We propose quantum versions of the Bell-Ziv-Zakai lower bounds for the error in multiparameter estimation. As an application, we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power-law spectrum $\sim 1/|\omega {|}^p$, with $p>1$. With no other assumptions, we show that the mean-square error has a lower bound scaling as $1/{\mathcal{N}}^{2(p-1)/(p+1)}$, where $\mathcal{N}$ is the time-averaged mean photon flux. Moreover, we show that this scaling is achievable by sampling and interpolation, for any $p>1$. This bound is thus a rigorous generalization of the Heisenberg limit, for measurement of a single unknown optical phase, to a stochastically varying optical phase.

We present the theory of the $k$-core pruning process (progressive removal of nodes with degree less than $k$) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree $⟨q⟩$ of the initial network is above, equal to, or below the threshold $⟨q{⟩}_c$ corresponding to the emergence of the giant $k$-core. We find that above the threshold the network relaxes exponentially to the $k$-core. The system manifests the phenomenon known as “critical slowing-down,” as the relaxation time diverges when $⟨q⟩$ tends to $⟨q{⟩}_c$. At the threshold, the dynamics become critical, characterized by a power-law relaxation ($\propto 1/t^2$). Below the threshold, a long-lasting transient process (a “plateau” stage) occurs. This transient process ends with a collapse in which the entire network disappears completely. The duration of the process diverges when $⟨q⟩\to ⟨q{⟩}_c$. We show that the critical dynamics of the pruning are determined by branching processes of spreading damage. Clusters of nodes of degree exactly $k$ are the evolving substrate for these branching processes. Our theory completely describes this branching cascade of damage in uncorrelated networks by providing the time-dependent distribution function of branching. These theoretical results are supported by our simulations of the $k$-core pruning in Erdős-Rényi graphs.

In recent years, ultracold atoms in optical lattices have proven their great value as quantum simulators for studying strongly correlated phases and complex phenomena in solid-state systems. Here, we reveal their potential as quantum simulators for molecular physics and propose a technique to image the three-dimensional molecular orbitals with high resolution. The outstanding tunability of ultracold atoms in terms of potential and interaction offer fully adjustable model systems for gaining deep insight into the electronic structure of molecules. We study the orbitals of an artificial benzene molecule and discuss the effect of tunable interactions in its conjugated $\pi$ electron system with special regard to localization and spin order. The dynamical time scales of ultracold atom simulators are on the order of milliseconds, which allows for the time-resolved monitoring of a broad range of dynamical processes. As an example, we compute the hole dynamics in the conjugated $\pi$ system of the artificial benzene molecule.

Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single-particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions, which lead to extreme nonlinearities in laser-coupled atomic ensembles. As a result, multiple excitation of a micrometer-sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called a “superatom,” is a valuable resource for quantum information, providing a collective qubit. Here, we report on the preparation of 2 orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub-shot-noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in situ detection of the Rydberg excitations and observe the characteristic square-root scaling of the optical coupling with the number of atoms. Enabled by the full control over the atomic sample, including the motional degrees of freedom, we infer the overlap of the produced many-body state with a $W$ state from the observed Rabi oscillations and deduce the presence of entanglement. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.

For quantitative understanding of probabilistic behaviors of living cells, it is essential to construct a correct mathematical description of intracellular networks interacting with complex cell environments, which has been a formidable task. Here, we present a novel model and stochastic kinetics for an intracellular network interacting with hidden cell environments, employing a complete description of cell state dynamics and its coupling to the system network. Our analysis reveals that various environmental effects on the product number fluctuation of intracellular reaction networks can be collectively characterized by Laplace transform of the time-correlation function of the product creation rate fluctuation with the Laplace variable being the product decay rate. On the basis of the latter result, we propose an efficient method for quantitative analysis of the chemical fluctuation produced by intracellular networks coupled to hidden cell environments. By applying the present approach to the gene expression network, we obtain simple analytic results for the gene expression variability and the environment-induced correlations between the expression levels of mutually noninteracting genes. The theoretical results compose a unified framework for quantitative understanding of various gene expression statistics observed across a number of different systems with a small number of adjustable parameters with clear physical meanings.

