Non-perturbative Regime Research Articles

Radiative properties of an artificial atom coupled to a Josephson-junction array

We study the radiative properties -- the Lamb shift, Purcell decay rate and the spontaneous emission dynamics -- of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to non-perturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson junction array (JJA). As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are non-trivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode non-perturbative regime. This modal framework generalizes the normal mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high impedance Josephson junction arrays.

Ultrafast pulse propagation in graphene-comprising nanophotonic waveguides considering nonperturbative electrodynamic nonlinearity

We outline a comprehensive model for ultrafast optical pulse propagation along nonlinear graphene-comprising integrated photonic waveguides. An electrodynamic graphene hot-electron model (GHEM) is used to capture the temporal dynamics and intertwined absorptive and refractive nonlinearity to explore a strongly nonperturbative photoconductivity regime that transcends third-order phenomena. We propose a formalism to abstract the 2D material-related modal properties of the waveguides in the static/continuous-wave regime that can also be plugged into a generalized nonlinear Schrödinger equation (NLSE) framework. Our model of optical pulse propagation consists of a coupled NLSE along with the nonlinear equation system of the GHEM. We demonstrate pulsed applications pertinent to integrated photonic components, namely, improvement of the extinction ratio (ER) of a nonreturn-to-zero (NRZ)-modulated bitstream, pulse shaping, spectral broadening, and optical-shock formation leading to pulse breaking and soliton formation. Our NLSE-GHEM extracts graphene nonlinearity from fundamental physics without resorting to phenomenological correction terms or fitted parameters, shows good agreement with recent experiments, and can potentially be used in the study of high-power on-chip applications such as pulsed lasers and frequency combs.

Optimal photon polarization toward the observation of the nonlinear Breit-Wheeler pair production

We investigate the optimization of the photon polarization to increase the yield of the Breit-Wheeler pair production in arbitrarily polarized plane wave backgrounds. We show that the optimized photon polarization can improve the positron yield by more than $20\%$ compared to the unpolarized case, in the intensity regime of current laser-particle experiments. The seed photon's optimal polarization is resulting from the polarization coupling with the polarization of the laser pulse. The compact expressions of the coupling coefficients in both the perturbative and nonperturbative regime are given. Because of the evident difference in the coupling coefficients for the linear and circular polarization components, the seed photon's optimal polarization state in an elliptically polarized laser background, deviates considerably from the orthogonal state of the laser polarization.

The exact exchange–correlation potential in time-dependent density functional theory: Choreographing electrons with steps and peaks

The time-dependent exchange–correlation potential has the unusual task of directing fictitious non-interacting electrons to move with exactly the same probability density as true interacting electrons. This has intriguing implications for its structure, especially in the non-perturbative regime, leading to step and peak features that cannot be captured by bootstrapping any ground-state functional approximation. We review what has been learned about these features in the exact exchange–correlation potential of time-dependent density functional theory in the past decade or so and implications for the performance of simulations when electrons are driven far from any ground state.

Explaining mass and spin in the visible matter: the next challenge

Understanding in depth …the origin of the nucleon mass, the nucleon spin, and the emergent properties of a dense gluon system… (Electron-ion collider Yellow Report, arXiv:2103.05419v) represents the frontier of modern hadron physics, both on the experimental and theoretical side. In this contribution, after briefly outlining the above challenges in view of the various experimental facilities planned in the near future, some insights into the non-perturbative regime of QCD will be provided. In particular, the most recent achievements in the description of the pion, playing a fundamental role in the hadron dynamics, will be illustrated within a genuinely relativistic quantum-field theoretical framework, based on actual solutions of the homogeneous Bethe-Salpeter equation.

