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Nonequilibrium Thermodynamics of Colloidal Gold Nanocrystals Monitored by Ultrafast Electron Diffraction and Optical Scattering Microscopy

Metal nanocrystals exhibit important optoelectronic and photocatalytic functionalities in response to light. These dynamic energy conversion processes have been commonly studied by transient optical probes to date, but an understanding of the atomistic response following photoexcitation has remained elusive. In this paper, we use femtosecond resolution electron diffraction to investigate transient lattice responses in optically excited colloidal gold nanocrystals, revealing the effects of nanocrystal size and surface ligands on the electron–phonon coupling and thermal relaxation dynamics. First, we uncover a strong size effect on the electron–phonon coupling, which arises from reduced dielectric screening at the nanocrystal surfaces and prevails independent of the optical excitation mechanism (i.e., inter- and intraband). Second, we find that surface ligands act as a tuning parameter for hot carrier cooling. Particularly, gold nanocrystals with thiol-based ligands show significantly slower carrier cooling as compared to amine-based ligands under intraband optical excitation due to electronic coupling at the nanocrystal/ligand interfaces. Finally, we spatiotemporally resolve thermal transport and heat dissipation in photoexcited nanocrystal films by combining electron diffraction with stroboscopic elastic scattering microscopy. Taken together, we resolve the distinct thermal relaxation time scales ranging from 1 ps to 100 ns associated with the multiple interfaces through which heat flows at the nanoscale. Our findings provide insights into optimization of gold nanocrystals and their thin films for photocatalysis and thermoelectric applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-resolution high-throughput spatiotemporal strain imaging reveals loss mechanisms in a surface acoustic wave device

Surface acoustic wave devices are key components for processing radio frequency signals in wireless communication because these devices offer simultaneously high performance, compact size and low cost. The optimization of the device structure requires a quantitative understanding of energy conversion and loss mechanisms. Here we use stroboscopic full-field diffraction x-ray microscopy to reveal an unanticipated acoustic loss in a prototypical one-port resonator device. A non-uniform acoustic excitation in the active area was responsible for the substantial end and side leakages observed at the design frequency. Quantitative analysis of the strain amplitude using a wave decomposition method allowed the determination of several key device parameters. This high-resolution high-throughput spatiotemporal strain imaging technique is more generally applicable to the study of dynamic strain modulation in nanoscale acoustic, electronic, optical and quantum devices. The high sensitivity allows precise measurement of the strain modulation with picometer-scale amplitude.

Zhou, Tao [ESRF - The European Synchrotron, Grenob↗

Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains

Floquet spin chains have been a venue for understanding topological states of matter that are qualitatively different from their static counterparts by, for example, hosting π edge modes that show stable period-doubled dynamics. However the stability of these edge modes to interactions has traditionally required the system to be many-body localized in order to suppress heating. In contrast, here we show that even in the absence of disorder, and in the presence of bulk heating, π edge modes are long lived. Their lifetime is extracted from exact diagonalization and is found to be non-perturbative in the interaction strength. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace. In this subspace, the π edge mode manifests as the quasi-stable edge mode of an inhomogeneous Su-Schrieffer-Heeger model whose dimerization vanishes in the bulk of the Krylov chain.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Laser-driven ultrafast transmission electron microscopy

Recent advances in lasers and electron optics technology have allowed transmission electron microscopes to achieve high spatial and temporal resolution, making them capable of tracking atoms, charges and spin motions down to the attosecond and nanometre scales. This Primer discusses the most common and practical experimental implementation of time-resolved transmission electron microscopy and the stroboscopic mode for evaluating ultrafast reversible dynamics. An in-depth discussion of photo-induced near-field electron microscopy, a technique unique to laser-assisted electron microscopy, is also provided, covering its prospective applications in the study of coherent phenomena in quantum materials. The experimental strategies and limitations in investigating the structural dynamics of materials and nanostructures by imaging, diffraction and spectroscopy are also described in detail, with a direct comparison with more conventional and established techniques. Here, we provide key information for new researchers who intend to use ultrafast transmission electron microscopy to address new challenges in specific materials science, condensed matter and nanophotonics.

Transmission electron microscopy↗

Statistically elucidated responses from low-signal contrast mechanisms in ultrafast electron microscopy

The emergence of ultrafast electron microscopy (UEM) has enabled the discovery of strongly correlated dynamic mechanisms, including electron–phonon coupling, structural phase transitions, thermal transport, and electromagnetic deflection. Most UEM systems operate stroboscopically, meaning that the technique is susceptible to artifacts, mistakes, and misinterpretation of the data due to extensive experimental effort. In contrast to the ultrafast designation, data acquisition is extraordinarily slow because the electron beam has significantly reduced signal compared to traditional transmission electron microscopy due to pulsing the electron beam. Consequently, the sample may drift, tilt, or undergo irreversible structural changes that are independent of the time-resolved dynamics throughout the experimental time frame. Furthermore, these datasets require significant user interpretation that can be problematic when proper controls are not implemented thoroughly. Here, we demonstrate a new algorithm designed to separate ultrafast structural dynamics from long-term artifacts using a LiNbO 3 sample experiencing electrically driven surface acoustic wave propagation. Additionally, we provide examples of the impact of user bias when analyzing the data and provide a methodology, which enables the extraction of time-resolved responses when the image signal is extraordinarily low. Overall, the goal of this publication is to provide methods that validate the experimental results and reduce researcher biases during UEM data interpretation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multi-extreme conditions at the Second Target Station