Weyl semimetals are a class of materials that can be regarded as three-dimensional analogs of graphene upon breaking time-reversal or inversion symmetry. Electrons in a Weyl semimetal behave as Weyl fermions, which have many exotic properties, such as chiral anomaly and magnetic monopoles in the crystal momentum space. The surface state of a Weyl semimetal displays pairs of entangled Fermi arcs at two opposite surfaces. However, the existence of Weyl semimetals has not yet been proved experimentally. Here, we report the experimental realization of a Weyl semimetal in TaAs by observing Fermi arcs formed by its surface states using angle-resolved photoemission spectroscopy. Our first-principles calculations, which match remarkably well with the experimental results, further confirm that TaAs is a Weyl semimetal.

A high-repetition rate electron source is generated by tightly focusing kHz, few-mJ laser pulses into an underdense plasma. This high-intensity laser-plasma interaction leads to stable electron beams over several hours but with strikingly complex transverse distributions even for good quality laser focal spots. We find that the electron beam distribution is sensitive to the laser wave front via the laser midfield distribution rather than the laser focal spot itself. We are able to measure the laser wave front around the focus and include it in realistic particle-in-cell simulations demonstrating the role of the laser wave front on the acceleration of electrons. Distortions of the laser wave front cause spatial inhomogeneities in the midfield laser intensity and, consequently, the laser pulse drives an inhomogeneous transverse wakefield whose focusing and defocusing properties affect the electron distribution. These findings explain the experimental results and suggest the possibility of controlling the electron spatial distribution in laser-plasma accelerators by tailoring the laser wave front.

Topological states of matter are particularly robust, since they exploit global features of a material’s band structure. Topological states have already been observed for electrons, atoms, and photons. It is an outstanding challenge to create a Chern insulator of sound waves in the solid state. In this work, we propose an implementation based on cavity optomechanics in a photonic crystal. The topological properties of the sound waves can be wholly tuned in situ by adjusting the amplitude and frequency of a driving laser that controls the optomechanical interaction between light and sound. The resulting chiral, topologically protected phonon transport can be probed completely optically. Moreover, we identify a regime of strong mixing between photon and phonon excitations, which gives rise to a large set of different topological phases and offers an example of a Chern insulator produced from the interaction between two physically distinct particle species, photons and phonons.

Under ideal conditions, quantum metrology promises a precision gain over classical techniques scaling quadratically with the number of probe particles. At the same time, no-go results have shown that generic, uncorrelated noise limits the quantum advantage to a constant factor. In frequency estimation scenarios, however, there are exceptions to this rule and, in particular, it has been found that transversal dephasing does allow for a scaling quantum advantage. Yet, it has remained unclear whether such exemptions can be exploited in practical scenarios. Here, we argue that the transversal-noise model applies to the setting of recent magnetometry experiments and show that a scaling advantage can be maintained with one-axis-twisted spin-squeezed states and Ramsey-interferometry-like measurements. This is achieved by exploiting the geometry of the setup that, as we demonstrate, has a strong influence on the achievable quantum enhancement for experimentally feasible parameter settings. When, in addition to the dominant transversal noise, other sources of decoherence are present, the quantum advantage is asymptotically bounded by a constant, but this constant may be significantly improved by exploring the geometry.

We demonstrate a photonic circuit with integrated long-lived quantum memories. Precharacterized quantum nodes—diamond microwaveguides containing single, stable, negatively charged nitrogen-vacancy centers—are deterministically integrated into low-loss silicon nitride waveguides. These quantum nodes efficiently couple into the single-mode waveguides with $>1\mathrm{Mcps}$ collected into the waveguide, have narrow single-scan linewidths below 400 MHz, and exhibit long electron spin coherence times up to $120\mu \mathrm{s}$. Our system facilitates the assembly of multiple quantum nodes with preselected properties into a photonic integrated circuit with near unity yield, paving the way towards the scalable fabrication of quantum information processors.

