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Pointwise maximal leakage (PML) is an operationally meaningful privacy measure that quantifies the amount of information leaking about a secret $X$ to a single outcome of a related random variable $Y$. In this paper, we extend the notion of PML to random variables on arbitrary probability spaces. We develop two new definitions: First, we extend PML to countably infinite random variables by considering adversaries who aim to guess the value of discrete (finite or countably infinite) functions of $X$. Then, we consider adversaries who construct estimates of $X$ that maximize the expected value of their corresponding gain functions. We use this latter setup to introduce a highly versatile form of PML that captures many scenarios of practical interest whose definition requires no assumptions about the underlying probability spaces., Comment: Accepted for presentation at ISIT2023

We analyze the renormalization group fixed point of the two-dimensional Ising model at criticality. In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed point using operator-algebraic renormalization (OAR) is possible. Specifically, the fixed point is characterized in terms of spin-spin correlation functions. Explicit error bounds for the approximation of continuum correlation functions are given., Comment: 7+5 pages, 3 Figures

We propose and demonstrate a novel scheme for optical arbitrary waveform measurement (OAWM) that exploits chip-scale Kerr soliton combs as highly scalable multiwavelength local oscillators (LO) for ultra-broadband full-field waveform acquisition. In contrast to earlier concepts, our approach does not require any optical slicing filters and thus lends itself to efficient implementation on state-of-the-art high-index-contrast integration platforms such as silicon photonics. The scheme allows to measure truly arbitrary waveforms with high accuracy, based on a dedicated system model which is calibrated by means of a femtosecond laser with known pulse shape. We demonstrated the viability of the approach in a proof-of-concept experiment by capturing an optical waveform that contains multiple 16 QAM and 64 QAM wavelength-division multiplexed (WDM) data signals with symbol rates of up to 80 GBd, reaching overall line rates of up to 1.92 Tbit/s within an optical acquisition bandwidth of 610 GHz. To the best of our knowledge, this is the highest bandwidth that has so far been demonstrated in an OAWM experiment.

This paper introduces a paradigm shift in the way privacy is defined, driven by a novel interpretation of the fundamental result of Dwork and Naor about the impossibility of absolute disclosure prevention. We propose a general model of utility and privacy in which utility is achieved by disclosing the value of low-entropy features of a secret $X$, while privacy is maintained by hiding the value of high-entropy features of $X$. Adopting this model, we prove that, contrary to popular opinion, it is possible to provide meaningful inferential privacy guarantees. These guarantees are given in terms of an operationally-meaningful information measure called pointwise maximal leakage (PML) and prevent privacy breaches against a large class of adversaries regardless of their prior beliefs about $X$. We show that PML-based privacy is compatible with and provides insights into existing notions such as differential privacy. We also argue that our new framework enables highly flexible mechanism designs, where the randomness of a mechanism can be adjusted to the entropy of the data, ultimately, leading to higher utility., Comment: Accepted to the Journal of Privacy and Confidentiality

We present the first study of spatially integrated higher-order stellar kinematics over cosmic time. We use deep rest-frame optical spectroscopy of quiescent galaxies at redshifts z=0.05, 0.3 and 0.8 from the SAMI, MAGPI and LEGA-C surveys to measure the excess kurtosis $h_4$ of the stellar velocity distribution, the latter parametrised as a Gauss-Hermite series. Conservatively using a redshift-independent cut in stellar mass ($M_\star = 10^{11}\,{\rm M}_\odot$), and matching the stellar-mass distributions of our samples, we find 7 $\sigma$ evidence of $h_4$ increasing with cosmic time, from a median value of 0.019$\pm$0.002 at z=0.8 to 0.059$\pm$0.004 at z=0.06. Alternatively, we use a physically motivated sample selection, based on the mass distribution of the progenitors of local quiescent galaxies as inferred from numerical simulations; in this case, we find 10 $\sigma$ evidence. This evolution suggests that, over the last 7 Gyr, there has been a gradual decrease in the rotation-to-dispersion ratio and an increase in the radial anisotropy of the stellar velocity distribution, qualitatively consistent with accretion of gas-poor satellites. These findings demonstrate that massive galaxies continue to accrete mass and increase their dispersion support after becoming quiescent., Comment: 19 pages, 9 figures Accepted for publication in MNRAS

