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Single-photon emission from a two-level system offers promising perspectives for the development of quantum technologies, where multiphotons are generally regarded as accidental, undesired and should be suppressed. In quantum mechanics, however, multiphoton emission can turn out to be even more fundamental and interesting than the single-photon emission, since in a coherently driven system, the multiphoton suppression arises from quantum interferences between virtual multiphoton fluctuations and the mean field in a Poisson superposition of all number states. Here, we demonstrate how one can control the multiphoton dynamics of a two-level system by disrupting these quantum interferences through a precise and independent homodyne control of the mean field. We show that, counterintuitively, quantum fluctuations always play a major qualitative role, even and in fact especially, when their quantitative contribution is vanishing as compared to that of the mean field. Our findings provide new insights into the paradoxical character of quantum mechanics and open pathways for mean-field engineering as a tool for precision multiphoton control.

In recent decades, event studies have emerged as a central methodology in health and social research for evaluating the causal effects of staggered interventions. In this paper, we analyze event studies from experimental design principles for observational studies, with a focus on information borrowing across measurements. We develop robust weighting estimators that increasingly use more information across units and time periods, justified by increasingly stronger assumptions on the treatment assignment and potential outcomes mechanisms. As a particular case of this approach, we offer a novel decomposition of the classical dynamic two-way fixed effects (TWFE) regression estimator for event studies. Our decomposition is expressed in closed form and reveals in finite samples the hypothetical experiment that TWFE regression adjustments approximate. This decomposition offers insights into how standard regression estimators borrow information across different units and times, clarifying and supplementing the notion of forbidden comparison noted in the literature. The proposed approach enables the generalization of treatment effect estimates to a target population and offers new diagnostics for event studies, including covariate balance, sign reversal, effective sample size, and the contribution of each observation to the analysis. We also provide visualization tools for event studies and illustrate them in a case study of the impact of divorce reforms on female suicide.

In experimental design, aliasing of effects occurs in fractional factorial experiments, where certain low order factorial effects are indistinguishable from certain high order interactions: low order contrasts may be orthogonal to one another, while their higher order interactions are aliased and not identified. In observational studies, aliasing occurs when certain combinations of covariates -- e.g., time period and various eligibility criteria for treatment -- perfectly predict the treatment that an individual will receive, so a covariate combination is aliased with a particular treatment. In this situation, when a contrast among several groups is used to estimate a treatment effect, collections of individuals defined by contrast weights may be balanced with respect to summaries of low-order interactions between covariates and treatments, but necessarily not balanced with respect to summaries of high-order interactions between covariates and treatments. We develop a theory of aliasing in observational studies, illustrate that theory in an observational study whose aliasing is more robust than conventional difference-in-differences, and develop a new form of matching to construct balanced confounded factorial designs from observational data.

We introduce a one-way, one-quantum cascade, whereby a single excitation proceeds one-directionwise in a ladder of energy levels. This makes a variation from more famous two-way cascades where the excitation can go up and down following its excitation or relaxation in the ladder. We provide closed-form solutions for two-photon correlation functions between any transitions in such circular cascades. We discuss how the rich correlations that result from what appears to be an extremely simple implementation, are essentially those which have been obtained from complex architectures relying on strongly-correlated, many-body physics or cavity QED effects, and might constitute the liquid phase of the new family of time materials., Comment: 14 pages, 5 figures, submitted to Phys. Rev. A. Added discussion on time crystals and details on the structure of each peak

This paper presents the validation of shared control strategies for critical maneuvers in automated driving systems. Shared control involves collaboration between the driver and automation, allowing both parties to actively engage and cooperate at different levels of the driving task. The involvement of the driver adds complexity to the control loop, necessitating comprehensive validation methodologies. The proposed approach focuses on two critical maneuvers: overtaking in low visibility scenarios and lateral evasive actions. A modular architecture with an arbitration module and shared control algorithms is implemented, primarily focusing on the lateral control of the vehicle. The validation is conducted using a dynamic simulator, involving 8 real drivers interacting with a virtual environment. The results demonstrate improved safety and user acceptance, indicating the effectiveness of the shared control strategies in comparison with no shared-control support. Future work involves implementing shared control in drive-by-wire systems to enhance safety and driver comfort during critical maneuvers. Overall, this research contributes to the development and validation of shared control approaches in automated driving systems., Comment: 8 pages, 19 figures. Published in IEEE 26th International Conference on Intelligent Transportation Systems (ITSC)

