Search

Biphoton frequency combs are promising resources for quantum networking due in large part to their compatibility with the telecommunication infrastructure. In this work, we propose a method to periodically compress broadband frequency-entangled photons into biphoton frequency combs by utilizing time-varying linear cavities. Our approach hinges on rapid modulation of the input cavity coupling, yielding high spectral purity in each output comb line similar to that achieved with narrowband filters, but without the associated loss in flux. We examine the dependence of spectral purity and compression on coupling strength, cavity loss, and switching speed, finding realistic regimes supporting purities in excess of 0.999 and peak enhancement factors of 100 and beyond., Comment: 5 pages, 4 figures

We demonstrate spectral shaping of entangled photons with a six-channel microring-resonator-based silicon photonic pulse shaper. Through precise calibration of thermal phase shifters in a microresonator-based pulse shaper, we demonstrate line-by-line phase control on a 3~GHz grid for two frequency-bin-entangled qudits, corresponding to Hilbert spaces of up to $6\times 6$ ($3\times 3$) dimensions for shared (independent) signal-idler filters. The pulse shaper's fine spectral resolution enables control of nanosecond-scale temporal features, which are observed by direct coincidence detection of biphoton correlation functions that show excellent agreement with theory. This work marks, to our knowledge, the first demonstration of biphoton pulse shaping using an integrated spectral shaper and holds significant promise for applications in quantum information processing.

We demonstrate nonlocal modulation of entangled photons with truly distributed RF clocks. Leveraging a custom radio-over-fiber (RFoF) system characterized via classical spectral interference, we validate its effectiveness for quantum networking by multiplexing the RFoF clock with one photon from a frequency-bin-entangled pair and distributing the coexisting quantum-classical signals over fiber. Phase modulation of the two photons reveals nonlocal correlations in excellent agreement with theory: in-phase modulation produces additional sidebands in the joint spectral intensity, while out-of-phase modulation is nonlocally canceled. Our simple, feedback-free design attains sub-picosecond synchronization -- namely, drift less than $\sim$0.5 ps in a 5.5 km fiber over 30 min (fractionally only $\sim$2$\times$10$^{-8}$ of the total fiber delay) -- and should facilitate frequency-encoded quantum networking protocols such as high-dimensional quantum key distribution and entanglement swapping, unlocking frequency-bin qubits for practical quantum communications in deployed metropolitan-scale networks.

Efficient spatiotemporal control of optical beams is of paramount importance in diverse technological domains. Conventional systems focusing on quasi-static beam control demand precise phase or wavelength tuning for steering. This work presents a time-efficient solution for dynamic beam steering, emphasizing high-duty-cycle operation with fast scan rates, and eliminating the need for active tuning of the beam direction. We achieve 100%-duty-cycle scans at a rate of $\sim$9.8 GHz within an angular range of $\sim$1$^\circ$. Furthermore, leveraging the dispersion characteristics of a virtually imaged phased array (VIPA), we devise a broadband source array that seamlessly transitions from continuous-angular steering to pulsed discrete-angular operation, unlocking possibilities for high-sensitivity angle-, range-, and time-resolved imaging. We also elucidate the adaptability of integrated photonic designs incorporating wavelength-selective switches and spectral dispersers, for enabling a versatile on-chip realization of the proposed beam steering schemes.

Optical pulse shaping stands as a formidable technique in ultrafast optics, radio-frequency photonics, and quantum communications. While existing systems rely on bulk optics or integrated platforms with planar waveguide sections for spatial dispersion, they face limitations in achieving finer (few- or sub-GHz) spectrum control. These methods either demand considerable space or suffer from pronounced phase errors and optical losses when assembled to achieve fine resolution. Addressing these challenges, we present a foundry-fabricated six-channel silicon photonic shaper using microresonator filter banks with inline phase control and high spectral resolution. Leveraging existing comb-based spectroscopic techniques, we devise a novel system to mitigate thermal crosstalk and enable the versatile use of our on-chip shaper. Our results demonstrate the shaper's ability to phase-compensate six comb lines at tunable channel spacings of 3, 4, and 5 GHz. Specifically, at a 3 GHz channel spacing, we showcase the generation of arbitrary waveforms in the time domain. This scalable design and control scheme holds promise in meeting future demands for high-precision spectral shaping capabilities., Comment: 21 pages, 12 figures

We showcase a fully on-chip CMOS-fabricated silicon photonic integrated circuit employing a bidirectionally pumped microring and polarization splitter-rotators tailored for the generation of ultrabroadband ($>$9 THz), high-fidelity (90-98%) polarization-entangled photons. Spanning the optical C+L-band and producing over 116 frequency-bin pairs on a 38.4 GHz-spaced grid, this source is ideal for flex-grid wavelength-multiplexed entanglement distribution in multiuser networks.