We present the first statistical study of spatially integrated non-Gaussian stellar kinematics spanning 7 Gyr in cosmic time. We use deep, rest-frame optical spectroscopy of massive galaxies (stellar mass $M_\star > 10^{10.5} {\rm M}_\odot$) at redshifts z = 0.05, 0.3 and 0.8 from the SAMI, MAGPI and LEGA-C surveys, to measure the excess kurtosis $h_4$ of the stellar velocity distribution, the latter parametrised as a Gauss-Hermite series. We find that at all redshifts where we have large enough samples, $h_4$ anti-correlates with the ratio between rotation and dispersion, highlighting the physical connection between these two kinematic observables. In addition, and independently from the anti-correlation with rotation-to-dispersion ratio, we also find a correlation between $h_4$ and $M_\star$, potentially connected to the assembly history of galaxies. In contrast, after controlling for mass, we find no evidence of independent correlation between $h_4$ and aperture velocity dispersion or galaxy size. These results hold for both star-forming and quiescent galaxies. For quiescent galaxies, $h_4$ also correlates with projected shape, even after controlling for the rotation-to-dispersion ratio. At any given redshift, star-forming galaxies have lower $h_4$ compared to quiescent galaxies, highlighting the link between kinematic structure and star-forming activity., Comment: 26 pages, 15 figures Accepted for publication in MNRAS

Recent advances in the development of ultra-low loss silicon nitride integrated photonic circuits have heralded a new generation of integrated lasers capable of reaching fiber laser coherence. However, these devices presently are based on self-injection locking of distributed feedback (DFB) laser diodes, increasing both the cost and requiring tuning of laser setpoints for their operation. In contrast, turn-key legacy laser systems use reflective semiconductor optical amplifiers (RSOA). While this scheme has been utilized for integrated photonics-based lasers, so far, no cost-effective RSOA-based integrated lasers exist that are low noise and simultaneously feature fast, mode-hop-free and linear frequency tuning as required for frequency modulated continuous wave (FMCW) LiDAR or for laser locking in frequency metrology. Here we overcome this challenge and demonstrate a RSOA-based, frequency agile integrated laser, that can be tuned with high speed, with high linearity at low power. This is achieved using monolithic integration of piezoelectrical actuators on ultra-low loss silicon nitride photonic integrated circuits in a Vernier filter-based laser scheme. The laser operates at 1550 nm, features 6 mW output power, 400 Hz intrinsic laser linewidth, and allows ultrafast wavelength switching within 7 ns rise time and 75 nW power consumption. In addition, we demonstrate the suitability for FMCW LiDAR by showing laser frequency tuning over 1.5 GHz at 100 kHz triangular chirp rate with nonlinearity of 0.25% after linearization, and use the source for measuring a target scene 10 m away with a 8.5 cm distance resolution.

Local and low-redshift ($z$<$3$) galaxies are known to broadly follow a bimodal distribution: actively star forming galaxies with relatively stable star-formation rates, and passive systems. These two populations are connected by galaxies in relatively slow transition. In contrast, theory predicts that star formation was stochastic at early cosmic times and in low-mass systems: these galaxies transitioned rapidly between starburst episodes and phases of suppressed star formation, potentially even causing temporary quiescence -- so-called mini-quenching events. However, the regime of star-formation burstiness is observationally highly unconstrained. Directly observing mini-quenched galaxies in the primordial Universe is therefore of utmost importance to constrain models of galaxy formation and transformation. Early quenched galaxies have been identified out to redshift $z<5$, and these are all found to be massive ($M_{*}>10^{10}~M_{\odot}$) and relatively old. Here we report a (mini-)quenched galaxy at z$=$7.3, when the Universe was only 700~Myr old. The JWST/NIRSpec spectrum is very blue ($U$-$V$$=$0.16$\pm0.03$~mag), but exhibits a Balmer break and no nebular emission lines. The galaxy experienced a short starburst followed by rapid quenching; its stellar mass (4-6$\times 10^8~M_\odot$) falls in a range that is sensitive to various feedback mechanisms, which can result in perhaps only temporary quenching., Comment: Accepted for publication in Nature

