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At least 73 records · Page 4

Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons

We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton–polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light–matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton–phonon coupling among polariton states due to the strong light–matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temporally decoherent and spatially coherent vibrations in metal halide perovskites

The long carrier lifetime and defect tolerance in metal halide perovskites (MHPs) are major contributors to the superb performance of MHP optoelectronic devices. Large polarons were reported to be responsible for the long carrier lifetime. Yet microscopic mechanisms of the large polaron formation, including the so-called phonon melting, are still under debate. In this study, time-of-flight inelastic neutron scattering experiments and first-principles density-functional theory calculations were employed to investigate the lattice vibrations (or phonon dynamics) in methylammonium lead iodide, a prototypical example of MHPs. Our findings are that optical phonons lose temporal coherence gradually with increasing temperature which vanishes at the orthorhombic-to-tetragonal structural phase transition. Surprisingly, however, we found that the spatial coherence is still retained throughout the decoherence process. We argue that the temporally decoherent and spatially coherent vibrations contribute to the formation of large polarons in this metal halide perovskite.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ultrafast Formation of Jahn–Teller Polarons Revealed by State-Selective Excitation in Correlated Spinel Co 3 O 4

Jahn–Teller polarons are quasiparticles that stem from symmetry breaking and strong local electron–phonon coupling. They originate from an excess charge carrier being dressed by a local lattice distortion, caused by the Jahn–Teller effect, and they critically impact electrical, structural, and magnetic properties in transition metal oxides. The observation of the microscopic steps involved in their formation is essential for enabling control over material properties through the targeted activation of local, site-specific modifications with light pulses. While Jahn–Teller distortion associated with polaron formation was predicted to contribute significantly to changes in electronic band gap and optical properties in Co 3 O 4 , its experimental observation remains elusive, requiring signatures of local symmetry reduction. In this work, we demonstrate Jahn–Teller polaron formation in spinel Co 3 O 4 . By exciting electronic transitions at 3.10 eV and 1.55 eV, we target either the Oh Cobalt(III) or the Td Cobalt(II) ions, and drive the subsequent coherent responses of the system through two different pathways. For the former, we demonstrate that ligand-to-metal charge transfer leads to Jahn–Teller polaron formation, which is linked to the deformation potential and magnetoelastic coupling. For the latter, we identify the coherent excitation of a T 2g phonon mode launched by on-site d-d electronic transitions. Key to our observations is the ability to target site-specific electronic excitations in spinel Co 3 O 4 using ultrafast optical pulses, while monitoring the ensuing low-energy collective modes through the coherent time-domain response of the material. Our approach, which combines the comparative analysis of experimental fingerprints with the support from density functional theory calculations, is broadly applicable to systems in which Jahn–Teller polaron physics has been theoretically predicted but remains experimentally unverified, and it underscores the potential of electronic-state targeting as a route to selectively excite and probe quasiparticle dynamics in solids.

Lattices↗

Room temperature sodium diffusion in sodium iron phosphate investigated with neutron scattering

Sodium iron phosphate, Na x FePO 4 , is currently one of the most promising cathode materials for sodium ion batteries. Here we employ a systematic approach using three neutron scattering techniques to investigate temperature dependent properties with a focus on the charge transfer processes. Two distinct Na + diffusive motions are observed with quasielastic neutron scattering, including room temperature motion. These processes correspond to rapid double jumps through extrinsic vacancy sites of ∼6 Å along with the more fundamental nearest neighbor jumps of 3.1 Å. Experimental observations of room temperature ionic diffusion are highly desirable, as the diffusion pathways are naturally well suited for efficient transport. Inelastic neutron scattering was used to probe the vibrational density of states that assist in the ionic and electronic (polaronic) transport processes, which are further supported with density functional theory. Neutron diffraction examines the disordering of the sodium sublattice upon transition to the solid-solution phase, which is believed to enhance the overall kinetics during sodium insertion/extraction. Finally, 57 Fe Mössbauer spectroscopy measurements probes polaron hopping and the local structural evolution that modifies the electron density surrounding the redox active iron sites. This study sheds light on the temperature induced atomic scale dynamics that occur in olivine Na x FePO 4 .