Three concepts for the application of multi-extreme conditions under in situ neutron scattering are described here. The first concept is a neutron diamond anvil cell made from a non-magnetic alloy. It is shrunk in size to fit existing magnets and future magnet designs and is designed for best pressure stability upon cooling. This will allow for maximum pressures above 10 GPa to be applied simultaneously with (steady-state) high magnetic field and (ultra-)low temperature. Additionally, an implementation of miniature coils for neutron diamond cells is presented for pulsed-field applications. The second concept presents a set-up for laser-heating a neutron diamond cell using a defocused CO 2 laser. Cell, anvil, and gasket stability will be achieved through stroboscopic measurements and maximum temperatures of 1500 K are anticipated at pressures to the megabar. The third concept presents a hybrid levitator to enable measurements of solids and liquids at temperatures in excess of 4000 K. This will be accomplished by a combination of bulk induction and surface laser heating and hyperbaric conditions to reduce evaporation rates. The potential for deployment of these multi-extreme environments within this first instrument suite of the Second Target Station is described with a special focus on VERDI, PIONEER, CENTAUR, and CHESS. Furthermore, considerations for deployment on future instruments, such as the one proposed as TITAN, are discussed. Overall, the development of these multi-extremes at the Second Target Station, but also beyond, will be highly advantageous for future experimentation and will give access to parameter space previously not possible for neutron scattering.

47 OTHER INSTRUMENTATION↗

Bilinear dynamic mode decomposition for quantum control

Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.

97 MATHEMATICS AND COMPUTING↗

Engineering micromotion in Floquet prethermalization via space-time symmetries

We present a systematic framework for Floquet prethermalization under strong resonant driving, emphasizing the pivotal role of dynamical space-time symmetries. Our approach demonstrates how dynamical space-time symmetries map onto the projective static symmetry group of the prethermal Hamiltonian governing the prethermal regime. We introduce techniques for detecting dynamical symmetries through the time evolution of local observables, facilitating a detailed analysis of micromotion within each period and surpassing the limitations of conventional stroboscopic Floquet prethermal dynamics. To implement this framework, we present a prethermal protocol that preserves order-2 dynamical symmetry in a spin-ladder model, confirming the predicted relationships between the expectation values of local observables at distinct temporal points in the Floquet cycle, linked by this symmetry.

floquet systems↗

Floquet Engineering of Interactions and Entanglement in Periodically Driven Rydberg Chains

Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.

Floquet systems↗

Magneto-optical spectroscopy based on pump-probe strobe light

Here, we demonstrate a pump-probe strobe light spectroscopy for sensitive detection of magneto-optical dynamics in the context of hybrid magnonics. The technique uses a combinatorial microwave-optical pump-probe scheme, leveraging both the high-energy resolution of microwaves and high-efficiency detection using optical photons. In contrast with conventional stroboscopy using continuous-wave light, we apply microwave and optical pulses with varying pulse widths, and demonstrate magneto-optical detection of magnetization dynamics in Y 3 Fe 5 O 12 films. The detected magneto-optical signals depend strongly on the characteristics of both the microwave and the optical pulses, as well as their relative time delays. We show that good magneto-optical sensitivity and coherent stroboscopic character are maintained, even at a microwave pump pulse of 1.5 ns and an optical probe pulse of 80 ps, under a 7 MHz clock rate, corresponding to a pump-probe footprint of approximately 1% in one detection cycle. Our results show that time-dependent strobe light measurement of magnetization dynamics can be achieved in the gigahertz frequency range under a pump-probe detection scheme.

36 MATERIALS SCIENCE↗

Floquet operator dynamics and orthogonal polynomials on the unit circle

Operator spreading under stroboscopic time evolution under a unitary is studied. An operator Krylov space is constructed and mapped to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parametrizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC under persistent m-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the Z 3 clock model. The numerically obtained Krylov angles of the Z 3 clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior.

