We develop a field-theoretic formalism, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a $2\times 2$ matrix radiance, reminiscent of the radiative transfer equation but capable of capturing coherent interference effects. This framework goes beyond the limitations of the Dorokhov-Mello-Pereyra-Kumar theory by accounting for both quasiballistic and diffusive regimes. It also handles open geometries inaccessible to standard wave-equation solvers such as infinite slabs. Analytical and numerical solutions are provided for these geometries, highlighting in particular the impact of the waveguide shape and the grazing modes on the transmission eigenvalue distribution in the quasiballistic regime. By removing the macroscopic assumptions of random matrix models, this microscopic theory enables the calculation of transmission statistics in regimes previously out of reach. It also provides a foundation for exploring more complex observables and physical effects relevant to wavefront shaping in realistic disordered systems.

Fock-state lattices (FSLs) are becoming an emerging research hotspot in quantum physics, not only because the FSLs provide a new perspective for studying atom-field interactions, but also because they build a connection between quantum optics and condensed matter physics. Because of the multiple transition paths in the lattices, an inherent quantum interference effect exists in these systems, and hence finding new quantum-coherent phenomena and exploiting their applications become a significant and desired task in this field. In this work, we study the dark-state effect in the FSLs generated by the multimode Jaynes-Cummings (JC) models. By considering the FSLs in certain excitation-number subspaces, we study the dark states with respect to the states associated with the atomic excited state using the arrowhead-matrix method. We find that dark-state subspaces exist with dimensions determined by the number of orthogonal dark states. When the dimension is greater than one, the forms of these dark-state bases are not unique. Further, we obtain the number and form of the orthogonal dark states in the two-, three-, and four-mode JC models. In addition, we find that for a general $N$-mode JC model, there are $C_{N+n-2}^{N-2}$ orthogonal dark states in the $n$-excitation subspace. We also build the relationship between the dark states and dark modes. Our work paves the way for exploring quantum optical effects and quantum information processing based on the FSLs.

A cell routinely responds to one of many competing environmental cues. A fundamental question is whether the cell follows the cue prioritized by its internal signaling network or the cue that carries the most external information. We introduce a theoretical framework to answer this question. We derive information limits for four types of directional cues: external and self-generated chemical gradients, fluid flow, and contact inhibition of locomotion. When the cues compete as pairs, these limits predict which cue a cell should follow if its decision is based on environmental information alone. We compare these predicted decision boundaries with data from our and others' cell migration experiments, finding cases where the boundary is obeyed and cases where it is violated by orders of magnitude. Both outcomes are informative, and we find that they rationalize known properties, or predict putative properties, of cells' internal signaling networks. Our work introduces a physical framework to quantify the degree to which a cell acts like an autonomous agent, rather than a passive detector, favoring a cue even when it is less informative.

The number of observable degrees of freedom is typically limited in experiments. Here we consider discrete Markov networks in which an observer has access to a few visible transitions and the waiting times between these transitions. Focusing on the underlying structure of a discrete network, we present methods to infer local and global properties of the network from observed data. First, we derive bounds on the microscopic entropy production along the hidden paths between two visible transitions, which complement extant bounds on mean entropy production and affinities of hidden cycles. Second, we demonstrate how the operationally accessible data encodes information about the topology of shortest hidden paths, which can be used to identify potential clusters of states or exclude their existence. Finally, we outline a systematic way to combine the inferred data, resulting in an algorithm that finds the candidates for a minimal graph of the underlying network, i.e., a graph that is part of the original one and compatible with the observations. Our results highlight the interplay between thermodynamic methods, waiting-time distributions, and topological aspects like network structure, which can be expected to provide novel insights in other setups of coarse graining as well.

The emergence of high-intensity femtosecond duration x-rays from Free-Electron Lasers has enriched our understanding of the structure and dynamics of biological molecules at the atomic level. In serial femtosecond crystallography experiments, the magnitude of the interaction between photons and matter can vary significantly due to variations in the x-ray pulse's intensity, energy bandwidth and duration, as well as fluctuations in the synchronicity between the x-ray pulse and the sample. Accurate characterization of the conditions from each exposure is valuable for experiment and theory. In this theoretical work, we propose using x-ray emission spectra emanating from sulfur atoms, which are prevalent in biomolecules, to obtain individual hit information. We train a neural network based on synthetic K-shell emission spectra from a lysozyme crystal to predict x-ray fluence and pulse duration. The model achieves a training relative error of $<12\%$ when predicting both parameters concurrently. We use interpretation methods to identify the regions in the spectra that have the most predictive power. For fluence predictions, the model emphasizes K-L emission shifts to higher energies due to the presence of highly charged sulfur ions. For pulse duration predictions, the model places a greater focus on the emission signal from double core hole K-L emission. These results demonstrate that it is possible to predict x-ray exposure information on the sample based on physically interpretable features in sulfur's K-shell emission spectra.