We discuss two-photon physics, taking for illustration the particular but topical case of resonance fluorescence. We show that the basic concepts of interferences and correlations provide at the two-photon level an independent and drastically different picture than at the one-photon level, with landscapes of correlations that reveal various processes by spanning over all the possible frequencies at which the system can emit. Such landscapes typically present lines of photon bunching and circles of antibunching. The theoretical edifice to account for these features rests on two pillars: i) a theory of frequency-resolved photon correlations and ii) admixing classical and quantum fields. While experimental efforts have been to date concentrated on correlations between spectral peaks, strong correlations exist between photons emitted away from the peaks, which are accessible only through multiphoton observables. These could be exploited for both fundamental understanding of quantum-optical processes as well as applications by harnessing these unsuspected resources., Comment: Contribution to "Celebrating the 15th anniversary of the Royal Society Newton International Fellowship" issue in Philosophical Transactions A, in Editor's template. Synthesis of 15 years of the Corresponding Author's research, with original results

We study spatial correlations of vortices in different quantum states or with Bose or Fermi statistics. This is relevant for both optical vortices and condensed-matter ones such as microcavity polaritons, or any platform that can prepare and image fields in space at the few-particle level. While we focus on this particular case for illustration of the formalism, we already reveal unexpected features of spatial condensation whereby bosons exhibit a bimodal distribution of their distances which places them farther apart than fermions in over 40% of the cases, or on the opposite conceal spatial correlations to behave like coherent states. Such experiments upgrade in the laboratory successful techniques in uncontrolled extreme environments (stars and nuclei)., Comment: Pre-submission version welcoming comments and suggestions

We provide a mechanism to imprint local temporal correlations in photon streams which have the same character as spatial correlations in liquids. Usual single-photon emitters correspond, in this picture, to a (temporal) gas while uncorrelated light is the ideal gas. We argue that good single-photon sources are those that exhibit such temporal liquid features, i.e., with a plateau for their short-time correlations (as opposed to a linear dependence) and oscillations at later times, which is a direct manifestation of photon time-ordering. We obtain general, closed-form analytical expressions for the second-order coherence function of a broad family of "liquid light" which can be arbitrarily correlated, though never completely crystallized., Comment: Pre-submission version welcoming comments, missing references, etc

A growing number of researchers are conducting randomized experiments to analyze causal relationships in network settings where units influence one another. A dominant methodology for analyzing these experiments is design-based, leveraging random treatment assignments as the basis for inference. In this paper, we generalize this design-based approach to accommodate complex experiments with a variety of causal estimands and different target populations. An important special case of such generalized network experiments is a bipartite network experiment, in which treatment is randomized among one set of units, and outcomes are measured on a separate set of units. We propose a broad class of causal estimands based on stochastic interventions for generalized network experiments. Using a design-based approach, we show how to estimate these causal quantities without bias and develop conservative variance estimators. We apply our methodology to a randomized experiment in education where participation in an anti-conflict promotion program is randomized among selected students. Our analysis estimates the causal effects of treating each student or their friends among different target populations in the network. We find that the program improves the overall conflict awareness among students but does not significantly reduce the total number of such conflicts.

Weighting is a general and often-used method for statistical adjustment. Weighting has two objectives: first, to balance covariate distributions, and second, to ensure that the weights have minimal dispersion and thus produce a more stable estimator. A recent, increasingly common approach directly optimizes the weights toward these two objectives. However, this approach has not yet been feasible in large-scale datasets when investigators wish to flexibly balance general basis functions in an extended feature space. For example, many balancing approaches cannot scale to national-level health services research studies. To address this practical problem, we describe a scalable and flexible approach to weighting that integrates a basis expansion in a reproducing kernel Hilbert space with state-of-the-art convex optimization techniques. Specifically, we use the rank-restricted Nystr\"{o}m method to efficiently compute a kernel basis for balancing in {nearly} linear time and space, and then use the specialized first-order alternating direction method of multipliers to rapidly find the optimal weights. In an extensive simulation study, we provide new insights into the performance of weighting estimators in large datasets, showing that the proposed approach substantially outperforms others in terms of accuracy and speed. Finally, we use this weighting approach to conduct a national study of the relationship between hospital profit status and heart attack outcomes in a comprehensive dataset of 1.27 million patients. We find that for-profit hospitals use interventional cardiology to treat heart attacks at similar rates as other hospitals, but have higher mortality and readmission rates.

Federated or multi-site studies have distinct advantages over single-site studies, including increased generalizability, the ability to study underrepresented populations, and the opportunity to study rare exposures and outcomes. However, these studies are challenging due to the need to preserve the privacy of each individual's data and the heterogeneity in their covariate distributions. We propose a novel federated approach to derive valid causal inferences for a target population using multi-site data. We adjust for covariate shift and covariate mismatch between sites by developing multiply-robust and privacy-preserving nuisance function estimation. Our methodology incorporates transfer learning to estimate ensemble weights to combine information from source sites. We show that these learned weights are efficient and optimal under different scenarios. We showcase the finite sample advantages of our approach in terms of efficiency and robustness compared to existing approaches., Comment: Accepted at NeurIPS 2023

We propose a simple and general framework for nonparametric estimation of heterogeneous treatment effects under fairness constraints. Under standard regularity conditions, we show that the resulting estimators possess the double robustness property. We use this framework to characterize the trade-off between fairness and the maximum welfare achievable by the optimal policy. We evaluate the methods in a simulation study and illustrate them in a real-world case study.

