We demonstrate experimentally and theoretically the presence of the post-collision interaction (PCI) effect in sulfur ${\mathrm{KL}}_{2,3}{\mathrm{L}}_{2,3}$ Auger electron spectra measured in the gas-phase thiophene and in solid-state organic polymers: polythiophene (PT) and poly(3-hexylthiophene-2,5-diyl), commonly known as P3HT. PCI manifests itself through a distortion and a blueshift of the normal Auger S ${\mathrm{KL}}_{2,3}{\mathrm{L}}_{2,3}$ spectrum when S $1s$ ionization occurs close to the ionization threshold. Our investigation shows that the PCI-induced shift of the Auger spectra is stronger in the solid-state polymers than in the gas-phase organic molecule. Theoretical modeling within the framework of the eikonal approximation provides good agreement with the experimental observations. In a solid medium, two effects influence the interaction between the photoelectron and the Auger electron. In detail, stronger PCI in the polymers is attributed to the photoelectron scattering in the solid, which overcompensates the polarization screening of electron charges which causes a reduction of the interaction. Our paper demonstrates the general nature of the PCI effect occurring in different media.

In recent decades, the laws of thermodynamics have been pushed down to smaller and smaller scales, within the theoretical field of stochastic thermodynamics and state-of-the-art experiments performed on microfabricated mesoscopic systems. These measurements concern thermal properties of electrons, photons, and mesoscopic mechanical objects. Here we report on the measurements of thermal fluctuations of a single mechanical mode in equilibrium with a heat reservoir. The device under study is a nanomechanical beam with a first flexural mode resonating at $3.8\mathrm{MHz}$, cooled down to temperatures in the range from 100 to $400\mathrm{mK}$. The technique is constructed around a microwave optomechanical setup using a cryogenic high electron mobility transistor, and is based on two parametric amplifications implemented in series: an in-built optomechanical “blue detuned” pumping plus a traveling wave parametric amplifier stage. We demonstrate our ability to resolve energy fluctuations of the mechanical mode in real time up to the fastest relevant speed given by the mechanical relaxation rate. The energy probability distribution is then exponential, matching the expected Boltzmann distribution. The variance of fluctuations is found to be ${\left(k_{B}T\right)}^2$ with no free parameters. Our microwave detection floor is about three times the standard quantum limit at $6\mathrm{GHz}$; the resolution of our fastest acquisition tracks reached about $100\mathrm{phonons}$, and is directly related to the rather poor optomechanical coupling of the device ($g_0/2\pi \approx 0.5\mathrm{Hz}$). This result is deeply in the classical regime, but shall be extended to the quantum case in the future with systems presenting a much larger $g_0$ (up to $2\pi \times 250\mathrm{Hz}$), potentially reaching the resolution of a single mechanical quantum. We believe that it will open an experimental field, phonon-based quantum stochastic thermodynamics, with fundamental implications for quantum heat transport and macroscopic mechanical quantum coherence.

We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ [where spin symmetry is enlarged to $\mathrm{SU}\left(M\right)]$ study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of $T_c$ when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in $T_c$ between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.

We provide further analytical insights into the recently established noninteracting (free-fermion) Page curve, focusing on both the kinematic and dynamical aspects. First, we unveil the underlying canonical typicality and atypicality for random free-fermion states. The former appears for a small subsystem and is exponentially weaker than the well-known result in the interacting case. The latter explains why the free-fermion Page curve differs remarkably from the interacting one when the subsystem is macroscopically large, i.e., comparable with the entire system. Second, we find that the free-fermion Page curve emerges with unexpectedly high accuracy in some simple tight-binding models in long-time quench dynamics. This contributes a rare analytical result concerning quantum thermalization on a macroscopic scale, where conventional paradigms such as the generalized Gibbs ensemble and quasiparticle picture are not applicable.