In this work, we describe a procedure for synthesizing racetrack resonators with large quality factors and apply it to realize a multi-channel wavelength-selective switch (WSS) on a silicon photonic chip. We first determine the contribution of each component primitive to propagation loss in a racetrack resonator and use this data to develop a model for the frequency response of arbitrary order, coupled-racetrack channel dropping filters. We design second-order racetrack filters based on this model and cascade multiple such filters to form a 1x7 WSS. We find good agreement between our model and device performance with second-order racetrack that have ~1 dB of drop-port loss, ~2 GHz FWHM linewidth, and low optical crosstalk due to the quick filter roll-off of ~ 5.3 dB/GHz. Using a control algorithm, we show three-channel operation of our WSS with a channel spacing of only 10 GHz. Owing to the high quality factor and quick roll-off of our filter design, adjacent channel crosstalk is measured to be <-25 dB for channels spaced on a 10 GHz grid. As a further demonstration, we use five of seven WSS channels to perform a demultiplexing operation on both an 8 GHz and a 10 GHz grid. These results suggest that a low-loss WSS with fine channel resolution can be realized in a scalable manner using the silicon photonics platform.

We generate ultrabroadband photon pairs entangled in both polarization and frequency bins through an all-waveguided Sagnac source covering the entire optical C- and L-bands (1530--1625 nm). We perform comprehensive characterization of high-fidelity states in multiple dense wavelength-division multiplexed channels, achieving full tomography of effective four-qubit systems. Additionally, leveraging the inherent high dimensionality of frequency encoding and our electro-optic measurement approach, we demonstrate the scalability of our system to higher dimensions, reconstructing states in a 36-dimensional Hilbert space consisting of two polarization qubits and two frequency-bin qutrits. Our findings hold potential significance for quantum networking, particularly dense coding and entanglement distillation in wavelength-multiplexed quantum networks.

CMOS-compatible Kerr microcombs have drawn substantial interest as mass-manufacturable, compact alternatives to bulk frequency combs. This could enable deployment of many comb-reliant applications previously confined to laboratories. Particularly enticing is the prospect of microcombs performing optical frequency division in compact optical atomic clocks. Unfortunately, it is difficult to meet the self-referencing requirement of microcombs in these systems due to the $\sim$THz repetition rates typically required for octave-spanning comb generation. Additionally, it is challenging to spectrally engineer a microcomb system to align a comb mode with an atomic clock transition with sufficient signal-to-noise ratio. Here, we adopt a Vernier dual-microcomb scheme for optical frequency division of a stabilized ultranarrow-linewidth continuous-wave laser at 871 nm to a $\sim$235 MHz output frequency. In addition to enabling measurement of the comb repetition rates, this scheme brings the freedom to pick comb lines from either or both of the combs. We exploit this flexibility to shift an ultra-high-frequency ($\sim$100 GHz) carrier-envelope offset beat down to frequencies where detection is possible and to place a comb line close to the 871 nm laser - tuned so that if frequency-doubled it would fall close to the clock transition in $^{171}$Yb$^+$. Moreover, we introduce a novel scheme which suppresses frequency noise arising from interferometric phase fluctuations in our dual-comb system and reduces the frequency instability down to our measurement limit. Our dual-comb system can potentially combine with an integrated ion trap toward future chip-scale optical atomic clocks.

Frequency-bin qubits possess unique synergies with wavelength-multiplexed lightwave communications, suggesting valuable opportunities for quantum networking with the existing fiber-optic infrastructure. Although the coherent manipulation of frequency-bin states requires highly controllable multi-spectral-mode interference, the quantum frequency processor (QFP) provides a scalable path for gate synthesis leveraging standard telecom components. Here we summarize the state of the art in experimental QFP characterization. Distinguishing between physically motivated ''open box'' approaches that treat the QFP as a multiport interferometer, and ''black box'' approaches that view the QFP as a general quantum operation, we highlight the assumptions and results of multiple techniques, including quantum process tomography of a tunable beamsplitter -- to our knowledge the first full process tomography of any frequency-bin operation. Our findings should inform future characterization efforts as the QFP increasingly moves beyond proof-of-principle tabletop demonstrations toward integrated devices and deployed quantum networking experiments.

