Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to simulate many-body systems we develop a model-independent formalism to straightforwardly compute bounds on the number of Trotter steps needed to accurately simulate the system's time evolution based on the first-order commutator scaling. We apply this formalism to two closely related many-body models prominent in condensed matter physics, the Hubbard and t-J models. We find that, while a naive comparison of the Trotter depth first seems to favor the Hubbard model, careful consideration of the model parameters and the allowable error for accurate simulation leads to a substantial advantage in favor of the t-J model. These results and formalism set the stage for significant improvements in quantum simulation costs. less

The ANITA collaboration have reported observation of two anomalous events that appear to be $\varepsilon_{\rm cr} \approx 0.6$ EeV cosmic ray showers emerging from the Earth with exit angles of $27^\circ$ and $35^\circ$, respectively. While EeV-scale upgoing showers have been anticipated as a result of astrophysical tau neutrinos converting to tau leptons during Earth passage, the observed exit angles are much steeper than expected in Standard Model (SM) scenarios. Indeed, under conservative extrapolations of the SM interactions, there is no particle that can propagate through the Earth with probability $p > 10^{-6}$ at these energies and exit angles. We explore here whether "beyond the Standard Model" (BSM) particles are required to explain the ANITA events, if correctly interpreted, and conclude that they are. Seeking confirmation or refutation of the physical phenomenon of sub-EeV Earth-emergent cosmic rays in data from other facilities, we find support for the reality of the ANITA events, and three candidate analog events, among the Extremely High Energy Northern Track neutrinos of the IceCube Neutrino Observatory. Properties of the implied BSM particle are anticipated, at least in part, by those predicted for the "stau" slepton ($\tilde{\tau}_R$) in some supersymmetric models of the fundamental interactions, wherein the stau manifests as the next-to-lowest mass supersymmetric partner particle. less

The absence of electrical resistance exhibited by superconducting materials would have enormous potential for applications if it existed at ambient temperature and pressure conditions. Despite decades of intense research efforts, such a state has yet to be realized. At ambient pressures, cuprates are the material class exhibiting superconductivity to the highest critical superconducting transition temperatures (Tc), up to about 133 K. Over the past decade, high-pressure ‘chemical precompression of hydrogen-dominant alloys has led the search for high-temperature superconductivity, with demonstrated Tc approaching the freezing point of water in binary hydrides at megabar pressures. Ternary hydrogen-rich compounds, such as carbonaceous sulfur hydride, offer an even larger chemical space to potentially improve the properties of superconducting hydrides. Here we report evidence of superconductivity on a nitrogen-doped lutetium hydride with a maximum Tc of 294 K at 10 kbar, that is, superconductivity at room temperature and near-ambient pressures. The compound was synthesized under high-pressure high-temperature conditions and then—after full recoverability—its material and superconducting properties were examined along compression pathways. These include temperature-dependent resistance with and without an applied magnetic field, the magnetization (M) versus magnetic field (H) curve, a.c. and d.c. magnetic susceptibility, as well as heat-capacity measurements. X-ray diffraction (XRD), energy-dispersive X-ray (EDX) and theoretical simulations provide some insight into the stoichiometry of the synthesized material. Nevertheless, further experiments and simulations are needed to determine the exact stoichiometry of hydrogen and nitrogen, and their respective atomistic positions, in a greater effort to further understand the superconducting state of the material. less

A folded floating-gate CMOS biosensor is realized for the detection of charged biochemical molecules. The biosensor comprises a field-effect transistor with a floating-gate, a control-gate, and a sensing area. Charged biochemical molecules placed on the sensing area induce a voltage on the floating-gate and a relative shift in the threshold characteristics. Compared to conventional devices, the floating-gate here is folded to span the entire device. This allows us to place the sensing area above the field-effect transistor (FET), thus reducing the total device area. The fabricated devices show good sensitivity to the polarity and concentration of charged poly amino acids. Possible applications of the device include electronic detection of spatial and temporal charge migration such as in biological processes. less

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy dominated era. Modeling the growth rate of perturbations with the ``growth index'' γ, we find that current cosmological data strongly prefer a higher growth index than the value γ=0.55 predicted by general relativity in a flat ΛCDM cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities separately favor growth suppression. When combined, they yield γ=0.633+0.025−0.024, excluding γ=0.55 at a statistical significance of 3.7σ. The combination of fσ8 and Planck measurements prefers an even higher growth index of γ=0.639+0.024−0.025, corresponding to a 4.2σ-tension with the concordance model. In Planck data, the suppressed growth rate offsets the preference for nonzero curvature and fits the data equally well as the latter model. A higher γ leads to a higher matter fluctuation amplitude S8 inferred from galaxy clustering and weak lensing measurements, and a lower S8 from Planck data, effectively resolving the S8 tension. less

The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of sp2 carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and twisted bilayer graphene. Subsequently, we illuminate the origin of flat bands in twisted bilayer graphene at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of twisted bilayer graphene not covered by this review but may readily be approached with the help of this primer. less