We report the discovery of a remarkable Ly$\alpha$ emitting galaxy at z = 7.2782, JADES-GS-z7-LA, with EW$_0$(Ly$\alpha$) $= 388.0 \pm 88.8$\AA and UV magnitude -17.0. The spectroscopic redshift is confirmed via rest-frame optical lines [O II], H$\beta$ and [O III] in its JWST/NIRSpec Micro-Shutter Assembly (MSA) spectrum. The Ly$\alpha$ line is detected in both lower resolution PRISM as well as medium resolution G140M grating spectra. The LSF-deconvolved Ly$\alpha$ FWHM in the grating is $383.9 \pm 56.2$ km/s and the Ly$\alpha$ velocity offset compared to the systemic redshift is $113.3 \pm 80.0$ km/s, indicative of very little neutral gas or dust within the galaxy. We estimate the Ly$\alpha$ escape fraction to be >70%. JADES-GS-z7-LA has a O32 ratio of $11.1 \pm 2.2$ and a R23 ratio of $11.2 \pm 2.6$, consistent with low metallicity and high ionization parameters. Deep NIRCam imaging also revealed a close companion source (separated by 0.23"), which exhibits similar photometry to that of JADES-GS-z7-LA, with a photometric excess in the F410M NIRCam image consistent with [O III]+H$\beta$ emission at the same redshift. The spectral energy distribution of JADES-GS-z7-LA indicates a "bursty" star formation history, with a low stellar mass of $\approx 10^7$ $M_\odot$. Assuming that the Ly$\alpha$ transmission through the intergalactic medium is the same as its measured escape fraction, an ionized region of size > 1.5 pMpc is needed to explain the high Ly$\alpha$ EW and low velocity offset compared to systemic seen in JADES-GS-z7-LA. Owing to its UV-faintness, we show that it is incapable of single-handedly ionizing a region large enough to explain its Ly$\alpha$ emission. Therefore, we suggest that JADES-GS-z7-LA (and possibly the companion source) may be a part of a larger overdensity, presenting direct evidence of overlapping ionized bubbles at $z>7$., Comment: 14 pages, 8 figures, Accepted for publication in A&A

We report the discovery of an extreme galaxy overdensity at $z = 5.4$ in the GOODS-S field using JWST/NIRCam imaging from JADES and JEMS alongside JWST/NIRCam wide field slitless spectroscopy from FRESCO. We identified potential members of the overdensity using HST+JWST photometry spanning $\lambda = 0.4-5.0\ \mu\mathrm{m}$. These data provide accurate and well-constrained photometric redshifts down to $m \approx 29-30\,\mathrm{mag}$. We subsequently confirmed $N = 81$ galaxies at $5.2 < z < 5.5$ using JWST slitless spectroscopy over $\lambda = 3.9-5.0\ \mu\mathrm{m}$ through a targeted line search for $\mathrm{H} \alpha$ around the best-fit photometric redshift. We verified that $N = 42$ of these galaxies reside in the field while $N = 39$ galaxies reside in a density around $\sim 10$ times that of a random volume. Stellar populations for these galaxies were inferred from the photometry and used to construct the star-forming main sequence, where protocluster members appeared more massive and exhibited earlier star formation (and thus older stellar populations) when compared to their field galaxy counterparts. We estimate the total halo mass of this large-scale structure to be $12.6 \lesssim \mathrm{log}_{10} \left( M_{\mathrm{halo}}/M_{\odot} \right) \lesssim 12.8$ using an empirical stellar mass to halo mass relation, which is likely an underestimate as a result of incompleteness. Our discovery demonstrates the power of JWST at constraining dark matter halo assembly and galaxy formation at very early cosmic times., Comment: Resubmitted to ApJ based on reviewer report; main text has 15 pages, 6 figures and 1 table; appendix has 1 page, 2 figure sets, and 2 tables