Entanglement -- the coherent correlations between parties in a joint quantum system -- is well-understood and quantifiable in the two-dimensional, two-party case. Higher (>2)-dimensional entangled systems hold promise in extending the capabilities of various quantum information applications. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We review entanglement certification approaches and the large number of -- often difficult -- measurements required to apply them. We present a novel certification method whose measurement requirements scale linearly with subsystem dimension (scaling with the square-root of the system dimension) and which requires only a single complex measurement. The certification method places a lower-bound on the relative entropy of entanglement of any maximally correlated state thereby certifying system entanglement. A lower bound is also shown for any maximally correlated state in the presence of noise -- the expected experimental case. We discuss experimental realization of all required measurements., Comment: 23 pages, 2 figures

Biphoton frequency combs (BFCs) are promising quantum sources for large-scale and high-dimensional quantum information and networking systems. In this context, the spectral purity of individual frequency bins will be critical for realizing quantum networking protocols like teleportation and entanglement swapping. Measurement of the temporal auto-correlation function of the unheralded signal or idler photons comprising the BFC is a key tool for characterizing their spectral purity and in turn verifying the utility of the biphoton state for networking protocols. Yet the experimentally obtainable precision for measuring BFC correlation functions is often severely limited by detector jitter. The fine temporal features in the correlation function$-$not only of practical value in quantum information, but also of fundamental interest in the study of quantum optics$-$are lost as a result and have remained unexplored. We propose a scheme to circumvent this challenge through electro-optic phase modulation, experimentally demonstrating time-resolved Hanbury Brown-Twiss characterization of BFCs generated from an integrated 40.5 GHz Si$_3$N$_4$ microring, up to a 3$\times$3-dimensional two-qutrit Hilbert space. Through slight detuning of the electro-optic drive frequency from the comb's free spectral range, our approach leverages Vernier principles to magnify temporal features which would otherwise be averaged out by detector jitter. We demonstrate our approach under both continuous-wave and pulsed pumping regimes, finding excellent agreement with theory. Importantly, our method reveals not only the collective statistics of the contributing frequency bins but also their temporal shapes$-$features lost in standard fully integrated auto-correlation measurements.

Electronic analog to digital converters (ADCs) are running up against the well-known bit depth vs bandwidth tradeoff. Towards this end, RF photonic-enhanced ADCs have been the subject of interest for some time. Optical frequency comb technology has been used as a workhorse underlying many of these architectures. Unfortunately, such designs must generally grapple with SWaP concerns, as well as frequency ambiguity issues which threaten to obscure critical spectral information of detected RF signals. In this work, we address these concerns via an RF photonic downconverter with potential for easy integration and field deployment by leveraging a novel hybrid microcomb / electro-optic comb design., Comment: Original submission replaced after publishing in Optics Letters. The new version includes an updated copyright statement

We report the experimental generation of all four frequency-bin Bell states in a single versatile setup via successive pumping of spontaneous parametric downconversion with single and dual spectral lines. Our scheme utilizes intensity modulation to control the pump configuration and offers turn-key generation of any desired Bell state using only off-the-shelf telecommunication equipment. We employ Bayesian inference to reconstruct the density matrices of the generated Bell states, finding fidelities $\geq$ 97% for all cases. Additionally, we demonstrate the sensitivity of the frequency-bin Bell states to common-mode and differential-mode temporal delays traversed by the photons comprising the state$\unicode{x2013}$presenting the potential for either enhanced resolution or nonlocal sensing enabled by our complete Bell basis synthesizer.

Timing and positioning measurements are key requisites for essential quantum network operations such as Bell state measurement. Conventional time-of-flight measurements using single-photon detectors are often limited by detection timing jitter. In this work, we demonstrate a nonlocal scheme to measure changes in relative link latencies with subpicosecond resolution by using tight timing correlation of broadband time-energy entangled photons. Our sensing scheme relies on spectral interference achieved via phase modulation, followed by filtering and biphoton coincidence measurements, and is resilient to microsecond-scale mismatch between the optical link traversed by the biphotons. Our experiments demonstrate a precision of +/-0.04 ps in measurements of nonlocal delay changes and +/-0.7{\deg} in measurements of radio-frequency phase changes. Furthermore, we complement our technique with time-tag information from single-photon detectors in the same setup to present unambiguous sensing of delay changes. The proposed technique can be implemented using off-the-shelf telecom equipment thus rendering it adaptable to practical quantum network infrastructure.

