The Dicke model describes an ensemble of two-level atoms that are coupled to a confined light mode of an optical cavity. Above a critical coupling, the cavity becomes macroscopically occupied, and the system enters the superradiant phase. This phase transition can be observed by detecting the photons that are emitted from the cavity; however, it only becomes apparent in the limit of long observation times, while actual experiments are of a finite duration. To circumvent this problem, we here make use of recent advances in Lee-Yang theories of phase transitions to show that the superradiant phase transition can be inferred from the factorial cumulants of the photon emission statistics obtained during a finite measurement time. Specifically, from the factorial cumulants, we can determine the complex singularities of generating functions that describe the photon emission statistics, and by extrapolating their positions to the long-time limit one can detect the superradiant phase transition. We also show that the convergence points determine the tails of the large-deviation statistics of the photon current. Our paper demonstrates how phase transitions in the Dicke model and in other quantum many-body systems can be detected from measurements of a finite duration.

A limit cycle is a self-sustained, periodic, isolated motion appearing in autonomous differential equations. As the period of a limit cycle is a priori unknown, finding it as a stationary state of a rotating ansatz is challenging. Correspondingly, its study commonly relies on numerical methodologies (e.g., brute-force time evolution, and variational shooting methods) or circumstantial evidence such as instabilities of fixed points. Alas, such approaches are (i) unable to find all solutions, as they rely on specific initial conditions, and (ii) do not provide analytical intuition about the physical origin of the limit cycles. Here, we (I) develop a multifrequency rotating ansatz with which we (II) find all limit cycles as stationary-state solutions via a semianalytical homotopy continuation. We demonstrate our approach and its performance on the Van der Pol oscillator. Moving beyond this simple example, we show that our method captures all coexisting fixed-point attractors and limit cycles in a modified nonlinear Van der Pol oscillator. Our results facilitate the systematic mapping of out-of-equilibrium phase diagrams, with implications across multiple fields of the natural sciences.

The quantum kernel method is one of the key approaches to quantum machine learning, which has the advantage of not requiring optimization and its theoretical simplicity. By virtue of these properties, several experimental demonstrations and discussions of the potential advantages have been developed so far. However, as is the case in classical machine learning, not all quantum machine learning models could be regarded as kernel methods. In this work, we explore a quantum machine learning model with a deep parametrized quantum circuit and aim to go beyond the conventional quantum kernel method. In this case, the expressive power and performance are expected to be enhanced, while the training process might be a bottleneck because of the barren plateaus. Moreover, the high computational cost of gradient-based optimization and the large search space of the gradient-free optimization directly make the training intractable. However, we find that parameters of a deep enough quantum circuit do not move much from their initial values during training, allowing for a first-order expansion with respect to the parameters. This behavior is similar to that of the neural tangent kernel in classical machine learning, and such a quantum machine learning with deep variational quantum circuits can be described by another emergent kernel, the quantum tangent kernel. We show that the proposed quantum tangent kernel has the potential to outperform the conventional quantum kernel method by performing a classification task on an ansatz-generated dataset. This work provides a different direction beyond the conventional quantum kernel method and explores the potential power of quantum machine learning with deep parametrized quantum circuits.

We have investigated interlayer interactions in the bilayer ${\mathrm{PtTe}}_2$ system, which influence the electronic energy bands near the Fermi level. Our diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer stackings (AA, AB, AC) manifest distinct interlayer binding characteristics among the stacking modes by revealing significantly different interlayer separations depending on the stacking, which is critical to understanding the interlayer coupling of the twisted bilayers consisting of various local stacking arrangements. Furthermore, a comparison between the interlayer separations obtained from DMC and density functional theory (DFT) shows that meta-generalized gradient approximation (GGA)-based van der Waals–DFT results agree with DMC for different layer stackings, including twisted bilayers, but only the ground-state AA stacking matches well with GGA-based DFT predictions. This underscores the importance of accurate exchange-correlation potentials even for capturing the stacking-dependent interlayer binding properties. We further show that the variability in DFT-predicted interlayer separations is responsible for the large discrepancy of band structures in the $21.{79}^{\circ }$ twisted bilayer ${\mathrm{PtTe}}_2$, affecting its classification as metallic or insulating. These results demonstrate the importance of obtaining a correct description of stacking-dependent interlayer coupling in modeling delicate bilayer systems at finite twists.

T1 transitions, also called cell intercalations, are important sources of fluidization of epithelial cell monolayers. We use a multiphase field model to quantify this tissue fluidization in terms of the relative dispersion of cells and characterize the T1 flow profile. We show that the ensemble-averaged flow profile of a T1 transition has a saddle-point pattern accompanied by a localized burst in cell speed. Although the temporal evolution of the relative dispersion of cells depends on specific model details, the different dispersion curves collapse robustly onto a linear function of the number of T1 transitions, implying an important connection between T1 transitions and mixing in dense systems.

While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial waves has not yet been reported. We provide closed-form expressions for the equations of state for weakly interacting systems with arbitrary partial waves in the normal phase. Thermodynamics, including contact, loss rate, and compressibility, are derived over the entire temperature regime. Our results offer an improved thermometer for ultracold atoms and molecules with weak high-partial wave interactions.