We present absolute frequency measurements of the ${}^1{P}_1\leftarrow {}^1{S}_0$ (229-nm) and ${}^3{P}_1\leftarrow {}^1{S}_0$ (326-nm) transitions for all naturally occurring isotopes of cadmium. The isotope shifts and hyperfine intervals of the fermionic isotopes are determined with an accuracy of 3.3 MHz. We find that quantum interference in the laser-induced fluorescence spectra of the ${}^1{P}_1\leftarrow {}^1{S}_0$ transition causes a variation of up to 29(5) MHz in determining the hyperfine splitting when not accounted for with an appropriate model. Using a King-plot analysis, we extract the field- and mass-shift parameters and determine nuclear charge radius differences for the fermions. The lifetime of the ${}^1{P}_1$ state is determined to be 1.60(5) ns by measuring the natural linewidth of the ${}^1{P}_1\leftarrow {}^1{S}_0$ transition. These results resolve significant discrepancies among previous measurements.

We measure telegraph noise of current fluctuations in an electrostatically defined quantum dot in bilayer graphene by real-time detection of single electron tunneling with a capacitively coupled neighboring quantum dot. Suppression of the second and third cumulant (related to shot noise) in a tunable graphene quantum dot is demonstrated experimentally. With this method we demonstrate the ability to measure very low current and noise levels. Furthermore, we use this method to investigate the first spin excited state, an essential prerequisite to measure spin relaxation.

We propose a class of geometric measures of entanglement for pure states by exploiting the matrix product state formalism. These measures are completely divested from the notion of separability and can be freely tuned as a function of the bond dimension to target states which vary in entanglement complexity. We first demonstrate its value in a toy spin-1 model where, unlike the conventional geometric entanglement, it successfully identifies the AKLT ground state. We then investigate the phase diagram of a Haldane chain with uniaxial and rhombic anisotropies, revealing that our measure can successfully detect all its phases; all of which are invisible to the conventional geometric entanglement. Finally we investigate the disordered spin-$1/2$ Heisenberg model, where we find that differences in our measure can be used as lucrative signatures of the ergodic-localized entanglement transition.

We report a comprehensive experimental investigation of the magnetic structure of the cycloidal phase in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, which mediates the spin reorientation transition and establishes its magnetic phase diagram. In zero applied field, single-crystal neutron diffraction data confirm the scenario deduced from an earlier resonant x-ray scattering study: For $46.7\mathrm{K}$ $<T<$ 49.0 K the magnetic moments form a cycloid in the $a\text{−}b$ plane with a propagation wave vector of $(\delta ,0,1)$ with $\delta \simeq 0.025$ and an ordered moment of about $1{\mu }_{\mathrm{B}}$, with the eccentricity of the cycloid evolving with temperature. In an applied magnetic field applied parallel to the $b$ axis, the intensity of the $(\delta ,0,1)$ satellite peaks decreases continuously up to about ${\mu }_{0}H\simeq 5\mathrm{T}$, above which field the system becomes field polarized. Both the eccentricity of the cycloid and the wave vector increase with field, the latter suggesting an enhancement of the antisymmetric Dzyaloshinskii-Moriya interaction over the symmetric exchange interactions via magnetostriction effects. Transitions between the various low-temperature magnetic phases have been carefully mapped out using magnetometry and resistivity. The resulting phase diagram reveals that the cycloid phase exists in a temperature window that expands rapidly with increasing field, before transitioning to a polarized paramagnetic state at 5 T. High-field magnetoresistance measurements show that below $T\simeq 70\mathrm{K}$ the resistivity increases continuously with decreasing temperature, indicating the inherent insulating nature at low temperatures of our high-quality, untwinned, single crystals. We discuss our results with reference to previous reports of the magnetic phase diagram of ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ that utilized samples which were more metallic and/or polydomain.

We derive a universal thermodynamic uncertainty relation (TUR) that applies to an arbitrary observable in a general Markovian system. The generality of our result allows us to make two findings: (1) for an arbitrary out-of-equilibrium system, both the entropy production and the degree of nonstationarity are required to tightly bound the strength of a thermodynamic current; (2) by removing the antisymmetric constraint on observables, the TUR in physics and a fundamental inequality in theoretical finance can be unified in a single framework.