The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms such as frequency bins. In this Letter, we show that d-point frequency-bin DFTs can be realized with a fixed three-component quantum frequency processor (QFP), simply by adding to the electro-optic modulation signals one radio-frequency harmonic per each incremental increase in d. We verify gate fidelity F > 0.9997 and success probability P > 0.965 up to d = 10 in numerical simulations, and experimentally implement the solution for d = 3, utilizing measurements with parallel DFTs to quantify entanglement and perform full tomography of multiple two-photon frequency-bin states. Our results furnish new opportunities for high-dimensional frequency-bin protocols in quantum communications and networking.

Spectral and temporal mode matching are required for the efficient interaction of photons and quantum memories. In our previous work, we proposed a new route to spectrally compress broadband photons to achieve spectral mode matching with narrowband memories, using a linear, time-variant optical cavity based on rapid switching of input coupling. In this work, we extend our approach to attain temporal mode matching as well by exploiting the time-variation of output coupling of the cavity. We numerically analyze the mode matching and loss performance of our time-varying cavity and present a possible implementation in integrated photonics., Comment: 5 pages, 4 figures

We demonstrate a Bell state analyzer that operates directly on frequency mismatch. Based on electro-optic modulators and Fourier-transform pulse shapers, our quantum frequency processor design implements interleaved Hadamard gates in discrete frequency modes. Experimental tests on entangled-photon inputs reveal accuracies of $\sim$98\% for discriminating between the $|\Psi^+\rangle$ and $|\Psi^-\rangle$ frequency-bin Bell states. Our approach resolves the tension between wavelength-multiplexed state transport and high-fidelity Bell state measurements, which typically require spectral indistinguishability., Comment: 5 pages, 3 figures

Owing in large part to the advent of integrated biphoton frequency combs (BFCs), recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography (QST) of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a novel solution that employs a pulse shaper and electro-optic phase modulator (EOM) to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of BFCs generated from an on-chip Si$_{3}$N$_{4}$ microring resonator(MRR) in up to an $8\times8$-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.

We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate-eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the Iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate-eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate-eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer., Comment: 17 pages, 11 figures, 2 tables

Practical quantum networking architectures are crucial for scaling the connection of quantum resources. Yet quantum network testbeds have thus far underutilized the full capabilities of modern lightwave communications, such as flexible-grid bandwidth allocation. In this work, we implement flex-grid entanglement distribution in a deployed network for the first time, connecting nodes in three distinct campus buildings time-synchronized via the Global Positioning System (GPS). We quantify the quality of the distributed polarization entanglement via log-negativity, which offers a generic metric of link performance in entangled bits per second. After demonstrating successful entanglement distribution for two allocations of our eight dynamically reconfigurable channels, we demonstrate remote state preparation -- the first realization on deployed fiber -- showcasing one possible quantum protocol enabled by the distributed entanglement network. Our results realize an advanced paradigm for managing entanglement resources in quantum networks of ever-increasing complexity and service demands.

Integrated photonics is at the heart of many classical technologies, from optical communications to biosensors, LIDAR, and data center fiber interconnects. There is strong evidence that these integrated technologies will play a key role in quantum systems as they grow from few-qubit prototypes to tens of thousands of qubits. The underlying laser and optical quantum technologies, with the required functionality and performance, can only be realized through the integration of these components onto quantum photonic integrated circuits (QPICs) with accompanying electronics. In the last decade, remarkable advances in quantum photonic integration and a dramatic reduction in optical losses have enabled benchtop experiments to be scaled down to prototype chips with improvements in efficiency, robustness, and key performance metrics. The reduction in size, weight, power, and improvement in stability that will be enabled by QPICs will play a key role in increasing the degree of complexity and scale in quantum demonstrations. In the next decade, with sustained research, development, and investment in the quantum photonic ecosystem (i.e. PIC-based platforms, devices and circuits, fabrication and integration processes, packaging, and testing and benchmarking), we will witness the transition from single- and few-function prototypes to the large-scale integration of multi-functional and reconfigurable QPICs that will define how information is processed, stored, transmitted, and utilized for quantum computing, communications, metrology, and sensing. This roadmap highlights the current progress in the field of integrated quantum photonics, future challenges, and advances in science and technology needed to meet these challenges., Comment: Submitted to the Journal of Physics: Photonics

Flexible-grid wavelength-division multiplexing is a powerful tool in lightwave communications for maximizing spectral efficiency. In the emerging field of quantum networking, the need for effective resource provisioning is particularly acute, given the generally lower power levels, higher sensitivity to loss, and inapplicability of digital error correction. In this Letter, we leverage flex-grid technology to demonstrate reconfigurable distribution of quantum entanglement in a four-user tabletop network. By adaptively partitioning bandwidth with a single wavelength-selective switch, we successfully equalize two-party coincidence rates that initially differ by over two orders of magnitude. Our scalable approach introduces loss that is fixed with the number of users, offering a practical path for the establishment and management of quality-of-service guarantees in large quantum networks., Comment: 5 pages, 3 figures