Comparison and contrast are the basic means to unveil causation and learn which treatments work. To build good comparison groups, randomized experimentation is key, yet often infeasible. In such non-experimental settings, we illustrate and discuss diagnostics to assess how well the common linear regression approach to causal inference approximates desirable features of randomized experiments, such as covariate balance, study representativeness, interpolated estimation, and unweighted analyses. We also discuss alternative regression modeling, weighting, and matching approaches and argue they should be given strong consideration in empirical work.

Gun violence is a major source of injury and death in the United States. However, relatively little is known about the effects of firearm injuries on survivors and their family members and how these effects vary across subpopulations. To study these questions and, more generally, to address a gap in the causal inference literature, we present a framework for the study of effect modification or heterogeneous treatment effects in difference-in-differences designs. We implement a new matching technique, which combines profile matching and risk set matching, to (i) preserve the time alignment of covariates, exposure, and outcomes, avoiding pitfalls of other common approaches for difference-in-differences, and (ii) explicitly control biases due to imbalances in observed covariates in subgroups discovered from the data. Our case study shows significant and persistent effects of nonfatal firearm injuries on several health outcomes for those injured and on the mental health of their family members. Sensitivity analyses reveal that these results are moderately robust to unmeasured confounding bias. Finally, while the effects for those injured vary largely by the severity of the injury and its documented intent, for families, effects are strongest for those whose relative's injury is documented as resulting from an assault, self-harm, or law enforcement intervention.

The linear regression model is widely used in the biomedical and social sciences as well as in policy and business research to adjust for covariates and estimate the average effects of treatments. Behind every causal inference endeavor there is a hypothetical randomized experiment. However, in routine regression analyses in observational studies, it is unclear how well the adjustments made by regression approximate key features of randomized experiments, such as covariate balance, study representativeness, sample boundedness, and unweighted sampling. In this paper, we provide software to empirically address this question. We introduce the lmw package for R to compute the implied linear model weights and perform diagnostics for their evaluation. The weights are obtained as part of the design stage of the study; that is, without using outcome information. The implementation is general and applicable, for instance, in settings with instrumental variables and multi-valued treatments; in essence, in any situation where the linear model is the vehicle for adjustment and estimation of average treatment effects with discrete-valued interventions.

We study counterfactual classification as a new tool for decision-making under hypothetical (contrary to fact) scenarios. We propose a doubly-robust nonparametric estimator for a general counterfactual classifier, where we can incorporate flexible constraints by casting the classification problem as a nonlinear mathematical program involving counterfactuals. We go on to analyze the rates of convergence of the estimator and provide a closed-form expression for its asymptotic distribution. Our analysis shows that the proposed estimator is robust against nuisance model misspecification, and can attain fast $\sqrt{n}$ rates with tractable inference even when using nonparametric machine learning approaches. We study the empirical performance of our methods by simulation and apply them for recidivism risk prediction.

We discuss two-photon correlations from the side peaks that are formed when a two-level system emitter is driven coherently, with a detuning between the driving source and the emitter (quasi-resonance fluorescence). We do so in the context of the theories of frequency-resolved photon correlations and homodyning, showing that their combination leads to a neat picture compatible with perturbative two-photon scattering that was popular in the early days of quantum electrodynamics. This should help to control, enhance and open new regimes of multiphoton emission. We also propose a way to evidence the quantum coherent nature of the process from photoluminescence only, through the observation of a collapse of the symmetry of the lineshape accompanied by a surge of its intensity of emission. We discuss several of our results in the light of recent experimental works., Comment: 17 pages, 4 figures -- added ideal two-photon cascade formula (Eq. 3), additional references, corrected some typos & other minor changes. Submitted to Quantum Sci. Technol

We study a new class of estimands in causal inference, which are the solutions to a stochastic nonlinear optimization problem that in general cannot be obtained in closed form. The optimization problem describes the counterfactual state of a system after an intervention, and the solutions represent the optimal decisions in that counterfactual state. In particular, we develop a counterfactual mean-variance optimization approach, which can be used for optimal allocation of resources after an intervention. We propose a doubly-robust nonparametric estimator for the optimal solution of the counterfactual mean-variance program. We go on to analyze rates of convergence and provide a closed-form expression for the asymptotic distribution of our estimator. Our analysis shows that the proposed estimator is robust against nuisance model misspecification, and can attain fast $\sqrt{n}$ rates with tractable inference even when using nonparametric methods. This result is applicable to general nonlinear optimization problems subject to linear constraints whose coefficients are unknown and must be estimated. In this way, our findings contribute to the literature in optimization as well as causal inference. We further discuss the problem of calibrating our counterfactual covariance estimator to improve the finite-sample properties of our proposed optimal solution estimators. Finally, we evaluate our methods via simulation, and apply them to problems in healthcare policy and portfolio construction.