A group of techniques known by the general name of single-molecule localization microscopy reaches a nanometer-scale spatial resolution of point light emitters, well below the diffraction limit of traditional microscopy. The key feature of these techniques is blinking, alternation of bright and dark states, of each emitter so that no more than one emitter is bright within the width of the point-spread function of the microscope during a time sufficient for its localization. We give a formulation of the optical part of these techniques in terms of quantum metrology, where the limit of precision is determined by the Fisher information on the emitters' positions contained in the measurement data. We show that the advantage in resolution provided by making the emitters blink is a consequence of the fundamental property of Fisher information, its convexity. In particular, we prove the weak matrix convexity and the trace convexity of the Fisher information matrix—two fundamental results in the multiparameter estimation theory. We show also that the advantage in information is inherent to the quantum state of light itself before the measurement and is related to the convexity of the quantum Fisher information matrix.

The distribution of urban services reveals critical patterns of human activity and accessibility. Proximity to amenities like restaurants, banks, and hospitals can reduce access barriers, but these services are often unevenly distributed, exacerbating spatial inequalities and socioeconomic disparities. In this paper, we present an accessibility measure based on the spatial distribution of points of interest within cities. Using the radial distribution function from statistical physics, we analyze the dispersion of services across different urban zones, combining local and remote access to services. This approach allows us to identify a city's central core, intermediate areas or secondary cores, and its periphery. Comparing the areas that we find with the resident population distribution highlights clusters of urban services and helps uncover disparities in access to opportunities.

In this paper, we design and experimentally implement various robust quantum unitary transformations (gates) acting on $d$-dimensional vectors (qudits) by tuning a single control parameter using optimal control theory. The quantum state is represented by the momentum components of a Bose-Einstein condensate placed in an optical lattice, with the lattice position varying over a fixed duration serving as the control parameter. To evaluate the quality of these transformations, we employ standard quantum process tomography. In addition, we show how controlled unitary transformations can be used to extend state stabilization to global stabilization within a controlled vector subspace. Finally, we apply them to state tomography, showing how the information about the relative phase between distant momentum components can be extracted by inducing an interference process.

Circuit cutting is a technique for simulating large quantum circuits by partitioning them into smaller subcircuits, which can be executed on smaller quantum devices. The results from these subcircuits are then combined in classical postprocessing to accurately reconstruct the expectation value of the original circuit. Circuit cutting introduces a sampling overhead that grows exponentially with the number of gates and qubit wires that are cut. Many recently developed quasiprobabilistic circuit cutting techniques leverage classical side information, obtained from intermediate measurements within the subcircuits, to enhance the postprocessing step. In this work, we provide a formalization of general circuit cutting techniques utilizing side information through quantum instruments. With this framework, we analyze the advantage that classical side information provides in reducing the sampling overhead of circuit cutting. Surprisingly, we find that in certain scenarios, side information does not yield any reduction in sampling overhead, whereas in others it is essential for circuit cutting to be feasible at all. Furthermore, we present a lower bound for the optimal sampling overhead with side information that can be evaluated efficiently via semidefinite programming and improves on all previously known lower bounds.

We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.

Machine-learning algorithms thrive on large data sets of good quality. Here we show that they can also excel in a typical research setting with little data of limited quality, through an interplay of insights coming from machine and human researchers. The question we address is the unsolved problem of ordering out of a spin-liquid phase described by an emergent rank-2 $\text{U}\left(1\right)$ gauge theory, as described by H. Yan et al. [Phys. Rev. Lett. 124, 127203 (2020)]. Published Monte Carlo simulations for this problem are consistent with a strong first-order phase transition, but were too noisy for the form of low-temperature order to be identified. Using a highly interpretable machine-learning approach based on a support vector machine with a tensorial kernel, we reanalyze these Monte Carlo data, gaining new information about the form of order that could in turn be interpreted by traditionally trained physicists. We find that the low-temperature ordered phase is a form of magnetic order analogous to a smectic liquid crystal. This arises due to a subtle thermal order-by-disorder mechanism, that can be understood from the fluctuations of the tensor electric field of the parent rank-2 gauge theory. These results were obtained by a back-and-forth process which closely resembles a collaboration between human researchers and machines. We argue that this “collaborative” approach may provide a blueprint for solving other problems that have not yielded to human insights alone.