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. %and a potential building block for scalable, fiber-compatible quantum information processing. In this work, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beamsplitter, with Bayesian tomography confirming state fidelities $\mathcal{F}_\rho>0.98$ for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation., Comment: 9 pages, 7 figures

Frequency-bin qudits constitute a promising tool for quantum information processing, but their high dimensionality can make for tedious characterization measurements. Here we introduce and compare compressive sensing and Bayesian mean estimation for recovering the spectral correlations of entangled photon pairs. Using a conventional compressive sensing algorithm, we reconstruct joint spectra with up to a 26-fold reduction in measurement time compared to the equivalent raster scan. Applying a custom Bayesian model to the same data, we then additionally realize reliable and consistent quantification of uncertainty. These efficient methods of biphoton characterization should advance our ability to use the high degree of parallelism and complexity afforded by frequency-bin encoding., Comment: 5 pages, 4 figures

A key challenge for quantum science and technology is to realise large-scale, precisely controllable, practical systems for non-classical secured communications, metrology and ultimately meaningful quantum simulation and computation. Optical frequency combs represent a powerful approach towards this, since they provide a very high number of temporal and frequency modes which can result in large-scale quantum systems. The generation and control of quantum optical frequency combs will enable a unique, practical and scalable framework for quantum signal and information processing. Here, we review recent progress on the realization of energy-time entangled optical frequency combs and discuss how photonic integration and the use of fiber-optic telecommunications components can enable quantum state control with new functionalities, yielding unprecedented capability., Comment: 22 pages, 6 figures, 125 references

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years., Comment: This is an updated version V2, including expanded text and listing of all co-authors. To whom correspondence should be addressed: Marko Lon\v{c}ar: loncar@seas.harvard.edu; Michael G. Raymer: raymer@uoregon.edu

Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers an alternate route to simulating such nonclassical behavior in a more robust platform. However, in photonic implementations to date, an increase to the depth of a continuous quantum walk requires modifying the footprint of the system. Here we report continuous walks of a two-photon quantum frequency comb with entanglement across multiple dimensions. The coupling between frequency modes is mediated by electro-optic phase modulation, which makes the evolution of the state completely tunable over a continuous range. With arbitrary control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting ballistic transport or strong energy confinement, to subspaces featuring bosonic or fermionic character. We also explore the role of entanglement dimensionality and demonstrate biphoton energy bound states, which are only possible with multilevel entanglement. This suggests the potential for such walks to quantify entanglement in high-dimensional systems.

Dissipative Kerr solitons are localized structures that exist in optical microresonators. They lead to the formation of microcombs --- chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion microresonators. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we report the discovery of reversible switching between coherent dark-pulse Kerr combs, whereby distinct states can be accessed deterministically. Furthermore, we reveal that the formation of dark-pulse Kerr combs is associated with the appearance of a new resonance, a feature that has never been observed for dark-pulses and is ascribed to soliton behavior. These results contribute to understanding the nonlinear physics in few-mode microresonators and provide insight into the generation of microcombs with high conversion efficiency.

The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer, and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs., Comment: 10 pages, 7 figures

The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms. Currently most implementations of the PEA are based on qubits, where the computational units in the quantum circuits are two-dimensional states. Performing quantum computing tasks with higher dimensional states -- qudits -- has been proposed, yet a qudit-based PEA has not been realized. Using qudits can reduce the resources needed for achieving a given precision or success probability. Compared to other quantum computing hardware, photonic systems have the advantage of being resilient to noise, but the probabilistic nature of photon-photon interaction makes it difficult to realize two-photon controlled gates that are necessary components in many quantum algorithms. In this work, we report an experimental realization of a qudit-based PEA on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. The controlled-unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. This first implementation of a qudit PEA, on any platform, successfully retrieves any arbitrary phase with one ternary digit of precision., Comment: 7 pages, 4 figures

Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode circumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instability mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both continuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. This result explains in part why it is difficult to access single solitons deterministically.

