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.

A theoretical framework is developed that permits construction of biskyrmion lattices observed in nonchiral magnetic films. Skyrmion and antiskyrmion configurations are discussed. We study films of finite thickness containing up to $1000\times 1000\times 100$ spins. Hexatic biskyrmion lattices in a pure two-dimensional (2D) exchange model are naturally described by the Weierstrass  $\wp$  and $\zeta$ elliptic functions. Starting with such a lattice as an initial state, we investigate how it evolves toward a minimum-energy state in a zero magnetic field in the presence of perpendicular magnetic anisotropy (PMA) and dipole-dipole interaction. Metastable biskyrmion lattices exist at low PMA. At higher PMA, we observe stable triangular lattices of biskyrmion bubbles containing Bloch lines, whose energies are lower than the energy of the uniformly magnetized state.

The heavy-fermion metal ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ realizes a field-induced quantum critical point with multiple vanishing energy scales $T_{\mathrm{N}}\left(B\right)$ and $T^{*}\left(B\right)$. We investigate their change with partial non-isoelectronic substitutions, chemical and hydrostatic pressure. Low-temperature electrical resistivity, specific heat, and magnetic susceptibility of $\mathrm{Yb}{\left({\mathrm{Rh}}_{1-x}{T}_x\right)}_2{\mathrm{Si}}_2$ with $T=\text{Fe}$ or Ni for $x\le 0.1$, magnetic fields $B\le 0.3\mathrm{T}$ (applied perpendicular to the $c$ axis), and hydrostatic pressure $p\le 1.5\mathrm{GPa}$ are reported. The data allow us to disentangle the combined influences of hydrostatic and chemical pressure, as well as non-isoelectronic substitution. In contrast to Ni and Co substitution, which enhance magnetic order, Fe substitution acts oppositely. For $x=0.1$, it also completely suppresses the $T^{*}$ crossover and eliminates ferromagnetic fluctuations. The pressure, magnetic field, and temperature dependences of $T^{*}$ are incompatible with its interpretation as Kondo breakdown signature.

In a viscous fluid, the past motion of an accelerating particle is retained as an imprint on the vorticity field, which decays slowly as $t^{-3/2}$. At low Reynolds number, the Basset-Boussinesq-Oseen (BBO) equation correctly describes nonuniform particle motion, capturing hydrodynamic memory effects associated with this slow algebraic decay. Using the BBO equation, we numerically simulate driven single-particle transport to show that memory effects persist indefinitely under rather general driving conditions. In particular, when driving forces do not vary smoothly, hydrodynamic memory substantially lowers the effective transport friction. Remarkably, this enables coasting over a spatially uneven potential that otherwise traps particles modeled with pure Stokes drag. Our results provide direct physical insight into the role of particle-fluid coupling in nonequilibrium microparticle transport.

The electric field inside typical conductors drops down exponentially with the screening length determined by an intrinsic length scale of the system such as the density of mobile carriers. We show that in a classically conformal system with boundaries, where the intrinsic length scale is absent, the screening of an external electric field is governed by the quantum conformal anomaly associated with the renormalization of the electric charge. The electric field decays algebraically with a fractional power determined by the beta function of the system. We argue that this “anomalous conformal screening effect” is an indirect manifestation of the Schwinger pair production in relativistic field theory. We discuss the experimental feasibility of the proposed phenomenon in Dirac semimetals that would allow a direct experimental access to the beta function.

We develop a Landau-like theory to characterize phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two states or phases is characterized by the behavioral change in the order parameter of the system namely the optimal restart rate which can undergo a first- or second-order transition depending on the details of the system. Nonetheless, there is no generic understanding of how the optimal restart rate behaves close to the transition with respect to the system parameters and what precisely characterizes the nature of the transition. We build a comprehensive theory to investigate both the transitions which, we show, can be understood by analyzing the first passage time moments. Our approach predicts the emergence of first- and second-order transition lines between the two phases that merge at a tricritical point. Power of our formulation is demonstrated on two canonical paradigm setup, namely, the Michaelis-Menten chemical reaction and diffusion under restart.