Optimal engine performances can be accomplished by quantum effects. Here we explore two routes toward ideal engines, namely (1) quantum systems that operate as hybrid machines being able to perform more than one useful task and (2) the suppression of fluctuations in doing such tasks. For classical devices, the absence of fluctuations is conditioned by a high entropy production, as dictates the thermodynamic uncertainty relations. Here we generalize such relations for multiterminal conductors that operate as hybrid thermal machines. These relations are overcome in quantum conductors as we show for a double quantum dot contacted to normal metals and a reservoir being a generator of entangled Cooper pairs.

Information processing in biological systems is realized by the appropriate transmission of information flows over complex networks, such as gene regulatory, signal transduction, and neural networks. These information flows are affected by the input-signal characteristics and structural properties of network systems, such as the network topology, regulation rules, and intrinsic and environmental noise. Many biological networks frequently include several typical patterns called network motifs, which are considered to play important roles in biological functions. However, their information-theoretic properties, particularly the dependence of the information flows in each network on the input signal, remain poorly understood. In our previous study [Mori and Okada, Phys. Rev. Res. 2, 043432 (2020)], we developed a graphical expansion method to describe transfer entropy (TE), a measure of information flow, in Boolean networks in terms of multiple information pathways. There, the input signal was limited to a simple case, and the effect of the input-signal characteristics on TE was not clarified. In this paper, we improve our method to render it applicable to Boolean networks that receive input signals with arbitrary stochastic characteristics. Our formula expresses how TE is determined by the input-signal characteristics, the assignment of Boolean functions, and the noise magnitude. We find that, in both positive and negative feedback loops, TE hardly depends on the signal timescale. In contrast, coherent and incoherent feedforward loops show low- and high-pass filtering properties, respectively, for a time-varying signal, which is consistent with previous reports. The emergence of either low- or high-pass filtering is determined by the Fourier components of the Boolean functions on specific pathways transmitting information flows. Thus our formula reveals the mechanism of information transfer in network motifs and provides insights into the origin of information processing in biological networks.

An approach to generalize any kind of collinear functional in density functional theory to noncollinear functionals is proposed. This approach satisfies the correct collinear limit for any kind of functional, guaranteeing that the exact collinear functional after generalization is still exact for collinear spins. Besides, it has well-defined and numerically stable functional derivatives, a desired feature for noncollinear and spin-flip time-dependent density functional theory. Furthermore, it provides local torque, hinting at its applications in spin dynamics.

Quantum error correction (QEC) for generic errors is challenging due to the demanding threshold and resource requirements. Interestingly, when physical noise is biased, we can tailor our QEC schemes to the noise to improve performance. Here we study a family of codes having XZZX-type stabilizer generators, including a set of cyclic codes generalized from the five-qubit code and a set of topological codes that we call generalized toric codes (GTCs). We show that these XZZX codes are highly qubit efficient if tailored to biased noise. To characterize the code performance, we use the notion of effective distance, which generalizes code distance to the case of biased noise and constitutes a proxy for the logical failure rate. We find that the XZZX codes can achieve a favorable resource scaling by this metric under biased noise. We also show that the XZZX codes have remarkably high thresholds that reach what is achievable by random codes, and furthermore they can be efficiently decoded using matching decoders. Finally, by adding only one flag qubit, the XZZX codes can realize fault-tolerant QEC while preserving their large effective distance. In combination, our results show that tailored XZZX codes give a resource-efficient scheme for fault-tolerant QEC against biased noise.