We propose an electro-optic approach for transparent optical networking, in which frequency channels are actively transformed into any desired mapping in a wavelength-multiplexed environment. Based on electro-optic phase modulators and Fourier-transform pulse shapers, our all-optical frequency processor (AFP) is examined numerically for the specific operations of frequency channel hopping and broadcasting, and found capable of implementing these transformations with favorable component requirements. Extending our analysis via a mutual-information--based metric for system optimization, we show how to optimize transformation performance under limited resources in a classical context, contrasting the results with those found using metrics motivated by quantum information, such as fidelity and success probability. Given its compatibility with on-chip implementation, as well as elimination of optical-to-electrical conversion in frequency channel switching, the AFP looks to offer valuable potential in silicon photonic network design., Comment: 11 pages, 5 figures

Phase modulation has emerged as a technique to create and manipulate high-dimensional frequency-bin entanglement. A necessary step to extending this technique to depolarized channels, such as those in a quantum networking environment, is the ability to perform phase modulation independent of photon polarization. This also necessary to harness hypertanglement in the polarization and frequency degrees of freedom for operations like Bell state discrimination. However, practical phase modulators are generally sensitive to the polarization of light and this makes them unsuited to such applications. We overcome this limitation by implementing a polarization diversity scheme to measure frequency-bin entanglement in arbitrarily polarized photon pairs.

We experimentally demonstrate phase retrieval of a single-soliton Kerr comb using electric field cross-correlation implemented via dual-comb interferometry. The phase profile of the Kerr comb is acquired through the heterodyne beat between the Kerr comb and a reference electro-optical comb with a pre-characterized phase profile. The soliton Kerr comb has a nearly flat phase profile, and the pump line is observed to show a phase offset which depends on the pumping parameters. The experimental results are in agreement with numerical simulations. Our all-linear approach enables rapid measurements (3.2 $\mu$s) with low input power (20 $\mu$W).

Simulating complex many-body quantum phenomena is a major scientific impetus behind the development of quantum computing, and a range of technologies are being explored to address such systems. We present the results of the largest photonics-based simulation to date, applied in the context of subatomic physics. Using an all-optical quantum frequency processor, the ground-state energies of light nuclei including the triton ($^3$H), $^{3}$He, and the alpha particle ($^{4}$He) are computed. Complementing these calculations and utilizing a 68-dimensional Hilbert space, our photonic simulator is used to perform sub-nucleon calculations of the two-body and three-body forces between heavy mesons in the Schwinger model. This work is a first step in simulating subatomic many-body physics on quantum frequency processors---augmenting classical computations that bridge scales from quarks to nuclei., Comment: 23 pages, 5 figures, 20 pages supplemental material

The realization of strong photon-photon interactions has presented an enduring challenge across photonics, particularly in quantum computing, where two-photon gates form essential components for scalable quantum information processing (QIP). While linear-optic schemes have enabled probabilistic entangling gates in spatio-polarization encoding, solutions for many other useful degrees of freedom remain missing. In particular, no two-photon gate for the important platform of frequency encoding has been experimentally demonstrated, due in large part to the additional challenges imparted by the mismatched wavelengths of the interacting photons. In this article, we design and implement the first entangling gate for frequency-bin qubits, a coincidence-basis controlled-NOT (CNOT), using line-by-line pulse shaping and electro-optic modulation. We extract a quantum gate fidelity of $0.91 \pm 0.01$ via a novel parameter inference approach based on Bayesian machine learning, which enables accurate gate reconstruction from measurements in the two-photon computational basis alone. Our CNOT imparts a single-photon frequency shift controlled by the frequency of another photon---an important capability in itself---and should enable new directions in fiber-compatible QIP., Comment: 9 pages, 5 figures

The probabilistic nature of single-photon sources and photon-photon interactions encourages encoding as much quantum information as possible in every photon for the purpose of photonic quantum information processing. Here, by encoding high-dimensional units of information (qudits) in time and frequency degrees of freedom using on-chip sources, we report deterministic two-qudit gates in a single photon with fidelities exceeding 0.90 in the computational basis. Constructing a two-qudit modulo SUM gate, we generate and measure a single-photon state with non-separability between time and frequency qudits. We then employ this SUM operation on two frequency-bin entangled photons, each carrying two 32-dimensional qudits, to realize a four-party high-dimensional Greenberger-Horne-Zeilinger state, occupying a Hilbert space equivalent to that of 20 qubits. Although high-dimensional coding alone is ultimately not scalable for universal quantum computing, our design shows the potential of deterministic optical quantum operations in large encoding spaces for practical and compact quantum information processing protocols.