We uncover the existence of Dirac and exceptional points in waveguides made of anisotropic materials, and study the transition between them. Dirac points in the dispersion diagram appear at propagation directions where the matrix describing the eigenvalue problem for bound states splits into two blocks, sorting the eigenmodes either by polarization or by inner mode symmetry. Introducing a non-Hermitian channel via a suitable leakage mechanism causes the Dirac points to transform into exceptional points connected by a Fermi arc. The exceptional points arise as improper hybrid leaky states and, importantly, are found to occur always out of the anisotropy symmetry planes.

Many-body spin systems represent a paradigmatic platform for the realization of emergent states of matter in a strongly interacting regime. Spin models are commonly studied in one-dimensional periodic chains, whose lattice constant is on the order of the interatomic distance. However, in cold atomic setups or functionalized twisted van der Waals heterostructures, long-range modulations of the spin physics can be engineered. Here we show that such superlattice modulations in a many-body spin Hamiltonian can give rise to observable topological boundary modes in the excitation spectrum of the spin chain. In the case of an XY spin-$1/2$ chain, these boundary modes stem from a mathematical correspondence with the chiral edge modes of a two-dimensional quantum Hall state. Our results show that the addition of many-body interactions does not close some of the topological gaps in the excitation spectrum, and the topological boundary modes visibly persist in the isotropic Heisenberg limit. These observations carry through when the spin moment is increased and a large-spin limit of the phenomenon is established. Our results show that such spin superlattices provide a promising route to observe many-body topological boundary effects in cold atomic setups and functionalized twisted van der Waals materials.

Quantum scars constitute one of the fundamental pillars in the traditional field of nonrelativistic quantum chaos. In relativistic quantum systems, chiral scars have been discovered recently whose wave functions concentrate on odd periodic orbits and break the time-reversal symmetry. We develop a theoretical framework to unify the scarring phenomena in nonrelativistic and relativistic quantum systems, which were previously thought to be distinct. In particular, we exploit massive Dirac billiard systems and derive semiclassical quantization rules to bridge the two opposite limits: the massless Dirac case and the large mass regime where the system effectively degenerates into one governed by the Schrödinger equation. A nontrivial phase is uncovered, which depends on the mass, the wave number, and the angle of reflection, and we demonstrate that this phase plays a key role in transforming the chiral scars and in bridging the relativistic and nonrelativistic quantum scars. In the large-mass limit, time-reversal symmetry is restored, as evidenced by a spectral analysis.

The honeycomb Kitaev spin model provides a quantum spin liquid in the ground state, where the spin excitations are fractionalized into itinerant and localized Majorana fermions; the former spectrum has a broad continuum ranging up to a high energy, while the latter has a sharp peak at a low energy. Despite tremendous efforts, it remains elusive to clearly identify these distinct Majorana excitations in experiments. Here we show their manifestation in the time evolution after quenching the magnetic field, by using the time-dependent Majorana mean-field theory for both the ferromagnetic and antiferromagnetic Kitaev models. We find that the transient spin dynamics from the quantum spin liquid states is qualitatively different from the conventional spin precessions by the quench from the high-field forced-ferromagnetic state. We obtain peculiar time evolutions with distinct timescales, i.e., short-time decay of high-energy components associated with the itinerant Majorana excitations, and long-lived excitations at a low energy by the localized ones. These peculiar behaviors are caused by the energy transfer between the two Majorana quasiparticles after the field quench. Moreover, we find that the Majorana semimetal with the point nodes in equilibrium turns into a Majorana metal with the transient “Fermi surfaces” by the energy transfer. In particular, for the quench from the intermediate-field quantum spin liquid in the antiferromagnetic Kitaev model, the Fermi surfaces change their topology in the time evolution, which is regarded as a dynamical version of the Majorana “Lifshitz transition.” Our results unveil that the real-time dynamics provides another route to not only the identification of the fractional Majorana excitations in candidate materials of Kitaev magnets but also unprecedented quantum phases that cannot be stabilized as the equilibrium states.