The ability to detect single photons has become increasingly essential due to the rise of photon-based quantum computing. In this theoretical work, we propose a system consisting of a quantum dot (QD) side-coupled to a superconducting nanowire. The coupling opens a gap in both the QD mode and the Majorana zero mode (MZM) at the nanowire edge, enabling photon absorption in the system. We show that the absorbed photoelectron decays via rapid (subnanosecond to nanosecond) nonradiative heat transfer to the nanowire phonon modes rather than by spontaneous emission. Furthermore, we calculate the temperature increase and associated resistance increase induced by the absorption of a photon for a given appropriate set of material and environmental parameters, yielding a temperature increase in the millikelvin range and a resistance increase in the kiloohm range, vastly exceeding the photon-absorption-induced temperature and resistance increases for competing 2D-3D hybrid systems by 5 and 9 orders of magnitude, respectively. Last, we determine the detector efficiency and discuss the system density required for deterministic photon number measurement, demonstrating that a photon absorption probability of over 99.9 percent can be achieved for an integrated system consisting of an array of nanowire-QD complexes on-chip inside a cavity. Our results thus provide a basis for a deterministic microwave photon number detector with an unprecedented photon-number-detection resolution.

We devise a semiclassical model to describe the transport properties of low-dimensional fermionic lattices under the influence of external quantum stochastic noise. These systems behave as quantum stochastic resistors, where the bulk particle transport is diffusive and obeys the Ohm/Fick's law. Here, we extend previous exact studies beyond the one-dimensional limit to ladder geometries and explore different dephasing mechanisms that are relevant to different physical systems, from solid-state to cold atoms. We show how the semiclassical description is useful to explain the nontrivial dependence of the conductance of these systems on the chemical potential of the reservoirs. This description provides an intuitive and simpler interpretation of transport in quantum stochastic resistors in good quantitative agreement with the exact numerical solution. Moreover, we find that the conductance of quantum ladders is insensitive to the coherence of the dephasing process along the direction transverse to transport, despite the fact that the system reaches different stationary states.

We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuous-time Markov chain formalism, frequently used to describe intracellular processes involving lowly abundant molecular species. Previously, we have shown how the path mutual information can be calculated for such systems when two molecular components interact directly with one another with no intermediate molecular components being present. In this paper, we generalize this approach to biochemical networks involving an arbitrary number of molecular components. We present an efficient Monte Carlo method as well as an analytical approximation to calculate the path mutual information and show how it can be decomposed into a pair of transfer entropies that capture the directed flow of information between two network components. We apply our methodology to study information transfer in a simple three-node feedforward network, as well as a more complex positive-feedback system that switches stochastically between two metastable modes.

The tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as the density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain, having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.

Diamagnetically levitated oscillators of millimeter and submillimeter size are emerging ultrasensitive sensors for gravitylike force and acceleration measurements. However, improving the levitation capability while keeping mechanical dissipation low remains an open challenge. Here, we propose and experimentally demonstrate an engineering conductive geometry scheme to efficiently reduce the mechanical dissipation of a diamagnetically levitated oscillator made of pyrolytic graphite. We show that with a specially designed conductive geometry, the eddy current damping is reduced, and the reduction factor increases as the engraving pattern being denser. Under high vacuum and room temperature, eddy current damping is the dominant contribution to mechanical dissipation, and we reduce it by a factor of 50 in the experiment. Our work opens up a new way to achieve diamagnetically levitated oscillator with ultralow mechanical dissipation and strong levitation capability, a candidate platform for studying a broad range of fundamental physics.

Brownian motion of a mobile impurity in a bath is affected by spin-orbit coupling (SOC). Here, we discuss a Caldeira-Leggett-type model that can be used to propose and interpret quantum simulators of this problem in cold Bose gases. First, we derive a master equation that describes the model and explore it in a one-dimensional (1D) setting. To validate the standard assumptions needed for our derivation, we analyze available experimental data without SOC; as a byproduct, this analysis suggests that the quench dynamics of the impurity is beyond the 1D Bose-polaron approach at temperatures currently accessible in a cold-atom laboratory—motion of the impurity is mainly driven by dissipation. For systems with SOC, we demonstrate that 1D spin-orbit coupling can be gauged out even in the presence of dissipation—the information about SOC is incorporated in the initial conditions. Observables sensitive to this information (such as spin densities) can be used to study formation of steady spin polarization domains during quench dynamics.