We construct an exactly solvable lattice model of a fractional Weyl semimetal. The low-energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function, they provide strong experimental signatures for this exotic gapless state of matter.

A closed-trajectory evolution of a quantum state generally imprints a phase that contains both dynamical and geometrical contributions. While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory. Here we generate and measure geometric phases in a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ using a combination of the dynamical quantum Zeno effect and measurement-free evolution. We show that the dynamical quantum Zeno effect can inhibit the formation of a geometric phase without altering the dynamical phase. This can be used to extract the geometric Aharonov-Anandan phase from any closed-trajectory evolution without requiring knowledge or control of the Hamiltonian.

In systems with broken Lorentz invariance the vacuum state of the field can depend on the choice of the inertial reference frame. This leads to observable effects. For example, the motion of an atom with a constant velocity above a flat metal surface can yield atomic excitation with simultaneous emission of a surface plasmon, while uniform motion of the atom through an optical cavity can yield atomic excitation with emission of a photon into cavity modes. We calculate the probability of these processes and make a connection with the Cherenkov radiation of a neutral atom uniformly moving through a medium and Unruh radiation of the atom accelerated in free space. In all these cases the moving atom becomes excited and the field quantum is emitted through vacuum fluctuations at the expense of the kinetic energy of the atom.

The degree of nonorthogonality of eigenstates of non-Hermitian systems governs nuclear scattering, electronic conductance, and wave propagation in disordered media. Here, we determine the impact of non-Hermiticity upon eigenstates inside an open random cavity from measurements of the modal overlap matrix of transmitted microwave radiation. Increasing eigenfunction correlation with spectral modal overlap brought about by the openness of the system leads to modal transmission greatly exceeding unity accompanied by strong modal anticorrelation guaranteeing that transmission does not exceed unity.

We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-spacetime geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.

We investigate the electronic structure of a recently discovered, heavily electron-doped iron-based superconductor ${\mathrm{LaFe}}_2{\mathrm{As}}_2$. Although first-principles calculation shows apparent absence of hole Fermi surfaces around the $\mathrm{\Gamma }$ point, we reveal, by hypothetically removing the La $d$ orbital contribution, that a hole Fermi surface around the $\mathrm{\Gamma }$ point is essentially present. In the collapsed phase of ${\mathrm{LaFe}}_2{\mathrm{As}}_2$, which is nonsuperconducting, the hole Fermi surface is found to be absent, and the difference from the uncollapsed superconducting phase can be naturally understood within the spin-fluctuation-mediated pairing scenario.

We present a comparison between stochastic simulations and mean-field theories for the epidemic threshold of the susceptible-infected-susceptible model on correlated networks (both assortative and disassortative) with a power-law degree distribution $P\left(k\right)\sim k^{-\gamma }$. We confirm the vanishing of the threshold regardless of the correlation pattern and the degree exponent $\gamma$. Thresholds determined numerically are compared with quenched mean-field (QMF) and pair quenched mean-field (PQMF) theories. Correlations do not change the overall picture: The QMF and PQMF theories provide estimates that are asymptotically correct for large sizes for $\gamma <5/2$, while they only capture the vanishing of the threshold for $\gamma >5/2$, failing to reproduce quantitatively how this occurs. For a given size, PQMF theory is more accurate. We relate the variations in the accuracy of QMF and PQMF predictions with changes in the spectral properties (spectral gap and localization) of standard and modified adjacency matrices, which rule the epidemic prevalence near the transition point, depending on the theoretical framework. We also show that, for $\gamma <5/2$, while QMF theory provides an estimate of the epidemic threshold that is asymptotically exact, it fails to reproduce the singularity of the prevalence around the transition.

We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channel scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length and so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter $s_{\text{res}}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.