Spontaneous breaking of translational symmetry, known as density-wave order, is common in nature. However, such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We analyze impurity effects on a particularly ubiquitous form of broken translation symmetry in solids: a spin-density wave (SDW) with spatially modulated magnetic order. Related phenomena occur in pair-density-wave (PDW) superconductors where the superconducting order is spatially modulated. For weak disorder, we find that the SDW or PDW order can generically give way to a SDW or PDW glass—new phases of matter with a number of striking properties, which we introduce and characterize here. In particular, they exhibit an interesting combination of conventional (symmetry-breaking) and spin-glass (Edwards-Anderson) order. This is reflected in the dynamic response of such a system, which—as expected for a glass—is extremely slow in certain variables, but, surprisingly, is fast in others. Our results apply to all uniaxial metallic SDW systems where the ordering vector is incommensurate with the crystalline lattice. In addition, the possibility of a PDW glass has important consequences for some recent theoretical and experimental work on ${\text{La}}_{2-x}{\text{Ba}}_x{\text{Cu}}_2{\mathrm{O}}_4$.

We investigate the influence of exciton-phonon coupling on the dynamics of a strongly coupled quantum dot-photonic crystal cavity system and explore the effects of this interaction on different schemes for nonclassical light generation. By performing time-resolved measurements, we map out the detuning-dependent polariton lifetime and extract the spectrum of the polariton-to-phonon coupling with unprecedented precision. Photon-blockade experiments for different pulse-length and detuning conditions (supported by quantum optical simulations) reveal that achieving high-fidelity photon blockade requires an intricate understanding of the phonons’ influence on the system dynamics. Finally, we achieve direct coherent control of the polariton states of a strongly coupled system and demonstrate that their efficient coupling to phonons can be exploited for novel concepts in high-fidelity single-photon generation.

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied to both the ground-state and nonzero-temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-$1/2$ $XXZ$ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.

Energy of propagating electromagnetic waves can be fully absorbed in a thin lossy layer, but only in a narrow frequency band, as follows from the causality principle. On the other hand, it appears that there are no fundamental limitations on broadband matching of thin resonant absorbing layers. However, known thin absorbers produce significant reflections outside of the resonant absorption band. In this paper, we explore possibilities to realize a thin absorbing layer that produces no reflected waves in a very wide frequency range, while the transmission coefficient has a narrow peak of full absorption. Here we show, both theoretically and experimentally, that a thin resonant absorber, invisible in reflection in a very wide frequency range, can be realized if one and the same resonant mode of the absorbing array unit cells is utilized to create both electric and magnetic responses. We test this concept using chiral particles in each unit cell, arranged in a periodic planar racemic array, utilizing chirality coupling in each unit cell but compensating the field coupling at the macroscopic level. We prove that the concept and the proposed realization approach also can be used to create nonreflecting layers for full control of transmitted fields. Our results can have a broad range of potential applications over the entire electromagnetic spectrum including, for example, perfect ultracompact wave filters and selective multifrequency sensors.

Quantum states of light can improve imaging whenever the image quality and resolution are limited by the quantum noise of the illumination. In the case of a bright illumination, quantum enhancement is obtained for a light field composed of many squeezed transverse modes. A possible realization of such a multi-spatial-mode squeezed state is a field which contains a transverse plane in which the local electric field displays reduced quantum fluctuations at all locations, on any one quadrature. Using a traveling-wave amplifier, we have generated a multi-spatial-mode squeezed state and showed that it exhibits localized quadrature squeezing at any point of its transverse profile, in regions much smaller than its size. We observe 75 independently squeezed regions. The amplification relies on nondegenerate four-wave mixing in a hot vapor and produces a bichromatic squeezed state. The result confirms the potential of this technique for producing illumination suitable for practical quantum imaging.