Novak, Eric [Swarthmore College, Swarthmore, PA (U↗

Oscillate and renormalize: Fast phonons reshape the Kondo effect in flat-band systems

Here, we examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency 𝜔 0 ≪ 𝑈/2, the onsite Coulomb scale 𝑈/2), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong-coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling 𝛼* when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast (𝜔 0 ≳ 𝑈/2), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively 𝑈 eff due to phonon-mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

Anderson impurity model↗

Ultrafast Carrier Self-Trapping Driven by Strong Exciton–Phonon Coupling in 2D MA 3 Bi 2 I 6 Cl 3 Perovskite

Two-dimensional (2D) hybrid bismuth halide perovskites have emerged as promising lead-free materials for optoelectronic applications due to their solution processability and tunable structures. Here, in this study, we investigate 2D layered hybrid perovskite MA 3 Bi 2 I 6 Cl 3 using temperature-dependent photoluminescence (PL) and femtosecond transient absorption spectroscopy. Our results reveal strong coupling between excitons and phonons, evidenced by giant Huang–Rhys factors, coherent phonon oscillations, and ultrafast carrier self-trapping into small-polaron and self-trapped exciton (STE) states. These processes appear as time-dependent ground-state bleach and photoinduced absorption features, highlighting the influence of the lattice in carrier dynamics. Wavelength- and time-resolved measurements reveal that PL emission is dominated by STEs, while free exciton emission is weak and short-lived. By comparing 2D MA 3 Bi 2 I 6 Cl 3 with 0D MA 3 Bi 2 I 9 , which contains molecularly isolated [BiI 6 ] 3− octahedra and 2D MA 3 Bi 2 Br 9 perovskites, we demonstrate how halide composition and structural dimensionality influence the balance between free exciton populations and carrier localization. These insights uncover the intrinsic kinetic landscape of photoexcited states in MA 3 Bi 2 I 6 Cl 3 . Overall, our study contributes to a mechanistic understanding of exciton–phonon interactions in lead-free 2D perovskites.

Pradeep, Kodimana Ramakrishnan [Northwestern Univ.↗

Light-Induced Transient Lattice Dynamics and Metastable Phase Transition in CH 3 NH 3 PbI 3 Nanocrystals

In this study, methylammonium lead iodide (MAPbI 3 ) perovskite nanocrystals (NCs) offer desirable optoelectronic properties with prospective utility in photovoltaics, lasers, and light-emitting diodes (LEDs). Structural rearrange-ments of MAPbI 3 in response to photoexcitation, such as lattice distortions and phase transitions, are of particular interest, as these engender long carrier lifetime and bolster carrier diffusion. Here, we use variable temperature X-ray diffraction (XRD) and synchrotron-based transient X-ray diffraction (TRXRD) to investigate lattice response following ultrafast optical excitation. MAPbI 3 NCs are found to slowly undergo a phase transition from the tetragonal to a pseudocubic phase over the course of 1 ns under 0.02-4.18 mJ/cm 2 fluence photoexcitation, with apparent nonthermal lattice distortions attributed to polaron formation. Lattice recovery exceeds time scales expected for both carrier recombination and thermal dissipation, indicating meta-stability likely due to the proximal phase transition, with symmetry-breaking along equatorial and axial directions. These findings are relevant for fundamental understanding and applications of structure-function properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anomalies in the electromagnetic response and peculiarities of the domain structure in the magnetic Weyl semimetal Co 3⁢ Sn 2 ⁢S 2

