Comment: 22 pages, 32 figures

Stimulated Brillouin scattering provides optical gain for efficient and narrow-linewidth lasers in high-Q microresonator systems. However, the thermal dependence of the Brillouin process, as well as the microresonator, impose strict temperature control requirements for long-term frequency-stable operation. Here, we study Brillouin back action and use it to both measure and phase-sensitively lock modal temperature to a reference temperature defined by the Brillouin phase-matching condition. At a specific lasing wavelength, the reference temperature can be precisely set by adjusting resonator free spectral range. This backaction control method is demonstrated in a chip-based Brillouin laser, but can be applied in all Brillouin laser platforms. It offers a new approach for frequency-stable operation of Brillouin lasers in atomic clock, frequency metrology, and gyroscope applications.

The development of integrated semiconductor lasers has miniaturized traditional bulky laser systems, enabling a wide range of photonic applications. A progression from pure III-V based lasers to III-V/external cavity structures has harnessed low-loss waveguides in different material systems, leading to significant improvements in laser coherence and stability. Despite these successes, however, key functions remain absent. In this work, we address a critical missing function by integrating the Pockels effect into a semiconductor laser. Using a hybrid integrated III-V/Lithium Niobate structure, we demonstrate several essential capabilities that have not existed in previous integrated lasers. These include a record-high frequency modulation speed of 2 exahertz/s (2.0$\times$10$^{18}$ Hz/s) and fast switching at 50 MHz, both of which are made possible by integration of the electro-optic effect. Moreover, the device co-lases at infrared and visible frequencies via the second-harmonic frequency conversion process, the first such integrated multi-color laser. Combined with its narrow linewidth and wide tunability, this new type of integrated laser holds promise for many applications including LiDAR, microwave photonics, atomic physics, and AR/VR.

There is considerable interest in the application of quantum information science to advance computations in plasma physics. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers it will require couching a classical problem in the language of quantum mechanics. Electromagnetic waves are routinely used in fusion experiments. The propagation of electromagnetic waves is described by Maxwell equations with an appropriate description of the plasma as a dielectric medium. Before advancing to the tensor dielectric of a magnetized plasma, this paper considers wave propagation in a one-dimensional inhomogeneous scalar dielectric. The classic theory of scattering of plane electromagnetic waves at a planar interface, separating two different dielectric media, leads to Fresnel equations for reflection and transmission coefficients. In contrast to plane waves, this paper is on the reflection and transmission of a spatially confined electromagnetic pulse. An analytical formulation for the scattering of a Gaussian pulse shows that the maximum transmission coefficient is modified by the square-root of the ratio of the two permittivities. The theory is complemented by numerical simulations using a quantum lattice algorithm for Maxwell equations. The algorithm, based on the Riemann-Silberstein-Weber representation of the electromagnetic fields and expressed in term of qubits, is an interleaved sequence of entangling operators at each lattice site and unitary streaming operators which transmit information from one site to an adjacent lattice site. Besides substantiating results from the theory for Gaussian pulses, numerical simulations show their validity for non-Gaussian pulses., Comment: 27 pages, 10 figures

Integrated photonics has profoundly impacted a wide range of technologies underpinning modern society. The ability to fabricate a complete optical system on a chip offers unrivalled scalability, weight, cost and power efficiency. Over the last decade, the progression from pure III-V materials platforms to silicon photonics has significantly broadened the scope of integrated photonics by combining integrated lasers with the high-volume, advanced fabrication capabilities of the commercial electronics industry. Yet, despite remarkable manufacturing advantages, reliance on silicon-based waveguides currently limits the spectral window available to photonic integrated circuits (PICs). Here, we present a new generation of integrated photonics by directly uniting III-V materials with silicon nitride (SiN) waveguides on Si wafers. Using this technology, we present the first fully integrated PICs at wavelengths shorter than silicon's bandgap, demonstrating essential photonic building blocks including lasers, photodetectors, modulators and passives, all operating at sub-um wavelengths. Using this platform, we achieve unprecedented coherence and tunability in an integrated laser at short wavelength. Furthermore, by making use of this higher photon energy, we demonstrate superb high temperature performance and, for the first time, kHz-level fundamental linewidths at elevated temperatures. Given the many potential applications at short wavelengths, the success of this integration strategy unlocks a broad range of new integrated photonics applications.