Context. The number of known strong gravitational lenses is expected to grow substantially in the next few years. The combination of large samples of lenses has the potential to provide strong constraints on the inner structure of galaxies. Aims: We investigate the extent to which we can calibrate stellar mass measurements and constrain the average dark matter density profile of galaxies by combining strong lensing data from thousands of lenses. Methods: We generated mock samples of axisymmetric lenses. We assume that, for each lens, we have measurements of two image positions of a strongly lensed background source, as well as magnification information from full surface brightness modelling, and a stellar-population-synthesis-based estimate of the lens stellar mass. We then fitted models describing the distribution of the stellar population synthesis mismatch parameter αsps (the ratio between the true stellar mass and the stellar-population-synthesis-based estimate) and the dark matter density profile of the population of lenses to an ensemble of 1000 mock lenses. Results: We obtain the average αsps, projected dark matter mass, and dark matter density slope with greater precision and accuracy compared with current constraints. A flexible model and knowledge of the lens detection efficiency as a function of image configuration are required in order to avoid a biased inference. Conclusions: Statistical strong lensing inferences from upcoming surveys provide a way to calibrate stellar mass measurements and to constrain the inner dark matter density profile of massive galaxies. less

Context. Time-delay lensing is a powerful tool for measuring the Hubble constant H0. However, in order to obtain an accurate estimate of H0 from a sample of time-delay lenses, very good knowledge of the mass structure of the lens galaxies is needed. Strong lensing data on their own are not sufficient to break the degeneracy between H0 and the lens model parameters on a single object basis. Aims: The goal of this study is to determine whether it is possible to break the H0-lens structure degeneracy with the statistical combination of a large sample of time-delay lenses, relying purely on strong lensing data with no stellar kinematics information. Methods: I simulated a set of 100 lenses with doubly imaged quasars and related time-delay measurements. I fitted these data with a Bayesian hierarchical method and a flexible model for the lens population, emulating the lens modelling step. Results: The sample of 100 lenses on its own provides a measurement of H0 with 3% precision, but with a −4% bias. However, the addition of prior information on the lens structural parameters from a large sample of lenses with no time delays, such as that considered in Paper I, allows for a 1% level inference. Moreover, the 100 lenses allow for a 0.03 dex calibration of galaxy stellar masses, regardless of the level of prior knowledge of the Hubble constant. Conclusions: Breaking the H0-lens model degeneracy with lensing data alone is possible, but 1% measurements of H0 require either many more than 100 time-delay lenses or knowledge of the structural parameter distribution of the lens population from a separate sample of lenses. less

Context. Existing samples of strong lenses have been assembled by giving priority to sample size, but this is often at the cost of a complex selection function. However, with the advent of the next generation of wide-field photometric surveys, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness. Aims: There are two main advantages of working with a complete sample of lenses. First, such completeness makes possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. The present work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features. Methods: I introduce a general formalism for the statistical analysis of a sample of strong lenses with known selection function, and then test it on simulated data. The simulation consists of a population of 105 galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of ∼103 strong lenses, which form a complete sample above an observational cut. Results: The method allows the user to recover the distribution of the galaxy population in Einstein radius and mass density slope in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available. Conclusions: Complete samples of lenses are a powerful asset with which to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population. less

Context. Strong lensing mass measurements require the knowledge of the redshift of both the lens and the source galaxy. Traditionally, spectroscopic redshifts are used for this purpose. Upcoming surveys, however, will lead to the discovery of ∼105 strong lenses, and it will be very difficult to obtain spectroscopic redshifts for most of them. Photometric redshift measurements will also be very challenging due to the blending between lens and source light. Aims: The goal of this work is to demonstrate how to carry out an inference of the structural properties of the galaxy population from the analysis of a set of strong lenses with no individual source redshift measurements, and to assess the loss in precision compared to the case in which spectroscopic redshifts are available. Methods: Building on the formalism introduced in Paper III, I developed a method that allows a statistical strong lensing inference to be carried out while marginalising over the source redshifts. This method, which relies on the knowledge of the properties of the unlensed background source population and of the selection function of the survey, generalises an approach known as photogeometric redshift, originally introduced by the Strong Lensing Legacy Survey collaboration. I tested the method on simulated data consisting of a subset of 137 strong lenses that is complete above a cut in observational space. Results: The method recovers the properties of the galaxy population with a precision that is comparable to that attainable in the case in which individual source redshifts are known. Conclusions: The photogeometric redshift method is a viable approach for the analysis of large sets of strong lenses provided that the background source population properties and lens selection function are well known. less

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims: We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods: We selected 2409 central massive elliptical galaxies (log M*/M⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u − g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, Lr, 10, and the light-weighted surface brightness slope, Γ10. Results: We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with Lr, 10 and anti-correlates with Γ10. At fixed redshift, Lr, 10 and Γ10, the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass. less