In this paper, we present a comprehensive study of magnetic properties of Co 3 ⁢Sn 2 ⁢S 2 (CoSnS) crystals using macroscopic characterization and observations of the domain structure (DS) in a wide range of easy- and hard-axis fields (𝐻) and temperatures (𝑇). From macroscopic measurements, we derive temperature dependences of the basic magnetic parameters of the material [saturation magnetization 𝑀 𝑠 ⁡(𝑇), uniaxial anisotropy constant 𝐾⁡(𝑇), and exchange stiffness 𝐴⁡(𝑇)] and, based on them, calculate the thermodynamic magnetization 𝑀⁡(𝐻,𝑇) curves and DS parameters for pinning-free samples. We find important qualitative and quantitative differences between the theory and experiment defined by the efficient pinning of domain walls (DWs) in our samples. It turns out that, already at temperatures close to the ferromagnetic transition 𝑇 𝑐 , the DW dynamics falls into the heavy creep regime, resulting in a strong deferral of the DS adjustment into the equilibrium state. Here, we suggest that specific magnetic defects, responsible for pinning and causing field-tuned reproducible domain nucleation patterns observed in our high-quality samples, are pointlike. Recently found magnetic polarons formed around vacancies and impurities, which carry strong diamagnetic moments of spin-orbit nature and are intrinsic for CoSnS and expected in other Weyl semimetals, are a possible source of pinning yielding peculiar 𝑀⁡(𝐻,𝑇) response of CoSnS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic Effect of Dopants on Bright and Dark Excitons in Strongly Confined Mn-Doped CsPbI 3 Quantum Dots

We investigated the magnetic effect of Mn 2+ ions on an exciton of Mn-doped CsPbI 3 quantum dots (QDs), where we looked for the signatures of an exciton magnetic polaron known to produce a large effective magnetic field in Mn-doped CdSe QDs. In contrast to Mn-doped CdSe QDs that can produce ~100 T of magnetic field upon photoexcitation, manifested as a large change in the energy and relaxation dynamics of a bright exciton, Mn-doped CsPbI 3 QDs exhibited little influence of a magnetic dopant on the behavior of a bright exciton. Furthermore, a μs-lived dark exciton in CsPbI 3 QDs showed 40% faster decay in the presence of Mn 2+ , equivalent to the effect of ~3 T of an external magnetic field. While further study is necessary to fully understand the origin of the large difference in the magneto-optic property of an exciton in two systems, we consider that the difference in antiferromagnetic coupling of the dopants is an important contributing factor.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Impact of Oxygen Non-Stoichiometry on Near-Ambient Temperature Ionic Mobility in Polaronic Mixed-Ionic-Electronic Conducting Thin Films

Enhanced ionic mobility in mixed ionic and electronic conducting solids contributes to improved performance of memristive memory, energy storage and conversion, and catalytic devices. Ionic mobility can be significantly depressed at reduced temperatures, for example, due to defect association and therefore needs to be monitored. Measurements of ionic transport in mixed conductors, however, proves to be difficult due to dominant electronic conductivity. This study examines the impact of different levels of quenched-in oxygen deficiency on the oxygen vacancy mobility near room temperature as measured by a novel dynamic current-voltage analysis. A Pr 0.1 Ce 0.9 O 2-δ film was grown by pulsed laser deposition and subsequently annealed, from 400-600° C, in various oxygen partial pressures to modify its oxygen vacancy concentration while minimizing microstructural growth and cation segregation. To monitor changes in film non-stoichiometry, we leverage the existence of an optical absorption center, related to the oxidation state of Pr ions in Pr0.1Ce0.9O2-δ. The oxygen vacancy migration enthalpy was found to exhibit a small increase from 0.73± 0.04 to 0.79 ± 0.02 eV with increasing oxygen deficiency, while the pre-factor was found to increase by a factor of 135. Here, a nearly 13-fold increase in ionic mobility at 60 °C for increases in oxygen non-stoichiometry from 0.032 ± 0.001 to 0.042± 0.001 was thereby detected. Raman spectroscopy was employed to rule out changes in strain as the primary cause for the significant change in mobility. Several factors potentially contributing to the large pre-factor changes are examined and discussed. Insights into how ionic defect concentration can markedly impact ionic mobility should help in elucidating the origins of variations seen in nanoionic devices.