Optical microresonators with high quality ($Q$) factors are essential to a wide range of integrated photonic devices. Steady efforts have been directed towards increasing microresonator $Q$ factors across a variety of platforms. With success in reducing microfabrication process-related optical loss as a limitation of $Q$, the ultimate attainable $Q$, as determined solely by the constituent microresonator material absorption, has come into focus. Here, we report measurements of the material-limited $Q$ factors in several photonic material platforms. High-$Q$ microresonators are fabricated from thin films of SiO$_2$, Si$_3$N$_4$, Al$_{0.2}$Ga$_{0.8}$As and Ta$_2$O$_5$. By using cavity-enhanced photothermal spectroscopy, the material-limited $Q$ is determined. The method simultaneously measures the Kerr nonlinearity in each material and reveals how material nonlinearity and ultimate $Q$ vary in a complementary fashion across photonic materials. Besides guiding microresonator design and material development in four material platforms, the results help establish performance limits in future photonic integrated systems., Comment: Maodong Gao, Qi-Fan Yang and Qing-Xin Ji contributed equally to this work. 9 pages, 4 figures, 1 table

A quantum lattice algorithm (QLA) is developed for the solution of Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation. For x-dependent and y-dependent inhomogeneities, the corresponding QLA requries 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the collisional entanglement of two qubits. However, z-dependent inhomogeneities require a QLA with 16 qubits/lattice site since the Pauli spin matrix $\sigma_z$ is diagonal. QLA simulations are performed for the time evolution of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. There is excellent agreement between all three representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, boundary layer., Comment: 22 pages, 17 figures

Utilizing the similarity between the spinor representation of the Dirac equation and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice (QLA) representation of unitary collision stream operators of Maxwell equations is derived for both homogeneous and inhomogeneous media. A second order accurate 4 spinor scheme is developed and tested successfully for two dimensional (2D) propagation of a Gaussian pulse in a uniform medium while for normal (1D) incidence of an electromagnetic Gaussian pulse onto a dielectric interface requires 8 component spinors. In particular, the well-known phase change, field amplitudes and profile widths are recovered by the QLA asymptotic profiles. The QLA simulations yield the time dependent electromagnetic fields as the pulse enters and straddles the dielectric boundary. QLA involves unitary interleaved noncommuting collision and streaming operators that can be coded onto a quantum computer. The noncommutation being the only reason why one perturbatively recovers the Maxwell equations., Comment: 20 pages, 20 figures. More explanations on the incorporation of the inhomogeneous dielectric media through Hermitian operators

Silicon nitride (SiN) waveguides with ultra-low optical loss enable integrated photonic applications including low noise, narrow linewidth lasers, chip-scale nonlinear photonics, and microwave photonics. Lasers are key components to SiN photonic integrated circuits (PICs), but are difficult to fully integrate with low-index SiN waveguides due to their large mismatch with the high-index III-V gain materials. The recent demonstration of multilayer heterogeneous integration provides a practical solution and enabled the first-generation of lasers fully integrated with SiN waveguides. However a laser with high device yield and high output power at telecommunication wavelengths, where photonics applications are clustered, is still missing, hindered by large mode transition loss, nonoptimized cavity design, and a complicated fabrication process. Here, we report high-performance lasers on SiN with tens of milliwatts output through the SiN waveguide and sub-kHz fundamental linewidth, addressing all of the aforementioned issues. We also show Hertz-level linewidth lasers are achievable with the developed integration techniques. These lasers, together with high-$Q$ SiN resonators, mark a milestone towards a fully-integrated low-noise silicon nitride photonics platform. This laser should find potential applications in LIDAR, microwave photonics and coherent optical communications., Comment: 8 pages, 3 figures