Right-handed neutrinos in supersymmetric models can act as the source of lepton flavor violation (LFV). We present experimental implications of lepton flavor-violating processes within a supersymmetric type-I seesaw framework in the three-extra-parameter nonuniversal Higgs model (NUHM3) for large [Pontecorvo-Maki-Nakawaga-Sakata- (PMNS-) like] and small [Cabibbo-–Kobayashi-–Maskawa- (CKM-) like] Yukawa mixing scenarios. We highlight LFV predictions for the natural (low ${\mathrm{\Delta }}_{\mathrm{EW}}$) portion of parameter space. Our numerical analysis includes full two-loop renormalization group running effects for the three neutrino masses and mass matrices. We show the projected discovery reach of various LFV experiments (i.e., Mu2e, Mu3e, MEG-II, Belle-II), and specify regions that have already been excluded by the LHC searches. Our results depend strongly on whether one has a normal sneutrino ordering (NSO) or an inverted sneutrino ordering (ISO). Natural supersymmetry (SUSY) with a NSO is already excluded by MEG-2013 results while large portions of ISO have been or will soon be tested. However, LFV processes from natural SUSY with small Yukawa mixing and an ISO seem below any projected sensitivities. A substantial amount of the remaining parameter space of models with large PMNS-like neutrino mixing will be probed by Mu2e and MEG-II experiments whereas small, CKM-like Yukawa mixing predicts LFV decays which can hide from LFV experiments.

Autonomous engines operating at the nanoscale can be prone to deleterious fluctuations in the heat and particle currents. Thermodynamic uncertainty relations (TURs) express a fundamental lower bound which translates a trade-off relation between precision and entropy production. Importantly, recent studies have shown that they can be violated in the quantum regime, thus motivating the search for analogous quantum counterparts. In this paper, we show that the geometry of quantum nonequilibrium steady states alone directly implies the existence of TUR, but with a looser bound, which is not violated by the above recent findings. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennan-Zubarev ensemble, which provides an exact description of nonequilibrium steady states. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the Cramer-Rao bound, a fundamental result from parameter estimation theory. By combining techniques from many-body physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines, where new general bound on the power output are found and discussed.

In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at macroscopic scales. In this work, we apply for the first time the recently developed theory of “topological quantum chemistry” to the study of band structures in photonic crystals. This method allows us to design and diagnose topological photonic band structures using only group theory and linear algebra. As an example, we focus on a family of crystals formed by elliptical rods in a triangular lattice. We show that the symmetry of Bloch states in the Brillouin zone can determine the position of the localized photonic wave packets describing groups of bands. By modifying the crystal structure and inverting bands, we show how the centers of these wave packets can be moved between different positions in the unit cell. Finally, we show that for shapes of dielectric rods, there exist isolated topological bands which do not admit a well-localized description, representing the first physical instance of “fragile” topology in a truly noninteracting system. Our work demonstrates how photonic crystals are the natural platform for the future experimental investigation of fragile topological bands.

The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology.

The precise determination of the excitation energies in condensed-phase molecular systems is important for understanding system-environment interactions as well as for the prerequisite input data of theoretical models used to study the dynamics of the system. The excitation energies are usually determined by fitting of the measured optical spectra that contain broad and unresolved peaks as a result of the thermally random dynamics of the environment. Herein, we propose a method for precise energy determination by strongly coupling the molecular system to an optical cavity and measuring the energy of the resulting polariton. The effect of thermal fluctuations induced by the environment on the polariton is also investigated, from which a power scaling law relating the polariton's linewidth to the number of molecules is obtained. The power exponent gives important information about the environmental dynamics.

When a quantum system is placed in thermal environments, we often assume that the system relaxes to the Gibbs state in which decoherence takes place in the system energy eigenbasis. However, when the coupling between the system and the environments is strong, the stationary state is not necessarily the Gibbs state due to environment-induced decoherence, which can be interpreted as a continuous measurement by the environment. Based on the einselection proposed by Zurek, we postulate that the Gibbs state is projected onto the pointer basis due to the continuous measurement. We justify the proposition by exact numerical simulation of a pair of coupled qubits interacting with boson gases. Furthermore, we demonstrate that heat conduction in nonequilibrium steady states can be suppressed in the strong coupling limit also by the environment-induced decoherence.

Spin-exchange collisions in alkali-metal vapors underlie several fundamental and applied investigations such as nuclear structure studies and tests of fundamental symmetries, ultrasensitive atomic magnetometers, magnetic resonance, and biomagnetic imaging. Spin-exchange collisions cause a loss of spin coherence and concomitantly produce spin noise, both phenomena being central to quantum metrology. We develop here the quantum-trajectory picture of spin-exchange collisions, consistent with their long-standing ensemble description using density matrices. We then use quantum trajectories to reveal the nature of spin-noise correlations that spontaneously build up in multispecies atomic vapors, frequently utilized in the most sensitive spin measurements.