We present JADES JWST/NIRSpec spectroscopy of GN-z11, the most luminous candidate $z>10$ Lyman break galaxy in the GOODS-North field with $M_{UV}=-21.5$. We derive a redshift of $z=10.603$ (lower than previous determinations) based on multiple emission lines in our low and medium resolution spectra over $0.8-5.3 \mu$m. We significantly detect the continuum and measure a blue rest-UV spectral slope of $\beta=-2.4$. Remarkably, we see spatially-extended Lyman-$\alpha$ in emission (despite the highly-neutral IGM expected at this early epoch), offset 555 km s$^{-1}$ redward of the systemic redshift. From our measurements of collisionally-excited lines of both low- and high-ionization (including [O II]$\lambda3727$, [Ne III]$\lambda 3869$ and C III]$\lambda1909$) we infer a high ionization parameter ($\log U\sim -2$). We detect the rarely-seen N IV]$\lambda1486$ and N III]$\lambda1748$ lines in both our low and medium resolution spectra, with other high ionization lines seen in the low resolution spectrum such as He II (blended with O III]) and C IV (with a possible P-Cygni profile). Based on the observed rest-UV line ratios, we cannot conclusively rule out photoionization from AGN, although the high C III]/He II and N III]/He II ratios are compatible with a star-formation explanation. If the observed emission lines are powered by star formation, then the strong N III]$\lambda1748$ observed may imply an unusually high $N/O$ abundance. Balmer emission lines (H$\gamma$, H$\delta$) are also detected, and if powered by star formation rather than an AGN we infer a star formation rate of $\sim 20-30 M_{\odot} yr^{-1}$ (depending on the IMF) and low dust attenuation. Our NIRSpec spectroscopy confirms that GN-z11 is a remarkable galaxy with extreme properties seen 430 Myr after the Big Bang., Comment: Accepted for publication in Astronomy & Astrophysics, 17 pages, 12 figures. Line fluxes updated

We present JWST NIRCam 9-band near-infrared imaging of the luminous $z=10.6$ galaxy GN-z11 from the JWST Advanced Deep Extragalactic Survey (JADES) of the GOODS-N field. We find a spectral energy distribution (SED) entirely consistent with the expected form of a high-redshift galaxy: a clear blue continuum from 1.5 to 4 microns with a complete dropout in F115W. The core of GN-z11 is extremely compact in JWST imaging. We analyze the image with a two-component model, using a point source and a S\'{e}rsic profile that fits to a half-light radius of 200 pc and an index $n=0.9$. We find a low-surface brightness haze about $0.4''$ to the northeast of the galaxy, which is most likely a foreground object but might be a more extended component of GN-z11. At a spectroscopic redshift of 10.60 (Bunker et al. 2023), the comparison of the NIRCam F410M and F444W images spans the Balmer jump. From population synthesis modeling, here assuming no light from an active galactic nucleus, we reproduce the SED of GN-z11, finding a stellar mass of $\sim$$10^{9}~M_{\odot}$, a star-formation rate of $\sim$$20~M_{\odot}~\mathrm{yr}^{-1}$ and a young stellar age of $\sim$$20~\mathrm{Myr}$. As massive galaxies at high redshift are likely to be highly clustered, we search for faint neighbors of GN-z11, finding 9 galaxies out to $\sim$5 comoving Mpc transverse with photometric redshifts consistent with $z=10.6$, and a 10$^{\rm th}$ more tentative dropout only $3''$ away. This is consistent with GN-z11 being hosted by a massive dark-matter halo ($\approx8\times10^{10}~M_{\odot}$), though lower halo masses cannot be ruled out., Comment: 18 pages, 8 figures, accepted for publication in ApJ

Large dust reservoirs (up to $\sim 10^8 \, \mathrm{M_\odot}$) have been detected in galaxies out to redshift $z \sim 8$, when the age of the universe was only about 600 Myr. Generating significant amounts of dust within such a short timescale has proven challenging for theories of dust formation and has prompted the revision of the modelling of potential sites of dust production such as the atmospheres of asymptotic giant branch (AGB) stars in low-metallicity environments, supernovae (SNe) ejecta, and the accelerated growth of grains in the interstellar medium (ISM). However, degeneracies between different evolutionary pathways remain when the total dust mass of galaxies is the only available observable. Here we report observations of the $2175 \, \mathring{\rm A}$ dust attenuation feature, well known in the Milky Way (MW) and galaxies at $z \lesssim 3$, in the near-infrared spectra of galaxies up to $z \sim 7$, corresponding to the first billion years of cosmic time. The relatively short timescale implied for the formation of carbonaceous grains giving rise to this feature suggests a rapid production process, likely in Wolf-Rayet (WR) stars or SN ejecta., Comment: 28 pages, 8 figures. Accepted for publication in Nature