Context. The Sérsic profile is a widely used model for describing the surface brightness distribution of galaxies. Spiral galaxies, however, are qualitatively different from a Sérsic model. Aims: The goal of this study is to assess how accurately the total flux and half-light radius of a galaxy with spiral arms can be recovered when fitted with a Sérsic profile. Methods: I selected a sample of bulge-dominated galaxies with spiral arms. Using photometric data from the Hyper Suprime-Cam survey, I estimated the contribution of the spiral arms to their total flux. Then I generated simulated images of galaxies with similar characteristics, fitted them with a Sérsic model, and quantified the error on the determination of the total flux and half-light radius. Results: Spiral arms can introduce biases on the photometry of galaxies in a way that depends on the underlying smooth surface brightness profile, the location of the arms, and the depth of the photometric data. A set of spiral arms accounting for 10% of the flux of a bulge-dominated galaxy typically causes the total flux and the half-light radius to be overestimated by 15% and 30%, respectively. This bias, however, is much smaller if the galaxy is disk-dominated. Conclusions: Galaxies with a prominent bulge and a non-zero contribution from spiral arms are the most susceptible to biases in the total flux and half-light radius when fitted with a Sérsic profile. If photometric measurements with high accuracy are required, then measurements over finite apertures are to be preferred over global estimates of the flux. less

Context. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, αsps , defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards larger stellar masses, smaller half-mass radii and larger dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of 0.5′′ , the strong lensing bias in αsps is 10% , while that in the central dark matter mass is 5% . The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Quadruply imaged quasar lenses, however, are biased towards higher ellipticity galaxies. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. less

How hot is the Universe today? How hot was it before? We report on the result of the observational determination of the mean temperature of hot gas in the Universe. We find that the mean gas temperature has increased ten times over the last 8 billion years, to reach about 2 million Kelvin today. As cosmic structures form, matter density fluctuations collapse gravitationally and baryonic matter is shock-heated and thermalized. We therefore expect a connection between the mean gravitational potential energy of collapsed halos and the mean thermal energy of baryons. Our result provides quantitative verification of such a connection via cosmic shock-heating. less

The observed pattern of linear polarization of the cosmic microwave background (CMB) photons is a sensitive probe of physics violating parity symmetry under inversion of spatial coordinates. A new parity-violating interaction might have rotated the plane of linear polarization by an angle β as the CMB photons have been traveling for more than 13 billion years. This effect is known as "cosmic birefringence." In this paper, we present new measurements of cosmic birefringence from a joint analysis of polarization data from two space missions, Planck and WMAP. This dataset covers a wide range of frequencies from 23 to 353 GHz. We measure β=0.342°+0.094°−0.091° (68% C.L.) for nearly full-sky data, which excludes β=0 at 99.987% C.L. This corresponds to the statistical significance of 3.6σ. There is no evidence for frequency dependence of β. We find a similar result, albeit with a larger uncertainty, when removing the Galactic plane from the analysis. less

We search for evidence of parity-violating physics in the Planck 2018 polarization data, and report on a new measurement of the cosmic birefringence angle, β. The previous measurements are limited by the systematic uncertainty in the absolute polarization angles of the Planck detectors. We mitigate this systematic uncertainty completely by simultaneously determining β and the angle miscalibration using the observed cross-correlation of the E- and B-mode polarization of the cosmic microwave background and the Galactic foreground emission. We show that the systematic errors are effectively mitigated and achieve a factor-of-2 smaller uncertainty than the previous measurement, finding β=0.35±0.14° (68% C.L.), which excludes β=0 at 99.2% C.L. This corresponds to the statistical significance of 2.4σ. less

Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z2 topological order [G. Semeghini et al., Science 374, 1242 (2021)], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of "magnetic" monopoles and the Higgs transition driven by a proliferation of "electric" charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator. less

Mutually distorted layers of graphene give rise to a moiré pattern and a variety of non-trivial phenomena. We show that the continuum limit of this class of models is equivalent to a (2+1)-dimensional field theory of Dirac fermions coupled to two classical gauge fields. We further show that the existence of a flat band implies an effective dimensional reduction in the field theory, where the time dimension is ``removed.'' The resulting two-dimensional Euclidean theory contains the chiral anomaly. The associated Atiyah-Singer index theorem provides a self-consistency condition for the existence of flat bands. In particular, it reproduces a series of quantized magic angles known to exist in twisted bilayer graphene in the chiral limit where there is a particle-hole symmetry. We also use this criterion to prove that an external magnetic field splits this series into pairs of magnetic field-dependent magic angles associated with flat moiré-Landau bands. The topological criterion we derive provides a generic practical method for finding flat bands in a variety of material systems including but not limited to moiré bilayers. less

We evaluate the spin-wave spectrum and dynamic susceptibility in a layered superconductors with helical interlayer magnetic structure. We especially focus on the structure in which the moments rotate 90∘ from layer to layer realized in the iron pnictide RbEuFe4As4. The spin-wave spectrum in superconductors is strongly renormalized due to the long-range electromagnetic interactions between the oscillating magnetic moments. This leads to a strong enhancement of the frequency of the mode coupled with a uniform field and this enhancement exists only within a narrow range of the c-axis wave vectors of the order of the inverse London penetration depth. The key feature of materials like RbEuFe4As4 is that this uniform mode corresponds to the maximum frequency of the spin-wave spectrum with respect to the c-axis wave vector. As a consequence, the high-frequency surface resistance acquires a very distinct asymmetric feature spreading between the bare and renormalized frequencies. We also consider the excitation of spin waves with Josephson effect in a tunneling contact between helical-magnetic and conventional superconductors and study the interplay between the spin-wave features and geometrical cavity resonances in the current-voltage characteristics. less