Quantum information is the next frontier in information science, promising unconditionally secure communications, enhanced channel capacities, and computing capabilities far beyond their classical counterparts. And as quantum information processing devices continue to transition from the lab to the field, the demand for the foundational infrastructure connecting them with each other and their users---the quantum internet---will only increase. Due to the remarkable success of frequency multiplexing and control in the classical internet, quantum information encoding in optical frequency offers an intriguing synergy with state-of-the-art fiber-optic networks. Yet coherent quantum frequency operations prove extremely challenging, due to the difficulties in mixing frequencies efficiently, arbitrarily, in parallel, and with low noise. Here we implement an original approach based on a reconfigurable quantum frequency processor, designed to perform arbitrary manipulations of spectrally encoded qubits. This processor's unique tunability allows us to demonstrate frequency-bin Hong-Ou-Mandel interference with record-high 94% visibility. Furthermore, by incorporating such tunability with our method's natural parallelizability, we synthesize independent quantum frequency gates in the same device, realizing the first high-fidelity flip of spectral correlations on two entangled photons. Compared to quantum frequency mixing approaches based on nonlinear optics, our linear method removes the need for additional pump fields and significantly reduces background noise. Our results demonstrate multiple functionalities in parallel in a single platform, representing a huge step forward for the frequency-multiplexed quantum internet., Comment: 21 pages, 5 figures

We report a measurement of the lifetime of the cesium $7s\,^2S_{1/2}$ state using time-correlated single-photon counting spectroscopy in a vapor cell. We excite the atoms using a Doppler-free two-photon transition from the $6s\,^2S_{1/2}$ ground state, and detect the 1.47$\mu$m photons from the spontaneous decay of the $7s\,^2S_{1/2}$ to the $6p\,^2P_{3/2}$ state. We use a gated single photon detector in an asynchronous mode, allowing us to capture the fluorescence profile for a window much larger than the detector gate length. Analysis of the exponential decay of the photon count yields a $7s\,^2S_{1/2}$ lifetime of 48.28$\pm$0.07ns, an uncertainty of 0.14%. These measurements provide sensitive tests of theoretical models of the Cs atom, which play a central role in parity violation measurements., Comment: 5 pages, 5 figures, 2 tables

Microresonator frequency combs harness the nonlinear Kerr effect in an integrated optical cavity to generate a multitude of phase-locked frequency lines. The line spacing can reach values in the order of 100 GHz, making it an attractive multi-wavelength light source for applications in fiber-optic communications. Depending on the dispersion of the microresonator, different physical dynamics have been observed. A recently discovered comb state corresponds to the formation of mode-locked dark pulses in a normal-dispersion microcavity. Such dark-pulse combs are particularly compelling for advanced coherent communications since they display unusually high power conversion efficiency. Here, we report the first coherent transmission experiments using 64-quadrature amplitude modulation encoded onto the frequency lines of a dark-pulse comb. The high conversion efficiency of the comb enables transmitted optical signal-to-noise ratios above 33 dB while maintaining a laser pump power level compatible with state-of-the-art hybrid silicon lasers.

We report experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity ($0.99998\pm0.00003$), requires only a single microwave drive tone for near-ideal performance, functions across the entire C-band (1530-1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits we implement a $3\times 3$ extension of the Hadamard gate: the balanced tritter. This tritter---the first ever demonstrated for frequency modes---attains fidelity $0.9989\pm0.0004$. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding., Comment: 10 pages, 6 figures

Microwave phased array antennas (PAAs) are very attractive to defense applications and high-speed wireless communications for their abilities of fast beam scanning and complex beam pattern control. However, traditional PAAs based on phase shifters suffer from the beam-squint problem and have limited bandwidths. True-time-delay (TTD) beamforming based on low-loss photonic delay lines can solve this problem. But it is still quite challenging to build large-scale photonic TTD beamformers due to their high hardware complexity. In this paper, we demonstrate a photonic TTD beamforming network based on a miniature microresonator frequency comb (microcomb) source and dispersive time delay. A method incorporating optical phase modulation and programmable spectral shaping is proposed for positive and negative apodization weighting to achieve arbitrary microwave beam pattern control. The experimentally demonstrated TTD beamforming network can support a PAA with 21 elements. The microwave frequency range is $\mathbf{8\sim20\ {GHz}}$, and the beam scanning range is $\mathbf{\pm 60.2^\circ}$. Detailed measurements of the microwave amplitudes and phases are performed. The beamforming performances of Gaussian, rectangular beams and beam notch steering are evaluated through simulations by assuming a uniform radiating antenna array. The scheme can potentially support larger PAAs with hundreds of elements by increasing the number of comb lines with broadband microcomb generation., Comment: 10 pages, 9 figures, Journal of Lightwave Technology, 2018

We demonstrate a two-photon interference experiment for phase coherent biphoton frequency combs (BFCs), created through spectral amplitude filtering of biphotons with a continuous broadband spectrum. By using an electro-optic phase modulator, we project the BFC lines into sidebands that overlap in frequency. The resulting high-visibility interference patterns provide an approach to verify frequency-bin entanglement even with slow single-photon detectors; we show interference patterns with visibilities that surpass the classical threshold for qubit and qutrit states. Additionally, we show that with entangled qutrits, two-photon interference occurs even with projections onto different final frequency states. Finally, we show the versatility of this scheme for weak-light measurements by performing a series of two-dimensional experiments at different signal-idler frequency offsets to measure the dispersion of a single-mode fiber.