We present emission line ratios from a sample of 26 Lyman break galaxies from $z\sim5.5-9.5$ with $-17.05.5$ spectra. We find that the emission line ratios exhibited by these $z\sim5.5-9.5$ galaxies occupy clearly distinct regions of line-ratio space compared to typical z~0-3 galaxies, instead being more consistent with extreme populations of lower-redshift galaxies. This is best illustrated by the [OIII]/[OII] ratio, tracing interstellar medium (ISM) ionisation, in which we observe more than half of our sample to have [OIII]/[OII]>10. Our high signal-to-noise spectra reveal more than an order of magnitude of scatter in line ratios such as [OII]/H$\beta$ and [OIII]/[OII], indicating significant diversity in the ISM conditions within the sample. We find no convincing detections of [NII] in our sample, either in individual galaxies, or a stack of all G395M/F290LP spectra. The emission line ratios observed in our sample are generally consistent with galaxies with extremely high ionisation parameters (log $U\sim-1.5$), and a range of metallicities spanning from $\sim0.1\times Z_\odot$ to higher than $\sim0.3\times Z_\odot$, suggesting we are probing low-metallicity systems undergoing periods of rapid star-formation, driving strong radiation fields. These results highlight the value of deep observations in constraining the properties of individual galaxies, and hence probing diversity within galaxy population., Comment: 20 pages, 9 figures, submitted to Astronomy & Astrophysics, updated values in tables

Ever growing pixel acquisition rates in the fields of augmented reality, autonomous driving and robotics have increased interest in solid state beam scanning without moving parts. Modern photonic integrated laser ranging advances towards passive beam steering solutions. Recently demonstrated imagers based on focal plane arrays, nanophotonic metasurfaces, and optical phased arrays enable unprecedented pixel resolution and measurement speed. However, parallelization of >100 lasers and detectors - successfully implemented in commercial time-of-flight sensors - has not been widely adopted for passive scanning approaches. Here, we show both inertia-free and parallel light detection and ranging (LiDAR) with microresonator frequency combs. We used 40 independent channels of a continuously scanned microresonator frequency comb operated in the chaotic regime in combination with optical dispersive elements to perform random modulation LiDAR with 2D passive beam steering.

We study an information theoretic privacy mechanism design problem for two scenarios where the private data is either observable or hidden. In each scenario, we first consider bounded mutual information as privacy leakage criterion, then we use two different per-letter privacy constraints. In the first scenario, an agent observes useful data $Y$ that is correlated with private data $X$, and wishes to disclose the useful information to a user. A privacy mechanism is designed to generate disclosed data $U$ which maximizes the revealed information about $Y$ while satisfying a bounded privacy leakage constraint. In the second scenario, the agent has additionally access to the private data. To this end, we first extend the Functional Representation Lemma and Strong Functional Representation Lemma by relaxing the independence condition and thereby allowing a certain leakage to find lower bounds for the second scenario with different privacy leakage constraints. Furthermore, upper and lower bounds are derived in the first scenario considering different privacy constraints. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds. Moreover, considering bounded mutual information as privacy constraint we show that if the common information and mutual information between $X$ and $Y$ are equal, then the attained upper bound in the second scenario is tight. Finally, the privacy-utility trade-off with prioritized private data is studied where part of $X$, i.e., $X_1$, is more private than the remaining part, i.e., $X_2$, and we provide lower and upper bounds., Comment: arXiv admin note: substantial text overlap with arXiv:2205.04881, arXiv:2201.08738

Finding and characterising the first galaxies that illuminated the early Universe at cosmic dawn is pivotal to understand the physical conditions and the processes that led to the formation of the first stars. In the first few months of operations, imaging from the James Webb Space Telescope (JWST) have been used to identify tens of candidates of galaxies at redshift (z) greater than 10, less than 450 million years after the Big Bang. However, none of these candidates has yet been confirmed spectroscopically, leaving open the possibility that they are actually low-redshift interlopers. Here we present spectroscopic confirmation and analysis of four galaxies unambiguously detected at redshift 10.3