36 MATERIALS SCIENCE↗

Ultrafast infrared nano-imaging of far-from-equilibrium carrier and vibrational dynamics

Ultrafast infrared nano-imaging has demonstrated access to ultrafast carrier dynamics on the nanoscale in semiconductor, correlated-electron, or polaritonic materials. However, mostly limited to short-lived transient states, the contrast obtained has remained insufficient to probe important long-lived excitations, which arise from many-body interactions induced by strong perturbation among carriers, lattice phonons, or molecular vibrations. Here, we demonstrate ultrafast infrared nano-imaging based on excitation modulation and sideband detection to characterize electron and vibration dynamics with nano- to micro-second lifetimes. As an exemplary application to quantum materials, in phase-resolved ultrafast nano-imaging of the photoinduced insulator-to-metal transition in vanadium dioxide, a distinct transient nano-domain behavior is quantified. In another application to lead halide perovskites, transient vibrational nano-FTIR spatially resolves the excited-state polaron-cation coupling underlying the photovoltaic response. These examples show how heterodyne pump-probe nano-spectroscopy with low-repetition excitation extends ultrafast infrared nano-imaging to probe elementary processes in quantum and molecular materials in space and time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Anionic Oxygen Redox in the High-Lithium Material Li 8 SnO 6

Lithiated transition metal oxide cathode materials that combine oxygen-anion redox [O 2 – /(O 2 ) n– ] with cation redox offer substantial capacities and higher voltage than cathodes without oxygen redox, but oxygen-anion redox is usually accompanied by the formation of peroxo or superoxo species that may cause oxygen release. To clarify the relationship between the oxygen release and peroxide and superoxide dimers without the complication of transition-metal redox, we performed density functional theory calculations to study the layered Li 8 SnO 6 cathode because it has only oxygen-anion redox during delithiation. Features with O–O distances of ~1.5 Å (corresponding to the formation of a peroxide) were observed at 75% lithium concentration, and further delithiation to 62.5% lithium concentration shortened the O–O bond distance to ~1.3 Å (corresponding to the formation of superoxide). The solely anionic oxygen redox stabilizes the delithiated structure of Li 8–x SnO 6 , and it does not cause structural disorder or release oxygen gas. Ab initio molecular dynamics calculations in the supercell at 300 K indicate that oxygen dimerization may occur at 75% lithium concentration. On the (0001) surface with a high lithium concentration (98%), oxygen dimerization is unfavorable. The calculations by HSE06 show that oxygen redox in Li 8 SnO 6 offers an initial voltage (vs Li/Li + ) greater than 4.2 V. The GGA+U calculations indicate that the Li + -polaron in Li 95 Sn 12 O 72 migrates with a migration barrier of only 0.43 eV. Here, this work also quantifies a solely anionic oxygen redox mechanism in Li 8 SnO 6 , and it provides a deeper understanding of anionic oxygen redox in Li-excess oxide cathode materials.

25 ENERGY STORAGE↗

Solution-phase sample-averaged single-particle spectroscopy of quantum emitters with femtosecond resolution