We consider a clean layered magnetic superconductor in which a continuous magnetic transition takes place inside superconducting state and the exchange interaction between superconducting and magnetic subsystems is weak so that superconductivity is not destroyed at the magnetic transition. An example of such material is RbEuFe4As4. We investigate the suppression of the superconducting gap and superfluid density by correlated magnetic fluctuations in the vicinity of the magnetic transition. The influence of nonuniform exchange field on superconducting parameters is sensitive to the relation between the magnetic correlation length, ξh, and superconducting coherence length ξs defining the 'scattering' (ξh<ξs) and 'smooth' (ξh>ξs) regimes. As a small uniform exchange field does not affect the superconducting gap and superfluid density at zero temperature, smoothening of the spatial variations of the exchange field reduces its effects on these parameters. We develop a quantitative description of this 'scattering-to-smooth' crossover for the case of quasi-two-dimensional magnetic fluctuations. Since the magnetic-scattering probability varies at the energy scale comparable with the gap, the quasiclassical approximation is not applicable in the crossover region and microscopic treatment is required. We find that the corrections to both the gap and superfluid density grow proportionally to ξh until it remains much smaller than ξs. When ξh exceeds ξs, both parameters have much weaker dependence on ξh. Moreover, the gap correction may decrease with increasing of ξh in the vicinity of the magnetic transition. We also find that the crossover is unexpectedly broad: the standard scattering approximation becomes sufficient only when ξh is substantially smaller than ξs. less

We construct a dynamical decoupling protocol for accurately generating local and global symmetries in general many-body systems. Multiple commuting and non-commuting symmetries can be created by means of a self-similar-in-time ("polyfractal") drive. The result is an effective Floquet Hamiltonian that remains local and avoids heating over exponentially long times. This approach can be used to realize a wide variety of quantum models, and non-equilibrium quantum phases. less

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One of the main challenges in the Variational Quantum Eigensolver (VQE) framework is construction of the unitary transformation. The dimensionality of the space for unitary rotations of N qubits is 4^N−1, which makes the choice of a polynomial subset of generators exponentially difficult process. Moreover, due to non-commutativity of generators, the order in which they are used strongly affects results. Choosing the optimal order in a particular subset of generators requires testing the factorial number of combinations. We propose an approach based on the Lie algebra - Lie group connection and corresponding closure relations that systematically eliminates the order problem. less

We study the effective model for superconducting magic-angle twisted bilayer graphene beyond mean-field approximation by using Monte Carlo simulations. We consider the parameter regime where the low-temperature phase is a superconductor that spontaneously breaks time-reversal symmetry. When fluctuations are taken into account, it is shown that a fluctuations-induced phase with a fermion quadrupling order appears, where a different condensate, formed by four electrons, breaks time-reversal symmetry. less

Quantum chemistry calculations for small molecules on quantum hardware have been demonstrated to date only on universal-gate quantum computers, not quantum annealers. The latter devices are limited to finding the lowest eigenstate of the Ising Hamiltonian whereas the electronic Hamiltonian could not be mapped to the Ising form without exponential growth of the Ising Hamiltonian with the size of the system [J. Phys. Chem. B 122, 3384 (2018)]. Here we propose a novel mixed discrete-continuous optimization algorithm, which finds the lowest eigenstate of the qubit coupled cluster (QCC) method using a quantum annealer for solving a discrete part of the problem. The QCC method is a potentially exact approach for constructing the electronic wave function in the qubit space. Therefore, our methodology allows for systematically improvable quantum chemistry calculations using quantum annealears. We illustrate capabilities of our approach by calculating QCC ground electronic states for the LiH, H2O, and C6H6 molecules. C6H6 calculations involve 36 qubits and are the largest quantum chemistry calculations made on a quantum annealer (the D-Wave 2000Q system) to date. Our findings opens up a new perspective for use quantum annealers in high-throughput material discovery. less

An arbitrary operator corresponding to a physical observable cannot be measured in a single measurement on currently available quantum hardware. To obtain the expectation value of the observable, one needs to partition its operator to measurable fragments. However, the observable and its fragments generally do not share any eigenstates, and thus the number of measurements needed to obtain the expectation value of the observable can grow rapidly even when the wavefunction prepared is close to an eigenstate of the observable. We provide a unified Lie algebraic framework for developing efficient measurement schemes for quantum observables, it is based on two elements: 1) embedding the observable operator in a Lie algebra and 2) transforming Lie algebra elements into those of a Cartan sub-algebra (CSA) using unitary operators. The CSA plays the central role because all its elements are mutually commutative and thus can be measured simultaneously. We illustrate the framework on measuring expectation values of Hamiltonians appearing in the Variational Quantum Eigensolver approach to quantum chemistry. The CSA approach puts many recently proposed methods for the measurement optimization within a single framework, and allows one not only to reduce the number of measurable fragments but also the total number of measurements. less

An important goal of modern condensed matter physics involves the search for states of matter with new emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at hetero-interfaces , precise alignment of low-dimensional materials and the use of extreme pressures . Here, we highlight a new paradigm, based on controlling light-matter interactions, which provides a new way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of novel phenomena. Photon-mediated superconductivity, cavity-fractional quantum Hall physics and optically driven topological phenomena in low dimensions are amongst the frontiers discussed in this perspective, which puts a spotlight on a new field that we term here “strongly-correlated electron-photon science.” less

Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field (MF) theories have not been formulated so far. To resolve this problem, first, we define what MF theory is, independently of a Hamiltonian realization in a particular set of operators. Second, using a Lie-algebraic framework we formulate a criterion for a Hamiltonian to be MF solvable. The criterion is applicable for both distinguishable and indistinguishable particle cases. For the electronic Hamiltonians, our approach reveals the existence of MF solvable Hamiltonians of higher fermionic operator powers than quadratic. Some of the MF solvable Hamiltonians require different sets of quasi-particle rotations for different eigenstates, which reflects a more complicated structure of such Hamiltonians. less

Application of current and near-term quantum hardware to the electronic structure problem is highly limited by qubit counts, coherence times, and gate fidelities. To address these restrictions within the variational quantum eigensolver (VQE) framework, many recent contributions have suggested dressing the electronic Hamiltonian to include a part of electron correlation, leaving the rest to be accounted by VQE state preparation. We present a new dressing scheme that combines preservation of the Hamiltonian hermiticity and an exact quadratic truncation of the Baker-Campbell-Hausdorff expansion. The new transformation is constructed as the exponent of an involutory linear combination (ILC) of anti-commuting Pauli products. It incorporates important strong correlation effects in the dressed Hamiltonian and can be viewed as a classical preprocessing step alleviating the resource requirements of the subsequent VQE application. The assessment of the new computational scheme for electronic structure of the LiH, H2O, and N2 molecules shows significant increase in efficiency compared to conventional qubit coupled cluster dressings. less

Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the parametric-shift-rule to formulating these gradients as linear combinations of expectation values for generators with general eigen-spectrum (i.e. with more than two eigenvalues). Our approaches are exact and do not use any auxiliary qubits, instead they rely on a generator eigen-spectrum analysis. Two main directions in the parametric-shift-rule extensions are 1) polynomial expansion of the exponential unitary operator based on a limited number of different eigenvalues in the generator and 2) decomposition of the generator as a linear combination of low-eigenvalue operators (e.g. operators with only 2 or 3 eigenvalues). These techniques have a range of scalings for the number of needed expectation values with the number of generator eigenvalues from quadratic (for polynomial expansion) to linear and even log2 (for generator decompositions). This allowed us to propose efficient differentiation schemes superior to previous approaches for commonly used 2-qubit transformations (e.g. match-gates, transmon and fSim gates) and Ŝ^2-conserving fermionic operators for the variational quantum eigensolver. less

We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the 1-norm of their coefficients, which is associated with the quantum circuit complexity. It is derived that the lowest possible LCU 1-norm for a given Hamiltonian is half of its spectral range. This lowest norm decomposition is practically unattainable for general Hamiltonians; therefore, multiple practical techniques to generate LCU decompositions are proposed and assessed. A technique using symmetries to reduce the 1-norm further is also introduced. In addition to considering LCU in the Schrödinger picture, we extend it to the interaction picture, which substantially further reduces the 1-norm. less

Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via Trotterization, where a sequence of short-time evolutions of fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is used. Given multiple choices of possible Hamiltonian decompositions to fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends on the choice of the fragments. We assess efficiency of multiple Hamiltonian partitioning techniques using fermionic and qubit algebras for the Trotterization. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. This reduction makes fermionic-based partitioning Trotter errors lower compared to those in qubit-based techniques. However, from the simulation-cost standpoint, fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step and thus are more computationally expensive compared to their qubit counterparts. less

Several experimental platforms, such as superconducting circuits or ultracold atomic in optical lattices, nowadays allow to probe many-body physics in unprecedented regimes, such as in non-equilibrium conditions resulting from controlled dissipation and driving, but theoretical techniques for describing those regimes are limited. In this work [1], we introduce an extension of the nonequilibrium dynamical mean-field theory (DMFT) for bosonic lattice models described by Markovian master equations. DMFT maps these lattice problems onto a problem of a single site coupled to a classical field and to a non-interacting bath, accounting for leading corrections to Gutzwiller mean-field theory due to finite dimensionality. Our approach relies on a new method for solving the effective single-site problem based on a non-crossing approximation in the coupling to the DMFT bath, going beyond standard Born-Markov approximations [2]. We then discuss an application to a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump, computing its steady-state properties. DMFT captures hopping-induced processes that are completely missed by Gutzwiller mean-field theory, which are crucial to obtain the correct stationary-state, such as to describe its quantum-Zeno behaviour when the losses are strong, or to predict the critical hopping for a phase transition between an incoherent phase and a coherent, limit-cycle phase. [1] O. Scarlatella, A. A. Clerk, R. Fazio, and M. Schiró, Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems, Phys. Rev. X 11, 031018 (2021). [2] O. Scarlatella and M. Schiro, Self-Consistent Dynamical Maps for Open Quantum Systems, arXiv:2107.05553. less