A privacy mechanism design problem is studied through the lens of information theory. In this work, an agent observes useful data $Y=(Y_1,...,Y_N)$ that is correlated with private data $X=(X_1,...,X_N)$ which is assumed to be also accessible by the agent. Here, we consider $K$ users where user $i$ demands a sub-vector of $Y$, denoted by $C_{i}$. The agent wishes to disclose $C_{i}$ to user $i$. Since $C_{i}$ is correlated with $X$ it can not be disclosed directly. A privacy mechanism is designed to generate disclosed data $U$ which maximizes a linear combinations of the users utilities while satisfying a bounded privacy constraint in terms of mutual information. In a similar work it has been assumed that $X_i$ is a deterministic function of $Y_i$, however in this work we let $X_i$ and $Y_i$ be arbitrarily correlated. First, an upper bound on the privacy-utility trade-off is obtained by using a specific transformation, Functional Representation Lemma and Strong Functional Representaion Lemma, then we show that the upper bound can be decomposed into $N$ parallel problems. Next, lower bounds on privacy-utility trade-off are derived using Functional Representation Lemma and Strong Functional Representaion Lemma. The upper bound is tight within a constant and the lower bounds assert that the disclosed data is independent of all $\{X_j\}_{i=1}^N$ except one which we allocate the maximum allowed leakage to it. Finally, the obtained bounds are studied in special cases., Comment: arXiv admin note: text overlap with arXiv:2205.04881, arXiv:2201.08738

Zero-noise extrapolation provides an especially useful error mitigation method for noisy intermediate-scale quantum devices. Our analysis, based on matrix product density operators, of the transverse-field Ising model with depolarizing noise, reveals both advantages and inherent problems associated with zero-noise extrapolation when simulating non-equilibrium many-body dynamics. On the one hand, interestingly, noise alters systematically the behavior of the Loschmidt echo at the dynamical phase transition times, doubling the number of non-analytic points, and hence inducing an error that, inherently, cannot be mitigated. On the other, zero-noise extrapolation may be employed to recover quantum revivals of the Loschmidt echo, which would be completely missed in the absence of mitigation, and to retrieve faithfully noise-free inter-site correlations. Our results, which are in good agreement with those obtained using quantum simulators, reveal the potential of matrix product density operators for the investigation of the performance of quantum devices with a large number of qubits and deep noisy quantum circuits.

Combining optical gain in direct-bandgap III-V materials with tunable optical feedback offered by advanced photonic integrated circuits is key to chip-scale external-cavity lasers (ECL), offering wideband tunability along with low optical linewidths. External feedback circuits can be efficiently implemented using low-loss silicon nitride (Si$_{3}$N$_{4}$) waveguides, which do not suffer from two-photon absorption and can thus handle much higher power levels than conventional silicon photonics. However, co-integrating III-V-based gain elements with tunable external feedback circuits in chip-scale modules still represents a challenge, requiring either technologically demanding heterogeneous integration techniques or costly high-precision multi-chip assembly. In this work, we demonstrate Si$_{3}$N$_{4}$-based hybrid integrated ECL that exploit 3D-printed structures such as intra-cavity photonic wire bonds and facet-attached microlenses for low-loss optical coupling with relaxed alignment tolerances, thereby overcoming the need for active alignment while maintaining the full flexibility of multi-chip integration techniques. In a proof-of-concept experiment, we demonstrate an ECL offering a 90 nm tuning range (1480 nm - 1570 nm) with on-chip output powers above 12 dBm and side-mode suppression ratios of up to 59 dB. We achieve an intrinsic linewidth of 979 Hz, which is among the lowest values reported for comparable feedback architectures. The optical loss of the intra-cavity photonic wire bond between the III-V gain element and the Si$_{3}$N$_{4}$-based tunable feedback circuit amounts to approximately (1.6 $\pm$ 0.2) dB. We use the ECL as a tunable pump laser to generate a dissipative Kerr soliton frequency comb. To the best of our knowledge, our experiments represent the first demonstration of a single-soliton Kerr comb generated with a pump that is derived from a hybrid ECL.

This work demonstrates the capabilities of an entangled photon-pair source at telecom wavelengths, based on a photonic integrated Si$_3$N$_4$ microresonator with monolithically integrated piezoelectric frequency tuning. Previously, frequency tuning of photon-pairs generated by microresonators has only been demonstrated using thermal control, however these have limited actuation bandwidth, and are not compatible with cryogenic environments. Here, the frequency-tunable photon-pair generation capabilities of a Si$_3$N$_4$ microresonator with a monolithically integrated aluminium nitride layer are shown. Fast-frequency locking of the microresonator to an external laser is demonstrated, with a resulting locking bandwidth orders of magnitude larger than reported previously using thermal locking. These abilities will have direct application in future schemes which interface such sources with quantum memories based on e.g. trapped-ion or rare-earth ion schemes.

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.

When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception are localized systems which are non-ergodic and do not thermalize, however local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states which feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current MBL phenomenology, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision., Comment: 11+3 pages, 6+3 figures; Close to published version