Here, the development of many optical quantum technologies depends on the availability of solid-state single quantum emitters with near-perfect optical coherence. However, a standing issue that limits systematic improvement is the significant sample heterogeneity and lack of mechanistic understanding of microscopic energy flow at the single emitter level and ultrafast timescales. Here we develop solution-phase single-particle pump-probe spectroscopy with photon correlation detection that captures sample-averaged dynamics in single molecules and/or defect states with unprecedented clarity at femtosecond resolution. We apply this technique to single quantum emitters in two-dimensional hexagonal boron nitride, which suffers from significant heterogeneity and low quantum efficiency. From millisecond to nanosecond timescales, the translation diffusion, metastable-state-related bunching shoulders, rotational dynamics, and antibunching features are disentangled by their distinct photon-correlation timescales, which collectively quantify the normalized two-photon emission quantum yield. Leveraging its femtosecond resolution, spectral selectivity and ultralow noise (two orders of magnitude improvement over solid-state methods), we visualize electron-phonon coupling in the time domain at the single defect level, and discover the acceleration of polaronic formation driven by multi-electron excitation. Corroborated with results from a theoretical polaron model, we show how this translates to sample-averaged photon fidelity characterization of cascaded emission efficiency and optical decoherence time. Our work provides a framework for ultrafast spectroscopy in single emitters, molecules, or defects prone to photoluminescence intermittency and heterogeneity, opening new avenues of extreme-scale characterization and synthetic improvements for quantum information applications.

36 MATERIALS SCIENCE↗

Charge Carrier Induced Structural Ordering And Disordering in Organic Mixed Ionic Electronic Conductors

Operational stability underpins the successful application of organic mixed ionic-electronic conductors (OMIECs) in a wide range of fields, including biosensing, neuromorphic computing, and wearable electronics. Here in this work, both the operation and stability of a p-type OMIEC material of various molecular weights are investigated. Electrochemical transistor measurements reveal that device operation is very stable for at least 300 charging/discharging cycles independent of molecular weight, provided the charge density is kept below the threshold where strong charge–charge interactions become likely. When electrochemically charged to higher charge densities, an increase in device hysteresis and a decrease in conductivity due to a drop in the hole mobility arising from long-range microstructural disruptions are observed. By employing operando X-ray scattering techniques, two regimes of polaron-induced structural changes are found: 1) polaron-induced structural ordering at low carrier densities, and 2) irreversible structural disordering that disrupts charge transport at high carrier densities, where charge–charge interactions are significant. These operando measurements also reveal that the transfer curve hysteresis at high carrier densities is accompanied by an analogous structural hysteresis, providing a microstructural basis for such instabilities. This work provides a mechanistic understanding of the structural dynamics and material instabilities of OMIEC materials during device operation.

36 MATERIALS SCIENCE↗

Exploring the Photophysics of N-Type Polymer N2200

The polymer interphase is a complex environment comprised of polymer chains, solvent molecules, and electrolyte ions. However, the microenvironments that these ingredients produce is both poorly-understood and difficult to investigate given the system's inherent structural heterogeneity. Nonetheless, a fundamental understanding of the structure, electrochemical behavior, and excited-state dynamics is a key prerequisite to optimizing devices based on such a system - for instance, photoelectrochemical cells for the direct, light-driven production of solar hydrogen, which may minimize efficiency losses compared to sequential light harvesting and electrochemical hydrogen production in separate but linked devices. This work combines transient absorption (TA) spectroscopy, which is a powerful tool for the observation of a variety of excited states on a femto- to microsecond timescale, with time-resolved microwave conductivity (TRMC) spectroscopy, which selectively probes the dynamics of free charge carriers (FC), of a blend of a donor polymer (PTB7-Th) and acceptor polymer (N2200) in a bulk heterojunction. Initial results indicate an extension of FC lifetime and homogenization of the microenvironment on a whole-film level, not just at the surface of the polymer; however, many questions are still under active investigation, including the changes in energy of the involved polaron states, effective conjugation length, FC mobility and migration distance, etc. Additional experiments regarding the photoinitiated behavior of the blend in different environments and on different timescales are ongoing.

charge recombination↗

Adsorption, charge transfer and a coverage-driven transition of alkali metals on rutile TiO 2 (110)