In general, magnetism and superconductivity are antagonistic to each other. However, there are several families of superconductors in which superconductivity coexists with magnetism, and a few examples are known where the superconductivity itself induces spontaneous magnetism. The best-known of these compounds are Sr2RuO4 and some non-centrosymmetric superconductors. Here, we report the finding of a narrow dome of an s+is′ superconducting phase with apparent broken time-reversal symmetry (BTRS) inside the broad s-wave superconducting region of the centrosymmetric multiband superconductor Ba1 − xKxFe2As2 (0.7 ≲ x ≲ 0.85). We observe spontaneous magnetic fields inside this dome using the muon spin relaxation (μSR) technique. Furthermore, our detailed specific heat study reveals that the BTRS dome appears very close to a change in the topology of the Fermi surface. With this, we experimentally demonstrate the likely emergence of a novel quantum state due to topological changes in the electronic system. less

By using intense coherent electromagnetic radiation, it may be possible to manipulate the properties of quantum materials very quickly, or even induce new and potentially useful phases that are absent in equilibrium. For instance, ultrafast control of magnetic dynamics is crucial for a number of proposed spintronic devices and can also shed light on the possible dynamics of correlated phases out of equilibrium. Inspired by recent experiments on spin-orbital ferromagnet YTiO3 we consider the nonequilibrium dynamics of Heisenberg ferromagnetic insulator with low-lying orbital excitations. We model the dynamics of the magnon excitations in this system following an optical pulse which resonantly excites infrared-active phonon modes. As the phonons ring down they can dynamically couple the orbitals with the low-lying magnons, leading to a dramatically modified effective bath for the magnons. We show this transient coupling can lead to a dynamical acceleration of the magnetization dynamics, which is otherwise bottlenecked by small anisotropy. Exploring the parameter space more we find that the magnon dynamics can also even completely reverse, leading to a negative relaxation rate when the pump is blue-detuned with respect to the orbital bath resonance. We therefore show that by using specially targeted optical pulses, one can exert a much greater degree of control over the magnetization dynamics, allowing one to optically steer magnetic order in this system. We conclude by discussing interesting parallels between the magnetization dynamics we find here and recent experiments on photo-induced superconductivity, where it is similarly observed that depending on the initial pump frequency, an apparent metastable superconducting phase emerges. less

We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator [ai,a†i]=1 is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms. less

We use field-theoretic methods to explore the statistics of eigenfunctions of the Floquet operator for a large family of Floquet random quantum circuits. The correlation function of the quasienergy eigenstates is calculated and shown to exhibit random matrix circular unitary ensemble statistics, which is consistent with the analogue of Berry's conjecture for quantum circuits. This quantity determines all key metrics of quantum chaos, such as the spectral form factor and thermalizing time-dependence of the expectation value of an arbitrary observable. It also allows us to explicitly show that the matrix elements of local operators satisfy the eigenstate thermalization hypothesis (ETH); i.e., the variance of the off-diagonal matrix elements of such operators is exponentially small in the system size. These results represent a proof of ETH for the family of Floquet random quantum circuits at a physical level of rigor. An outstanding open question for this and most of other sigma-model calculations is a mathematically rigorous proof of the validity of the saddle-point approximation in the large-N limit. less

This presentation reviews basics of quantum mechanics, quantum computing, and quantum sensing with an eye on practical applications, if any, of various quantum technologies. It discusses a realistic roadmap, time scales, and challenges facing this space and is intended for a business audience, C-level executives, and investors considering strategic decisions about engaging with nascent quantum technology (or not). P.S. Supporting video content, animation, and copies of the accompanying Nature article are available upon request (through the ScienceCast comment section below). less

Quantum simulation using time evolution in phase-estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based quantum simulation uses effective time evolution via measurement to allow runtime advantages over conventional circuit-based algorithms that use real-time evolution with quantum gates. We construct a hybrid algorithm to find energy eigenvalues in fermionic models using only measurements on graph states. We apply the algorithm to the Kitaev and Hubbard chains. Resource estimates show a runtime advantage if measurements can be performed faster than gates, and graph states compactification is fully used. In this letter, we set the stage to allow advances in measurement precision to improve quantum simulation. less

Quantum annealing is a powerful alternative model of quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive demonstration of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage (such as the adiabatic formulation of Grover's search problem) generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by experimental uncertainties and random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we explore three realistic noise channels and show that the speedup from RFQA is resilient to 1/f-like local potential fluctuations and local heating from interaction with a sufficiently low temperature bath. Another noise channel, bath-assisted quantum cooling transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. We also detail how RFQA may be implemented experimentally with current technology. less

This work reviews our recent theoretical ideas along with related experimental results related to engineering non-equilibrium protocols and electromagnetic environments to enhance superconductivity in solid-state materials. First, I'll discuss a generalization of the Kennes, Millis et al's protocol of using phonon squeezing to strongly enhance superconducting Tc, in particular close to the dynamical lattice instabilities caused by driving. Second, I will briefly review recent ideas of using cavity structures to engineer electromagnetic environments more favorable to superconductivity compared to materials in free space. Finally, I will zero in on hyperbolic metamaterial structures, which have been experimentally shown to strongly enhance superconducting Tc and the critical magnetic field in various compounds. These effects are usually attributed to hyperbolic plasmons, but I will argue that the conventional theory is probably unreliable. Based on our work in progress, I will speculate that it is likely boundary phonons that help bootstrap superconductivity in such systems. However, at the moment the nature of enhancement of superconductivity in hyperbolic metamaterials remains a bit of a mystery. less