Antiferromagnetism beyond the classical percolation threshold in the diluted half-filled one-band Hubbard model in three dimensions

We investigate the impact of site dilution by setting the on-site repulsion strength ($U$) to zero at a fraction of sites in the half-filled Hubbard model on a simple cubic lattice. We employ a semi-classical Monte-Carlo approach first to recover the zero dilution (undiluted $x=1$) properties, including $U$ dependence of insulator to metal crossover temperature scale $T^*$ and long-range staggered antiferromagnetic ordering temperature ($T_N$). For the non-perturbative regime of $U \sim$ bandwidth, we find a rapid suppression of $T^*$ with reducing $x$ from 1 to 0.7. However, $T_N$ remains unchanged in this dilution range, showing a weakening of the insulating state but not of the magnetic order. At $x \leq 0.7$, $T^*$ and $T_N$ coincide and are suppressed together with further increase in site-dilution. Finally, the system loses the magnetic order and the insulating state for $x=0.15$, significantly below the classical percolation threshold $x_p^{sc} (\sim 0.31$). We show that the induced moments on $U=0$ sites drive the magnetic order below the classical percolation limit by studying local moment systematics and finite-size analysis of magnetic order. At the end, we show that either increasing $U$ to large values or raising temperature beyond a $U$ dependent critical value, suppresses the induced local moments of the $U=0$ sites and recovers the classical percolation threshold.

Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime

We extend the recent rigorous convergence result of Abels and Moser (SIAM J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin boundary condition towards evolution by mean curvature flow with constant contact angle. More precisely, in the present work we manage to remove the perturbative assumption on the contact angle being close to 90^circ . We establish under usual double-well type assumptions on the potential and for a certain class of boundary energy densities the sub-optimal convergence rate of order {varepsilon ^{frac{1}{2}}} for general contact angles alpha in (0,pi ). For a very specific form of the boundary energy density, we even obtain from our methods a sharp convergence rate of order varepsilon ; again for general contact angles alpha in (0,pi ). Our proof deviates from the popular strategy based on rigorous asymptotic expansions and stability estimates for the linearized Allen–Cahn operator. Instead, we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233, 2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy technique. We develop a careful adaptation of their approach in order to encode the constant contact angle condition. In fact, we perform this task at the level of the notion of gradient flow calibrations. This concept was recently introduced in the context of weak-strong uniqueness for multiphase mean curvature flow by Fischer et al. (arXiv:2003.05478v2).

Structural aspects of FRG in quantum tunneling computations

We probe both the unidimensional quartic harmonic oscillator and the double well potential through a numerical analysis of the Functional Renormalization Group flow equations truncated at first order in the derivative expansion. The two partial differential equations for the potential Vk(φ) and the wave function renormalization Zk(φ), as obtained in different schemes and with distinct regulators, are studied down to k=0, and the energy gap between lowest and first excited state is computed, in order to test the reliability of the approach in a strongly non-perturbative regime. Our findings point out at least three ranges of the quartic coupling λ, one with higher λ where the lowest order approximation is already accurate, the intermediate one where the inclusion of the first correction produces a good agreement with the exact results and, finally, the one with smallest λ where presumably the higher order correction of the flow is needed. Some details of the specifics of the infrared regulator are also discussed.

Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams.

We investigate the efficiency of a quantum Carnot engine based on open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes and for the system-bath (SB) interactions controlling the transition between these processes. Numerical simulations are conducted in a nonperturbative and non-Markovian SB coupling regime by using the hierarchical equations of motion under these fields at different cycle frequencies. The work applied to the total system and the heat exchanged with the baths are rigorously evaluated. In addition, by regarding quasi-static work as free energy, we compute the quantum thermodynamic variables and analyze the simulation results by using thermodynamic work diagrams for the first time. Analysis of these diagrams indicates that, in the strong SB coupling region, the fields for the SB interactions are major sources of work, while in other regions, the field for the subsystem is a source of work. We find that the maximum efficiency is achieved in the quasi-static case and is determined solely by the bath temperatures, regardless of the SB coupling strength, which is a numerical manifestation of Carnot's theorem.

Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions.

Dissipative quantum phase transition has been widely believed to occur in a Josephson junction coupled to a resistor despite a lack of concrete experimental evidence. Here, on the basis of both numerical and analytical nonperturbative renormalization group analyses, we reveal breakdown of previous perturbative arguments and defy the common wisdom that the transition always occurs at the quantum resistance R_{Q}=h/(4e^{2}). We find that renormalization group flows in nonperturbative regimes induce nonmonotonic renormalization of the charging energy and lead to a qualitatively different phase diagram, where the insulator phase is strongly suppressed to the deep charge regime (Cooper pair box), while the system is always superconducting in the transmon regime. We identify a previously overlooked dangerously irrelevant term as an origin of the failure of conventional understandings. Our predictions can be tested in recent experiments realizing high-impedance long superconducting waveguides and would provide a solution to the long-standing controversy about the fate of dissipative quantum phase transition in the resistively shunted Josephson junction.