The problem of low Reynolds number turbulence in active nematic fluids is theoretically addressed. Using numerical simulations, I demonstrate that an incompressible turbulent flow, in two-dimensional active nematics, consists of an ensemble of vortices whose areas are exponentially distributed within a range of scales. Building on this evidence, I construct a mean-field theory of active turbulence by which several measurable quantities, including the spectral densities and the correlation functions, can be analytically calculated. Because of the profound connection between the flow geometry and the topological properties of the nematic director, the theory sheds light on the mechanisms leading to the proliferation of topological defects in active nematics and provides a number of testable predictions. A hypothesis, inspired by Onsager’s statistical hydrodynamics, is finally introduced to account for the equilibrium probability distribution of the vortex sizes.

We observe a spontaneous parity breaking bifurcation to a ferromagnetic state in a spatially trapped exciton-polariton condensate. At a critical bifurcation density under nonresonant excitation, the whole condensate spontaneously magnetizes and randomly adopts one of two elliptically polarized (up to 95% circularly polarized) states with opposite handedness of polarization. The magnetized condensate remains stable for many seconds at 5 K, but at higher temperatures, it can flip from one magnetic orientation to another. We optically address these states and demonstrate the inversion of the magnetic state by resonantly injecting 100-fold weaker pulses of opposite spin. Theoretically, these phenomena can be well described as spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations.

The interaction between light and matter can give rise to novel topological states. This principle was recently exemplified in Floquet topological insulators, where classical light was used to induce a topological electronic band structure. Here, in contrast, we show that mixing single photons with excitons can result in new topological polaritonic states—or “topolaritons.” Taken separately, the underlying photons and excitons are topologically trivial. Combined appropriately, however, they give rise to nontrivial polaritonic bands with chiral edge modes allowing for unidirectional polariton propagation. The main ingredient in our construction is an exciton-photon coupling with a phase that winds in momentum space. We demonstrate how this winding emerges from the finite-momentum mixing between $s$-type and $p$-type bands in the electronic system and an applied Zeeman field. We discuss the requirements for obtaining a sizable topological gap in the polariton spectrum and propose practical ways to realize topolaritons in semiconductor quantum wells and monolayer transition metal dichalcogenides.

Here, we report an experimental realization of multimode strong coupling in cavity quantum electrodynamics. This novel regime is achieved when a single artificial atom is simultaneously strongly coupled to a large, but discrete, number of nondegenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. Our experiment reveals complex quantum multimode dynamics and spontaneous generation of quantum coherence, as evidenced by resonance fluorescence spanning many modes and ultranarrow linewidth emission. This work opens a new avenue for future experiments in light-matter interactions and poses a challenge to current theoretical approaches to its study.

Strong-field physics is currently experiencing a shift towards the use of mid-IR driving wavelengths. This is because they permit conducting experiments unambiguously in the quasistatic regime and enable exploiting the effects related to ponderomotive scaling of electron recollisions. Initial measurements taken in the mid-IR immediately led to a deeper understanding of photoionization and allowed a discrimination among different theoretical models. Ponderomotive scaling of rescattering has enabled new avenues towards time-resolved probing of molecular structure. Essential for this paradigm shift was the convergence of two experimental tools: (1) intense mid-IR sources that can create high-energy photons and electrons while operating within the quasistatic regime and (2) detection systems that can detect the generated high-energy particles and image the entire momentum space of the interaction in full coincidence. Here, we present a unique combination of these two essential ingredients, namely, a 160-kHz mid-IR source and a reaction microscope detection system, to present an experimental methodology that provides an unprecedented three-dimensional view of strong-field interactions. The system is capable of generating and detecting electron energies that span a 6 order of magnitude dynamic range. We demonstrate the versatility of the system by investigating electron recollisions, the core process that drives strong-field phenomena, at both low (meV) and high (hundreds of eV) energies. The low-energy region is used to investigate recently discovered low-energy structures, while the high-energy electrons are used to probe atomic structure via laser-induced electron diffraction. Moreover, we present, for the first time, the correlated momentum distribution of electrons from nonsequential double ionization driven by mid-IR pulses.