​​​​​​​Integer quantum Hall effect, Chern insulators, topological insulators, and  topological superconductors are famous examples of topological phases in noninteracting or weakly correlated electron systems. In these states  the ground state is nondegenerate and the excitations carry the original quantum  numbers. Fractional quantum Hall effect (FQHE) and spin liquids, on the other hand, arise in strongly correlated electron systems and exhibit exotic properties such as  ground state degeneracy and fractionalized excitations, dubbed as topologically ordered states, with potential applications in quantum computations. While there are many material candidates for noninteracting topological phases of matter, the topological orders usually arise in texteme conditions such as strong magnetic fields and low temperatures, e.g., in FQHE, and in spin liquids, usually the extra interactions between spins spoil the realization of true topological orders.  Here, we ask the following question: Can we design the topological orders in  more conventional systems by properly coupling the degrees of freedom together? we try to present an understanding of one of the simplest topological orders, the Wen plaquette model, in a superconducting lattice model. Then, we discuss how one may obtain more exotic topological orders. less

The surface of a topological insulator hosts Dirac electronic states with the spin-momentum locking, which constrains spin orientation perpendicular to electron momentum. As a result, collective plasma excitations in the interacting Dirac liquid manifest themselves as coupled charge- and spin-waves. Here we demonstrate that the presence of the spin component enables effective coupling between plasma waves and spin waves at interfaces between the surface of a topological insulator and insulating magnet. Moreover, the helical nature of spin-momentum locking textures provides the phase winding in the coupling between the spin and plasma waves that makes the spectrum of hybridized spin-plasma modes to be topologically nontrivial. We also show that such topological modes lead to a large thermal Hall response. less

Due to its rotation, Earth traps a few equatorial ocean and atmospheric waves, including Kelvin, Yanai, Rossby, and Poincare modes. It has been recently demonstrated that the mathematical origin of equatorial waves is intricately related to the nontrivial topology of hydrodynamic equations describing oceans or the atmosphere. In the present work, we consider plasma oscillations supported by a two-dimensional electron gas confined at the surface of a sphere or a cylinder. We argue that in the presence of a uniform magnetic field, these systems host a set of equatorial magnetoplasma waves that are counterparts to the equatorial waves trapped by Earth. For a spherical geometry, the equatorial modes are well developed only if their penetration length is smaller than the radius of the sphere. For a cylindrical geometry, the spectrum of equatorial modes is weakly dependent on the cylinder radius and overcomes finite-size effects. We argue that this exceptional robustness can be explained by destructive interference effects. We discuss possible experimental setups, including grains and rods composed of topological insulators (e.g., Bi2Se3) or metal-coated dielectrics (e.g., Au2S). less

When studying strongly correlated systems using quantum circuits, it is important to prepare good initial states from which the target many-body states can easily be accessed. Here, we discuss an efficient quantum circuit preparation of the resonating valence bond (RVB) state, which plays an essential role in understanding the high-Tc superconductivity and the spin liquid physics. It is known that the RVB state is given by the Gutzwiller projection of a Bardeen-Cooper-Schrieffer (BCS) state for which an efficient quantum circuit construction is known. However, since the overlap between the RVB state and the BCS state decays exponentially in the system size, naive implementation of the Gutzwiller projection as projective measurements in quantum circuit would require exponentially many repetitions in order to obtain the RVB state. In this talk, we discuss how to systematically amplify the amplitude associated with the RVB state in the BCS state using a recently developed amplitude amplification technique. Following our construction, one can construct a quantum circuit for the RVB state with an arbitrarily high success probability. less

Systems harboring parafermion zero-modes hold promise as platforms for topological quantum computation. Recent experimental work (Gül et al., arXiv:2009.07836) provided evidence for proximity-induced superconductivity in fractional quantum Hall edges, a prerequisite in proposed realizations of parafermion zero-modes. The main evidence was the observation of a crossed Andreev reflection signal, in which electrons enter the superconductor from one chiral mode and are reflected as holes to another, counter-propagating chiral mode. Remarkably, while the probability for cross Andreev reflection was much smaller than one, it was stronger for $\nu=1/3$ fractional quantum Hall edges than for integer ones. We theoretically explain these findings, including the relative strengths of the signals in the two cases and their qualitatively different temperature dependencies. Beyond the coupling of the two counter-propagating modes through Andreev reflection and back-scattering, an essential part of our model is the coupling of the edge modes to normal states in the cores of Abrikosov vortices located close to the edges. These vortices are made dense by the magnetic field needed to form the quantum Hall states, and provide a metallic bath to which the edges are tunnel-coupled. The stronger crossed Andreev reflection in the fractional case originates from the suppression of electronic tunneling between the bath and the fractional quantum Hall edges. Our theory shows that the mere observation of crossed Andreev reflection signal does not necessarily imply the presence of localized parafermion zero-modes, and suggests ways to identify their presence from the behavior of this signal in the low-temperature limit. less

We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to the strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability. less

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multi dimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self dual under Wegner's duality, with the self dual point corresponding to the RK point of the original multi-dimer model. We argue that the self dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is non-bipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host Z2 topologically ordered phases. less