On gravitational preheating

We consider dark matter production during the inflaton oscillation epoch. It is conceivable that renormalizable interactions between dark matter and inflaton may be negligible. In this case, the leading role is played by higher dimensional operators generated by gravity and thus suppressed by the Planck scale. We focus on dim-6 operators and study the corresponding particle production in perturbative and non-perturbative regimes. We find that the dark matter production rate is dominated by non-derivative operators involving higher powers of the inflaton field. Even if they appear with small Wilson coefficients, such operators can readily account for the correct dark matter abundance.

Renormalizability of a Yang-Mills center-vortex ensemble

Recently, a new procedure to quantize the $SU(N)$ Yang-Mills theory in the nonperturbative regime was proposed. The idea is to divide the configuration space $\{A_\mu\}$ into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. As Singer's theorem on gauge copies only refers to gauge fixing conditions that are global in $\{A_\mu\}$, this construction might avoid the Gribov problem. In this work, we present a proof of the renormalizability in the center-vortex sectors, thus establishing the calculability of the Yang-Mills center-vortex ensemble.

Nonlinear Breit-Wheeler pair production in collisions of bremsstrahlung γ quanta and a tightly focused laser pulse

Experimental efforts toward the detection of the nonperturbative strong-field regime of the Breit-Wheeler pair creation process plan to combine incoherent sources of GeV $\gamma$ quanta and the coherent fields of tightly focussed optical laser pulses. This endeavour calls for a theoretical understanding of how the pair yields depend on the applied laser field profile. We provide estimates for the number of produced pairs in a setup where the high-energy radiation is generated via bremsstrahlung. Attention is paid to the role of the transversal and longitudinal focussing of the laser field, along with the incorporation of a Gaussian pulse envelope. We compare our corresponding results with predictions from plane-wave models and determine the parameters of focused laser pulses which maximize the pair yield at fixed pulse energy. Besides, the impact of various super-Gaussian profiles for the laser pulse envelope and its transverse shape is discussed.

Stimulated vacuum emission and photon absorption in strong electromagnetic fields

According to quantum electrodynamics (QED), a strong electromagnetic field can make the vacuum state decay via the production of electron-positron pairs. Here we investigate the emission of soft photons which accompanies a nonperturbative process of pair production. Our analysis is carried out within the Furry picture to first order in the fine-structure constant. Also, it is shown that the presence of photons in the initial state gives rise to an additional (stimulated) channel of photon emission besides the pure vacuum one. On the other hand, the number of final (signal) photons includes also a negative contribution due to photon absorption within the pair production process. These contributions are evaluated and compared. To obtain quantitative predictions in the domain of realistic field parameters, we employ the Wentzel-Kramers-Brillouin approach. We propose using an optical-probe photon beam, whose intensity changes as it traverses a spatial region where a strong electric component of a background laser field is present. It is demonstrated that relative intensity changes on the level of 1% can be experimentally observed once the intensity of the strong background field exceeds ${10}^{27}\text{ }\text{ }{\mathrm{W}/\mathrm{cm}}^{2}$ within a large laser-wavelength interval. This finding is expected to significantly support possible experimental investigations of nonlinear QED phenomena in the nonperturbative regime.

Nonperturbative waveguide quantum electrodynamics

Understanding physical properties of quantum emitters strongly interacting with quantized electromagnetic modes is one of the primary goals in the emergent field of waveguide quantum electrodynamics (QED). When the light-matter coupling strength is comparable to or even exceeds energies of elementary excitations, conventional approaches based on perturbative treatment of light-matter interactions, two-level description of matter excitations, and photon-number truncation are no longer sufficient. Here we study in and out of equilibrium properties of waveguide QED in such nonperturbative regimes on the basis of a comprehensive and rigorous theoretical approach using an asymptotic decoupling unitary transformation. We uncover several surprising features ranging from symmetry-protected many-body bound states in the continuum to strong renormalization of the effective mass and potential; the latter may explain recent experiments demonstrating cavity-induced changes in chemical reactivity as well as enhancements of ferromagnetism or superconductivity. To illustrate our general results with concrete examples, we use our formalism to study a model of coupled cavity arrays, which is relevant to experiments in superconducting qubits interacting with microwave resonators or atoms coupled to photonic crystals. We examine the relation between our results and delocalization-localization transition in the spin-boson model; notably, we point out that a reentrant transition can occur in the regimes where the coupling strength becomes the dominant energy scale. We also discuss applications of our results to other problems in different fields, including quantum optics, condensed matter physics, and quantum chemistry.