Non-Hermitian quantum systems have attracted significant interest in recent years due to the presence of unique spectral singularities in which eigenvalues and eigenvectors coalesce. Those singularities are known as exceptional points (EPs). The drastic changes of the non-Hermitian systems around their EPs have led to unique entanglement dynamics, which remained elusive until quite recently. In this work, we theoretically investigate the robustness of multipartite entanglement induced by EPs of the passive $\mathcal{PT}$-symmetric non-Hermitian superconducting qubits, both in stand-alone configurations and hybrid setups with Hermitian qubits. In particular, we consider the qubits with both all-to-all and nearest-neighbor couplings under uniform and nonuniform coupling strengths. Our results reveal that non-Hermitian qubits with all-to-all coupling generate GHZ states, while those with nearest-neighbor interactions produce W states. These entangled states are resilient to nonuniform couplings, off-resonant driving fields, and decoherence effects. Moreover, the hybrid configurations combining Hermitian and non-Hermitian qubits indicate the necessity of EPs for rapidly generating and maintaining genuine multipartite entanglement. Additionally, driving the $\mathcal{PT}$-symmetric qubits with a strong Rabi frequency can help sustain the entanglement over time by countering losses, while strong interqubit coupling favors the entangled states in the low dissipation regime. We also demonstrate that increasing the number of non-Hermitian qubits speeds up multipartite entanglement generation due to enhanced collective interactions. These findings reveal that exploiting non-Hermitian systems and their associated EPs is beneficial for generating robust and genuine entangled states which are useful for both fundamental studies and quantum technologies.

Coherent control by means of tailored excitation is a key to versatile experimental schemes for spectroscopic investigation and technological utilization of quantum systems. Here we study a quantum system which consists of a coupled electron-muon spin state, i.e., muonium, a light isotope of hydrogen. We demonstrate the most fundamental coherent control techniques by microwave excitation of spin transitions, namely driven Rabi oscillations and Ramsey fringes upon free evolution. Unprecedented performance is achieved by the microwave hardware devised for these experiments, which enables coherent spin manipulation of individual, isolated, muonium centers. For muonium formed in ${\mathrm{SiO}}_2$ with strong electron-muon hyperfine interaction, a virtually undamped free precession signal is observed up to a $3.5\mu \mathrm{s}$ time window. For muonium formed in Si with weak and anisotropic hyperfine interaction, a strong drive at the multi-quantum transition decouples the muonium center from its magnetic environment formed by the bath of ${}^{29}\mathrm{Si}$ nuclear spins at natural abundance. We expect that these capabilities will provide a powerful tool to investigate the effect of the environment on isolated coupled spins, uncover the details of coupled electron-muon systems in matter and validate quantum electrodynamics in the context of muonium spectroscopy.

Nonlinear dynamics are studied in diverse fields as climate models, avalanches, nanomechanical sensors, optical frequency converters, and electrical quantum amplifiers. A widely studied nonlinear model is the so-called Duffing (or Kerr) resonator, which features a quartic potential term. Two hallmark properties of this model are (i) a shift of a system's resonance frequency as a function of the driving strength, and (ii) monostable or bistable responses, depending on the drive strength and detuning from resonance. Together, these two properties can lead to dynamical phase transitions when several drives are applied simultaneously. Here, we report an experimental and theoretical study of a driven-dissipative nonlinear system with two detuned drives. We observe distinct response regimes characterized by the system's ability to follow the system's time-dependent vector-flow topology. Our work provides an example for understanding dynamical phase transitions in out-of-equilibrium nonlinear systems.

The polarization states of terahertz (THz) radiation generated in a photoionized gas driven by intense two- or multi-frequency fields with locally controlled polarization are studied. We reveal a universal property of the resulting THz waveforms: the ellipticity of their polarization state increases linearly with frequency. This “linear chirp of ellipticity” makes plasma-based THz generation unique among other THz sources. However, it also imposes some constraints on the polarization properties of the generated THz radiation. We derive a general expression for the THz ellipticity and demonstrate how the polarization states of the generated THz waveforms can be manipulated and controlled by the polarization of the pump pulses.

We investigate the hollowing transition of a shell-shaped Bose-Einstein condensate using collective excitations. The shell is created using an immiscible dual-species Bose-Einstein condensate mixture, with its hollowness controlled by tuning the repulsive interspecies interaction via a Feshbach resonance. Our results reveal two distinct monopole modes in which the two condensates oscillate either in phase or out of phase. The spectrum of the out-of-phase mode exhibits a nonmonotonic dependence on the interspecies interaction, providing a clear signature of the topology change from a filled to a hollow condensate. Furthermore, we find that the critical point of the hollowing transition depends strongly on the number ratio of the two species. Our findings provide a detailed understanding of the topology change in shell-shaped quantum gases and pave the way for future study of quantum many-body phenomena in curved spaces.