The interaction of alkali metals with metal oxide surfaces is central to tuning surface reactivity in heterogeneous catalysis and photocatalysis. Here we present a comprehensive DFT+U study of the adsorption of alkali metals (Li, Na, K, Rb, Cs) on the (110) surface of rutile TiO 2 . At low coverage (θ = 1/8), all alkali metals bind preferentially to bridging oxygen sites with adsorption energies in the range −4.06 to −3.33 eV, transferring nearly one full electron (0.92–0.99 |e|) to the substrate and inducing Ti 4+ → Ti 3+ reduction. The excess charge localizes preferentially at subsurface Ti sites in the form of small polarons. Diffusion barriers indicate facile motion along bridging-oxygen rows, whereas inter-row hopping is strongly hindered. Coverage effects were examined systematically for potassium: adsorption energy and charge transfer per K atom decrease monotonically with increasing θ. Strikingly, a sharp energy discontinuity occurs between θ = 4/8 and θ = 5/8 (ΔE ≈ 1 eV per atom), which we identify as a coverage-driven structural transition arising from steric packing constraints and enhanced K–K electrostatic repulsion once every (1×1) surface cell is occupied. This structural transition perfectly correlates with a dramatic drop in the work function down to an ultra-low minimum of 0.84 eV at θ=5/8, followed by a metallization- driven recovery at higher coverages. Ab initio molecular dynamics simulations confirm zigzag K arrangements at moderate coverage (θ = 1/3), while at high coverage (θ = 2/3) short-range K–K correlations emerge without long-range order. These results provide atomistic insight into the structure–activity relationships underlying alkali promotion effects on oxide-supported catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhanced mobility of cations and anions in the redox state: The polaronium mechanism

Hugely enhanced slow-ion diffusivity has been widely observed under extreme redox conditions and for unclear reasons. Aided by first-principles calculations on model systems of ZrO 2 , CeO 2 , BaTiO 3 and Li 4/3 Mn 2/3 O 2 , here we successfully explained the intriguing phenomenon by a polaronium mechanism. We found a polaronium, defined as a transitory complex of a polaronic electron or hole and a migrating counterion, becomes highly mobile when the counterion comes from a d 0 or f 0 cation (e.g., Zr 4+ , Ti 4+ and Ce 4 ) or a p 6 anion (e.g., O 2- ) in the host compound. Upon a redox reaction, the complex attains a d 1 /f 1 or p 5 configuration, which spontaneously forms because it is favored by an electron-phonon interaction (manifest as the Jahn-Teller effect in high symmetry systems) that enables local relaxation and lowers the system energy. Here our calculations found such interaction reaching its peak at the saddle point where the local environment is softest, so soft that it allows a reorientation of the anisotropic d/f/p orbital to minimize the electron repulsion locally. Since the complex may dissolve after a successful ion-migration event, the redox electron/hole can be recycled to form another free-radical-like polaronium elsewhere, thereby enhancing ion migration repeatedly. The proposed polaronium mechanism, which also operates in ceramics doped with mixed-valence cations, is most relevant under dynamic and extreme thermal/field/irradiation conditions where extra electrons/holes are abundantly generated by non-equilibrium redox reactions. For such operations, some with emerging applications, our diffusion-enhancing mechanism may provide new theoretical insight to help understand their material/microstructure stability and performance.

36 MATERIALS SCIENCE↗

An Exact Expression for Multidimensional Spectroscopy of a Spin‐Boson Hamiltonian

Multidimensional coherent spectroscopy is a powerful tool to characterize nonlinear optical response functions. Typically, multidimensional spectra are interpreted via a perturbative framework that straightforwardly provides intuition into the density matrix dynamics that give rise to specific spectral features. When the goal is to characterize system coupling to a thermal bath however, the perturbative formalism becomes unwieldy and yields less intuition. Here, an approach developed by Vagov et al. is extended to provide an exact expression for multidimensional spectra of a spin-boson Hamiltonian up to arbitrary order of electric field interaction. Furthermore, the utility of this expression is demonstrated by modeling polaron formation and coherent exciton-phonon coupling in quantum dots, which strongly agree with experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