Measurements of the groomed and ungroomed jet angularities in pp collisions at sqrt{s} = 5.02 TeV

The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into final-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at sqrt{s} = 5.02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (|η| < 0.9). The anti-kT algorithm is used with jet resolution parameters R = 0.2 and R = 0.4 for several transverse momentum {p}_{mathrm{T}}^{mathrm{ch}} jet intervals in the 20–100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underlying event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, λα, and groomed jet angularities, λα,g, to investigate the interplay between perturbative and nonperturbative effects at low jet momenta. Various angular exponent parameters α = 1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic accuracy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies.

Demonstration of nonperturbative and perturbative third-harmonic generation in MgO by altering the electronic structure

The surge of interest in nonperturbative high-harmonic generation in solids has been driven by the appeal of compact solid-state extreme ultraviolet sources and the prospect of untangling the material properties through high-harmonic generation response to strong fields. The traditional assumption is that the brighter, lower-order harmonics are purely perturbative in nature. However, the border between the perturbative and nonperturbative regimes often remains unclear. Here, we show that third-harmonic generation (THG) using 800-nm, 40-fs pulses displays a nonperturbative response in a wide-band-gap insulator MgO. Furthermore, we show that with the introduction of dopants, the nonperturbative THG reverts to the perturbative behavior. We attribute this to the blocking of intraband oscillations and the increased linear absorption pathways introduced by the dopant energy levels.

From theory to precision modelling of strong-field QED in the transition regime

Abstract The combination of energetic electron beams, delivered from conventional accelerators at a high repetition rate, and ultraintense lasers, makes it possible to perform precision measurements of strong-field QED. The LUXE collaboration aims to perform precision measurements of nonlinear Compton scattering and Breit-Wheeler pair creation in the transition from the perturbative to nonperturbative regimes. Here we present an overview of recent developments in the modelling of strong-field QED processes, which are needed to reach the required precision of a few percent for intensity parameters 0.1 &lt; ξ &lt; 10. We discuss how to go from plane-wave QED results to numerical simulations and present predicted signals and error estimates.

Ultrafast Plasmonics Beyond the Perturbative Regime: Breaking the Electronic-Optical Dynamics Correspondence.

The transient optical response of plasmonic nanostructures has recently been the focus of extensive research. Accurate prediction of the ultrafast dynamics following excitation of hot electrons by ultrashort laser pulses is of major relevance in a variety of contexts from the study of light harvesting and photocatalytic processes to nonlinear nanophotonics and the all-optical modulation of light. So far, all studies have assumed the correspondence between the temporal evolution of the dynamic optical signal, retrieved by transient absorption spectroscopy, and that of the photoexcited hot electrons, described in terms of their temperature. Here, we show both theoretically and experimentally that this correspondence does not hold under a nonperturbative excitation regime. Our results indicate that the main mechanism responsible for the breaking of the correspondence between electronic and optical dynamics is universal in plasmonics, being dominated by the nonlinear smearing of the Fermi–Dirac occupation probability at high hot-electron temperatures.

Sabotaging the harvesting of correlations from quantum fields

We study the nonperturbative harvesting of classical and quantum correlations between two parties coupled to a quantum field. First, we consider a scenario with an arbitrary number of two-level systems that couple to a quantum field locally in time. Then, we study the impact of the presence of additional detectors (interlopers) on the ability for two target detectors (Alice and Bob) to acquire correlations through their interaction with the field. We analyze the harvesting of different correlation measures in this nonperturbative regime and we demonstrate that even a single interloper can completely sabotage all correlation harvesting between Alice and Bob by acting on the causal past of one of them. Specifically, we show that the interloper is able to interact with the field so that the field itself ``floods'' one of the parties with entropy. This prevents Alice and Bob from acquiring any correlations. Furthermore, we show that this kind of attack cannot be defended against.