Floquet systems↗

Toward improved quantum simulations and sensing with trapped two-dimensional ion crystals via parametric amplification

Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on two-dimensional crystal arrays of approximately 100 9 ⁢Be + ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and enhance the spin-motion coupling while maintaining spin coherence. With a stroboscopic protocol, we measure 5.4 ± 0.9 dB of motional squeezing below the ground-state motion, from which theory predicts a 10-dB enhancement in the sensitivity for measuring small displacements using a recently demonstrated protocol [K. A. Gilmore et al., Science 373, 673 (2021)]. With a continuous squeezing protocol, we measure and accurately calibrate the parametric coupling strength. Theory suggests this protocol can be used to improve quantum spin squeezing, limited in our system by off-resonant light scatter. Finally, we illustrate numerically the trade-offs between strong parametric amplification and motional dephasing in the form of center-of-mass frequency fluctuations for improving quantum spin squeezing in our setup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Strong and almost strong modes of Floquet spin chains in Krylov subspaces

Integrable Floquet spin chains are known to host strong zero and π modes which are boundary operators that respectively commute and anticommute with the Floquet unitary generating stroboscopic time evolution, in addition to anticommuting with a discrete symmetry of the Floquet unitary. Thus the existence of strong modes implies a characteristic pairing structure of the full spectrum. Weak interactions modify the strong modes to almost strong modes that almost commute or anticommute with the Floquet unitary. Manifestations of strong and almost strong modes are presented in two different Krylov subspaces. One is a Krylov subspace obtained from a Lanczos iteration that maps the time evolution generated by the Floquet Hamiltonian onto dynamics of a single particle on a fictitious chain with nearest-neighbor hopping. The second is a Krylov subspace obtained from the Arnoldi iteration that maps the time evolution generated directly by the Floquet unitary onto dynamics of a single particle on a fictitious chain with longer-range hopping. While the former Krylov subspace is sensitive to the branch of the logarithm of the Floquet unitary, the latter obtained from the Arnoldi scheme is not. In this work, the effective single-particle models in the Krylov subspace are discussed, and the topological properties of the Krylov chain that ensure stable zero and π modes at the boundaries are highlighted. The role of interactions is discussed. Expressions for the lifetime of the almost strong modes are derived in terms of the parameters of the Krylov subspace, and are compared with exact diagonalization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Universal model of Floquet operator Krylov space

It is shown that the stroboscopic time evolution under a Floquet unitary, in any spatial dimension, and of any Hermitian operator, can be mapped to an operator Krylov space, which is identical to that generated by the edge operator of the noninteracting Floquet transverse-field Ising model (TFIM) in one-spatial dimension, and with inhomogeneous Ising and transverse field couplings. The latter has four topological phases reflected by the absence (topologically trivial) or presence (topologically nontrivial) of edge modes at 0 and/or π quasienergies. It is shown that the Floquet dynamics share certain universal features characterized by how the Krylov parameters vary in the topological phase diagram of the Floquet TFIM with homogeneous couplings. Furthermore, these results are highlighted through examples, all chosen for numerical convenience to be in one spatial dimension: nonintegrable Floquet spin 1/2 chains and Floquet Z 3 clock model where the latter hosts period-tripled edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Moment method and continued fraction expansion in Floquet operator Krylov space

Recursion methods such as Krylov techniques map complex dynamics to an effective noninteracting problem in one dimension. For example, the operator Krylov space for Floquet dynamics can be mapped to the dynamics of an edge operator of the one-dimensional Floquet inhomogeneous transverse field Ising model (ITFIM), where the latter, after a Jordan-Wigner transformation, is a Floquet model of noninteracting Majorana fermions and the couplings correspond to Krylov angles. We present an application of this showing that a moment method exists where given an autocorrelation function, one can construct the corresponding Krylov angles and from that the corresponding Floquet ITFIM. Consequently, when no solutions for the Krylov angles are obtained, it indicates that the autocorrelation is not generated by unitary dynamics. We highlight this by studying certain special cases: stable m-period dynamics derived using the method of continued fractions, exponentially decaying, and power-law decaying stroboscopic dynamics. Remarkably, our examples of stable m-period dynamics correspond to m-period edge modes for the Floquet ITFIM where, deep in the chain, the couplings correspond to a critical phase. Furthermore our results pave the way to engineer Floquet systems with desired properties of edge modes and also provide examples of persistent edge modes in gapless Floquet systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles

Here, we report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N = 200 atoms with a metrological squeezing parameter ξ 2 = 0.77⁢(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Floquet Insulators and Lattice Fermions

Floquet insulators are periodically driven quantum systems that can host novel topological phases as a function of the drive parameters. These new phases exhibit features reminiscent of fermion doubling in discrete-time lattice fermion theories. We make this suggestion concrete by mapping the spectrum of a noninteracting (1+1)D Floquet insulator for certain drive parameters onto that of a discrete-time lattice fermion theory with a time-independent Hamiltonian. The resulting Hamiltonian is distinct from the Floquet Hamiltonian that generates stroboscopic dynamics. Finally, it can take the form of a discrete-time Su-Schrieffer-Heeger model with half the number of spatial sites of the original model, or of a (1+1)D Wilson-Dirac theory with one quarter of the spatial sites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