Quantum interference can terminate energy growth in a continually kicked system, via a single-particle ergodicity-breaking mechanism known as dynamical localization. The effect of many-body interactions on dynamically localized states, while important to a fundamental understanding of quantum decoherence, has remained unexplored despite a quarter-century of experimental studies. We report the experimental realization of a tunably-interacting kicked quantum rotor ensemble using a Bose-Einstein condensate in a pulsed optical lattice. We observe signatures of a prethermal localized plateau, followed for interacting samples by interaction-induced anomalous diffusion with an exponent near one half. Echo-type time reversal experiments establish the role of interactions in destroying reversibility. These results quantitatively elucidate the dynamical transition to many-body quantum chaos, advance our understanding of quantum anomalous diffusion, and delimit some possibilities for protecting quantum information in interacting driven systems. less

We propose the Casimir effect as a general method to observe Lifshitz transitions in electron systems. The concept is demonstrated with a planar spin-orbit coupled semiconductor in a magnetic field. We calculate the Casimir force between two such semiconductors and between the semiconductor and a metal as a function of the Zeeman splitting in the semiconductor. The Zeeman field causes a Fermi pocket in the semiconductor to form or collapse by tuning the system through a topological Lifshitz transition. We find that the Casimir force experiences a kink at the transition point and noticeably different behaviors on either side of the transition. The simplest experimental realization of the proposed effect would involve a metal-coated sphere suspended from a micro-cantilever above a thin layer of InSb (or another semiconductor with large g-factor). Numerical estimates are provided and indicate that the effect is well within experimental reach. less

The vacuum catastrophe is a fundamental puzzle, where the observed scales of the cosmological constant are many orders of magnitude smaller than the natural scales expected in the theory. This work proposes a new ``bi-world'' construction that may offer an insight into the cosmological constant problem. The model generally includes a $(3+1)$-dimensional manifold with two different geometries and matter fields residing on them. The diffeomorphism invariance and causality highly constrain the two metrics to be conformally related, $\eta_{\mu \nu} = \phi^2 g_{\mu \nu}$. This reduces the theory to a standard single-world description, but introduces a new inherently geometrical ``moir{\'e} field,'' $\phi$. Interestingly, the moir{\'e} field has the character of both a dilaton and Higgs field familiar in the conventional theory. Integrating out the moir{\'e} field naturally gives rise to the Starobinsky action and inflationary dynamics. In the framework of the Friedmann-Lemaitre–Robertson–Walker solution, we reduce an effective action for the moir{\'e} field to that of a particle moving in a Mexican hat potential. The equations of motion are then solved numerically and the moir{\'e} field is shown to approach a Mexican-hat minimum in an oscillatory fashion, which is accompanied by the decay of the Hubble parameter. Under additional reasonable assumptions, the vacuum energy asymptotically approaches zero in the end of inflationary evolution. The physics presented here shares similarities with the moir{\'e} phenomena in condensed matter and elsewhere, where two similar structures superimposed upon give rise to a superstructure with low emergent energy scales compared to the native theories. less

The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED, it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one-dimensional systems. In this Letter, we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa’s path integral method, we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the nonlinear response of the system. In particular, we find an interaction-dependent density response due to a change in the magnetic field as well as a contribution to the nonequilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value. less

Ergodic theory provides a rigorous mathematical description of classical dynamical systems, including a formal definition of the ergodic hierarchy consisting of merely ergodic, weakly-, strongly-, and K-mixing systems. Closely related to this hierarchy is a less-known notion of cyclic approximate periodic transformations [see, e.g., I. Cornfield, S. Fomin, and Y. Sinai, Ergodic theory (Springer-Verlag New York, 1982)], which maps any "ergodic" dynamical system to a cyclic permutation on a circle and arguably represents the most elementary notion of ergodicity. This paper shows that cyclic ergodicity generalizes to quantum dynamical systems, which is proposed here as the basic rigorous definition of quantum ergodicity. It implies the ability to construct an orthonormal basis, where quantum dynamics transports an initial basis vector to all other basis vectors one by one, while minimizing the error in the overlap between the time-evolved initial state and a given basis state with a certain precision. It is proven that the basis, optimizing the error over all cyclic permutations, is obtained via the discrete Fourier transform of the energy eigenstates. This relates quantum cyclic ergodicity to level statistics. We then show that Wigner-Dyson level statistics implies quantum cyclic ergodicity, but that the reverse is not necessarily true. For the latter, we study an irrational flow on a 2D torus and argue that both classical and quantum flows are cyclic ergodic, while the level statistics is non-universal. We use the cyclic construction to motivate a quantum ergodic hierarchy of operators and argue that under the additional assumption of Poincare recurrences, cyclic ergodicity is a necessary condition for such operators to satisfy eigenstate thermalization. This work provides a general framework for transplanting some rigorous results of ergodic theory to quantum dynamical systems. less

A new paradigm for materials design emerges when a concerted interaction between strongly correlated materials, photons and phonons is established. Here we present some new avenues for the design and control of materials in and out of equilibrium by exploring the formation of strongly hybridized light-matter hybrids that lead the relation of fundamentally new materials functionalities. less