Dissipative soliton Kerr frequency combs in microresonators have recently been demonstrated with the self-injection locking process. They have the advantage of turnkey deterministic comb generation and simplifying dark soliton generation in the normal dispersion regime. Here, the formation process of dark pulses triggered by self-injection locking is studied by regarding them as a pair of domain walls that connect domains having different intracavity powers. The self-injection locking mechanism allows the domain walls to self-regulate their position so that a wide range of dark comb states can be accessed, and the duty cycle is controlled by the feedback phase. Direct imaging of the dark pulse shape using the electro-optic sampling technique is used to verify the theory. The results provide new physical insights as well as a new operational modality for this important class of nonlinear waves., Comment: 20 pages, 10 figures

Narrow-linewidth lasers are important to many applications spanning precision metrology to sensing systems. Characterization of these lasers requires precise measurements of their frequency noise spectra. Here we demonstrate a correlated self-heterodyne (COSH) method capable of measuring frequency noise as low as 0.01 Hz$^2$/Hz at 1 MHz offset frequency. The measurement setup is characterized by both commercial and lab-built lasers, and features low optical power requirements, fast acquisition time and high intensity noise rejection., Comment: 10 pages, 6 figures

Driven by narrow-linewidth bench-top lasers, coherent optical systems spanning optical communications, metrology and sensing provide unrivalled performance. To transfer these capabilities from the laboratory to the real world, a key missing ingredient is a mass-produced integrated laser with superior coherence. Here, we bridge conventional semiconductor lasers and coherent optical systems using CMOS-foundry-fabricated microresonators with record high $Q$ factor over 260 million and finesse over 42,000. Five orders-of-magnitude noise reduction in the pump laser is demonstrated, and for the first time, fundamental noise below 1 Hz$^2$ Hz$^{-1}$ is achieved in an electrically-pumped integrated laser. Moreover, the same configuration is shown to relieve dispersion requirements for microcomb generation that have handicapped certain nonlinear platforms. The simultaneous realization of record-high $Q$ factor, highly coherent lasers and frequency combs using foundry-based technologies paves the way for volume manufacturing of a wide range of coherent optical systems., Comment: 19 pages, 11 figures

EarthFinder is a NASA Astrophysics Probe mission concept selected for study as input to the 2020 Astrophysics National Academies Decadal Survey. The EarthFinder concept is based on a dramatic shift in our understanding of how PRV measurements should be made. We propose a new paradigm which brings the high precision, high cadence domain of transit photometry as demonstrated by Kepler and TESS to the challenges of PRV measurements at the cm/s level. This new paradigm takes advantage of: 1) broad wavelength coverage from the UV to NIR which is only possible from space to minimize the effects of stellar activity; 2) extremely compact, highly stable, highly efficient spectrometers (R>150,000) which require the diffraction-limited imaging possible only from space over a broad wavelength range; 3) the revolution in laser-based wavelength standards to ensure cm/s precision over many years; 4) a high cadence observing program which minimizes sampling-induced period aliases; 5) exploiting the absolute flux stability from space for continuum normalization for unprecedented line-by-line analysis not possible from the ground; and 6) focusing on the bright stars which will be the targets of future imaging missions so that EarthFinder can use a ~1.5 m telescope., Comment: NASA Probe Mission concept white paper for 2020 Astrophysics National Academies Decadal Survey

Coherently-pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of soliton microcombs. Here, this diffusive motion and its impact on Kerr soliton timing jitter is studied experimentally. Typically hidden below technical noise contributions, the quantum limit is discerned by measuring counter-propagating solitons. Their relative motion features only weak interactions and also presents excellent common mode suppression of technical noise. This is in strong contrast to co-propagating solitons which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong mutual motion correlation. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multi-soliton physics