A widely adopted computational protocol in contemporary materials research is to first relax materials' geometries using semilocal density functional approximations (DFA), and then determining their electronic band structures using the more expensive hybrid functionals. This procedure often works well, as the popular semilocal DFAs, such as the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, yield rather good geometries for a wide range of materials. However, here we show that, for some of the lead-free halide double perovskites (HDPs) ${\mathrm{Cs}}_{2}B{B}^{\prime }{X}_6$ ($B={\mathrm{Ag}}^{+}, {\mathrm{Na}}^{+}$; $B^{\prime }={\mathrm{In}}^{3+}, {\mathrm{Bi}}^{3+}$; $X={\mathrm{Cl}}^{-}, {\mathrm{Br}}^{-}$), the validity of this common practice is questionable. We find that, for these HDPs, the geometrical structures, in particular, the $B\left(B^{\prime }\right)\text{−}X$ bond lengths predicted by PBE show large deviations from the experimental values. Additionally, the band gaps of some of these materials (specifically, the In-based HDPs) are sensitive to the $B\left(B^{\prime }\right)\text{−}X$ bond lengths. As a consequence, the band gaps obtained using the hybrid functionals (such as the Heyd-Scuseria-Ernzerhof functional) based on the PBE geometries can still be quite off, in particular, for HDPs with $B^{\prime }={\mathrm{In}}^{3+}$. The situation is significantly improved by using hybrid functionals with tuned portion of exact exchange, based on the geometries determined consistently under the same level of theory. The successes and failures of several popular exchange-correlation (XC) functionals are traced back to the so-called delocalization error, and can be quantitatively analyzed and understood via a three-atom linear-chain $B\text{−}X\text{−}{B}^{\prime }$ molecular model. Finally, our findings provide a practical guide for choosing appropriate XC functionals for describing HDPs and point to a promising path for band structure engineering via doping and alloying.

Cooper quartets represent exotic fermion aggregates describing correlated matter at the basis of charge-$4e$ superconductivity and offer a platform for studying four-body interactions, of interest for topologically protected quantum computing, nuclear matter simulations, and more general strongly correlated matter. Focusing on solid-state systems, we show how to quantum design Cooper quartets in a double-dot system coupled to ordinary superconducting leads through the introduction of an attractive interdot interaction. A fundamentally novel, maximally correlated double-dot ground state, in the form of a superposition of vacuum $|0\rangle$ and four-electron state $|4e\rangle$, emerges as a narrow resonance in a many-body quartet correlator that is accompanied by negligible pair correlations and features a rich phenomenology. The system represents an instance of correlated Andreev matter and the results open the way to the exploration of interaction effects in hybrid superconducting devices, and the study of novel correlated states of matter with ingredients available in a quantum solid-state laboratory.

We investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as the Lévy-Lorentz gas. To gain insight into the microscopic properties of such a stochastically complex system, deterministic dynamics known as the slicer map and fly-and-die dynamics are used. We analytically derive the generalized position autocorrelation function of these dynamics and study the special case, the 3-point position correlation function. For this, we derive single-parameter-dependent scaling and compare it with the numerically estimated 3-point position autocorrelation of the Lévy-Lorentz gas, for which the analytical expression is still an open question. Here we obtained a remarkable agreement between them, irrespective of any functional relationship with time. Moreover, we demonstrate that the position moments and the position autocorrelations of these systems scale in the same fashion, provided the times are large enough and far enough apart. Other observables, such as velocity moments and correlations, are reported to distinguish the systems.

As one indispensable type of nonreciprocal mechanism, a system with temporal modulations is intrinsically open in the physical sense and inevitably non-Hermitian, but the space and time degrees of freedom are nonseparable in a large variety of circumstances, which restrains the application of the non-Bloch band theory. Here, we investigate the spatially photonic crystals (PhCs) composed of spatiotemporal modulation materials (STMs) and homogeneous media, dubbed as the STMPhC, wherein the spatial and temporal modulations are deliberately designed to be correlated. To bypass the difficulty of the spatiotemporal correlation, we first employ the effective medium theory to account for the dispersion of fundamental bands under the influence of Floquet sidebands. Based on the continuum generalized Brillouin zone condition, we then analytically give the criteria for the existence of the non-Hermitian skin effect in the STM. Assisted by developing a numerical method that embeds the plane wave expansion in the transfer matrix, we establish the non-Bloch band theory for the low-frequency Floquet bands in the STMPhCs, in which the identification of the generalized Brillouin zone is central. We finally delve into the topological properties, including non-Bloch Zak phases and non-Bloch bulk-boundary correspondence. Our work validates the idea that the effective medium assists the non-Bloch band theory applied to the STMPhCs, which delivers a prescription to broaden the horizons of non-Bloch theory.

The solitonlike superradiant regime of free-electron lasers (FEL) offers a promising path towards ultrashort pulses, beyond the natural limit dictated by the bandwidth of the high-gain FEL instability. In this work we present a three-dimensional theory of the superradiant regime, including the effects of beam emittance and energy spread. Our work takes advantage of recent developments in nonlinear FEL theory to provide a fully analytical description of solitonlike superradiance. Our theory proves the existence of a diffraction-dominated steady-state regime in which the superradiant peak power grows indefinitely while leaving the pulse duration and on-axis intensity almost unchanged. These results are in excellent agreement with three-dimensional simulations and are supported by recent experimental results at the Linac Coherent Light Source. This work advances nonlinear FEL theory and provides a theoretical framework for the next generation of attosecond x-ray FELs.