By proposing two schemes (namely, a multistage and a single-stage one) based on the continuous-time quantum walk (CTQW), we study the quantum search on balanced trees of height $r$ with $N$ vertices. For the multistage scheme, we achieve the search for a marked leaf vertex with a runtime $\mathrm{\Theta }\left(N^{(2r-1)/2r}\right)$ and a success probability close to $100\%$ when the branching factor is large. For the single-stage scheme with adjustable edge weights, we achieve the search with an optimal runtime $\mathrm{\Theta }\left(\sqrt{N}\right)$ and a success probability close to $100\%$ as well. Furthermore, we show that our search algorithms also work for real trees with unbalanced structures and are quite robust against various kinds of small perturbations.

Only numerical relativity simulations can capture the full complexities of binary black hole mergers. These simulations, however, are prohibitively expensive for direct data analysis applications such as parameter estimation. We present two fast and accurate surrogate models for the outputs of these simulations: the first model, NRSur7dq4, predicts the gravitational waveform and the second model, NRSur7dq4Remnant, predicts the properties of the remnant black hole. These models extend previous seven-dimensional, noneccentric precessing models to higher mass ratios and have been trained against 1528 simulations with mass ratios $q\le 4$ and spin magnitudes ${\chi }_1,{\chi }_2\le 0.8$, with generic spin directions. The waveform model, NRSur7dq4, which begins about 20 orbits before merger, includes all $\ell \le 4$ spin-weighted spherical harmonic modes, as well as the precession frame dynamics and spin evolution of the black holes. The final black hole model, NRSur7dq4Remnant, models the mass, spin, and recoil kick velocity of the remnant black hole. In their training parameter range, both models are shown to be more accurate than existing models by at least an order of magnitude, with errors comparable to the estimated errors in the numerical relativity simulations. We also show that the surrogate models work well even when extrapolated outside their training parameter space range, up to mass ratios $q=6$.

We report on experimental spectra of photons radiated by 50-GeV positrons crossing silicon single crystals of thicknesses 1.1, 2.0, 4.2, and 6.2 mm at sufficiently small angles to the (110) planes that their motion effectively is governed by the continuum crystal potential. The experiment covers a regime of interaction where each positron emits several hard photons, whose recoils are not negligible and which are formed on lengths where the variation of the crystal field cannot be ignored. As a result, neither the single-photon semiclassical theory of Baier et al. nor the conventional cascade approach to multiple hard photon emissions (quantum radiation reaction) based on the local constant field approximation are able to reproduce the experimental results. After developing a theoretical scheme which incorporates the essential physical features of the experiments, i.e., multiple emissions, photon recoil, and background field variation within the radiation formation length, we show that it provides results in convincing agreement with the data.

We investigate the behavior of a one-dimensional Bose-Hubbard gas in both a ring and a hard-wall box, whose kinetic energy is made to oscillate with zero time average, which suppresses first-order particle hopping. For intermediate and large driving amplitudes, the system in the ring has similarities to the Richardson model, but with a peculiar type of pairing and an attractive interaction in momentum space. This analogy permits an understanding of some key features of the interacting boson problem. The ground state is a macroscopic quantum superposition, or cat state, of two many-body states characterized by the preferential occupation of opposite momentum eigenstates. Interactions give rise to a reduction (or modified depletion) cloud that is common to both macroscopically distinct states. Symmetry arguments permit a precise identification of the two orthonormal macroscopic many-body branches which combine to yield the ground state. In the ring, the system is sensitive to variations of the effective flux but in such a way that the macroscopic superposition is preserved. We discuss other physical aspects that contribute to protect the catlike nature of the ground state.

We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a simple, one-dimensional classical stochastic differential equation approximately describing the phase dynamics of the system under the semiclassical approximation. The density matrix and power spectrum of the original quantum system can be approximately reconstructed from the reduced phase equation. The developed framework enables us to analyze synchronization dynamics of quantum limit-cycle oscillators using the standard methods for classical limit-cycle oscillators in a quantitative way. As an example, we analyze synchronization of a quantum van der Pol oscillator under harmonic driving and squeezing, including the case that the squeezing is strong and the oscillation is asymmetric. The developed framework provides insights into the relation between quantum and classical synchronization and will facilitate systematic analysis and control of quantum nonlinear oscillators.