Breathers are localized waves, that are periodic in time or space. The concept of breathers is useful for describing many physical systems including granular lattices, Bose-Einstein condensation, hydrodynamics, plasmas and optics. Breathers could exist in both the anomalous and the normal dispersion regime. However, the demonstration of optical breathers in the normal dispersion regime remains elusive to our knowledge. Kerr comb generation in optical microresonators provides an array of oscillators that are highly coupled via the Kerr effect, which can be exploited to explore the breather dynamics. Here, we present, experimentally and numerically, the observation of dark breathers in a normal dispersion silicon nitride microresonator. By controlling the pump wavelength and power, we can generate the dark breather, which exhibits an energy exchange between the central lines and the lines at the wing. The dark breather breathes gently and retains a dark-pulse waveform. A transition to a chaotic breather state is also observed by increasing the pump power. These dark breather dynamics are well reproduced by numerical simulations based on the Lugiato-Lefever equation. The results also reveal the importance of dissipation to dark breather dynamics and give important insights into instabilities related to high power dark pulse Kerr combs from normal dispersion microreosnators.

A shaped doublet pump pulse is proposed for simultaneous octave-spanning soliton Kerr frequency comb generation and second-harmonic conversion in a single microresonator. The temporal soliton in the cavity is trapped atop a doublet pulse pedestal, resulting in a greatly expanded soliton region compared to that with a general Gaussian pulse pump. The possibility of single-microresonator comb self-referencing in a single silicon nitride microring, which can facilitate compact on-chip optical clocks, is demonstrated via simulation., Comment: 4 pages, 3 figures

Quantum frequency combs from chip-scale integrated sources are promising candidates for scalable and robust quantum information processing (QIP). However, to use these quantum combs for frequency domain QIP, demonstration of entanglement in the frequency basis, showing that the entangled photons are in a coherent superposition of multiple frequency bins, is required. We present a verification of qubit and qutrit frequency-bin entanglement using an on-chip quantum frequency comb with 40 mode pairs, through a two-photon interference measurement that is based on electro-optic phase modulation. Our demonstrations provide an important contribution in establishing integrated optical microresonators as a source for high-dimensional frequency-bin encoded quantum computing, as well as dense quantum key distribution.

Microresonator-based frequency combs are strong contenders as light sources for wavelength-division multiplexing (WDM). Recent demonstrations have shown the potential of microresonator combs for replacing tens of WDM lasers with a single laser-pumped device. These experiments relied on microresonators displaying anomalous dispersion. Devices operating in the normal dispersion offer the prospect of attaining high power conversion efficiency - an aspect that will be crucial in the future for enabling energy-efficient coherent communications with higher order modulation formats or lighting several spatial channels in space-division multiplexing. Here we report the experimental demonstration of coherent communications using normal dispersion microresonator combs. With polarization multiplexed (PM) quadrature phase-shift keying, we transmitted data over more than 6300 km in single-mode fiber. In a second experiment, we reached beyond 700 km with PM 16 quadrature amplitude modulation format and an aggregate data rate above 900 Gbit/s assuming 6% error correction overhead. These results represent the longest fiber transmission ever achieved using an integrated comb source., Comment: 7 pages, 6 figures

We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on direct soliton generation (DSG) in microresonators. When the pump laser is scanned from blue to red and then stopped at a fixed wavelength, we find that the solitons generated sometimes remain (survive) and sometimes annihilate subsequent to the end of the scan. We refer to the possibility of these different outcomes arising under identical laser scan conditions as coexistence of soliton annihilation and survival. Numerical simulations that include the thermal dynamics show that the coexistence of soliton annihilation and survival is explained by TO chaos accompanying comb generation. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger spontaneous soliton generation after the laser scan ends. The coexistence of soliton annihilation and survival as well as spontaneous soliton generation are observed experimentally in a silicon-nitride microresonator. The elucidation of the role of TO chaos provides important insights into the soliton generation dynamics in microresonators, which may eventually facilitate straightforward soliton generation in fully-integrated microresonators.