Dark State Concentration Dependent Emission and Dynamics of CdSe Nanoplatelet Exciton-Polaritons.

The recent surge of interest in polaritons has prompted fundamental questions about the role of dark states in strong light-matter coupling phenomena. Here, we systematically vary the relative number of dark states by controlling the number of stacked CdSe nanoplatelets confined in a Fabry-Pérot cavity. We find the emission spectrum to change significantly with an increasing number of nanoplatelets, with a gradual shift of the dominant emission intensity from the lower polariton branch to a manifold of dark states. Through accompanying calculations based on a kinetic model, this shift is rationalized by an entropic trapping of excitations by the dark state manifold, while a weak dark state dispersion due to local disorder explains their nonzero emission. Our results point toward the relevance of the dark state concentration to the optical and dynamical properties of cavity-embedded quantum emitters with ramifications for Bose-Einstein condensate formation, polariton lasing, polariton-based quantum transduction schemes, and polariton chemistry.

Mixed quantum-classical modeling of exciton-phonon scattering in solids: Application to optical linewidths of monolayer MoS2.

We present a mixed quantum-classical framework for the microscopic and non-Markovian modeling of exciton-phonon scattering in solid-state materials and apply it to calculate the optical linewidths of monolayer MoS2. Within this framework, we combine reciprocal-space mixed quantum-classical dynamics with models for the quasiparticle band structure as well as the electron-hole and carrier-phonon interactions, parametrized against ab initio calculations, although noting that a direct interfacing with ab initio calculations is straightforward in principle. We introduce various parameters for truncating the Brillouin zone to select regions of interest. Variations of these parameters allow us to determine linewidths in the limit of asymptotic material sizes. The obtained asymptotic linewidths are found to agree favorably with experimental measurements across a range of temperatures. As such, our framework establishes itself as a promising route toward unraveling the non-Markovian and microscopic principles governing the nonadiabatic dynamics of solids.

Mixed Quantum-Classical Dynamics under Arbitrary Unitary Basis Transformations.

A common approach to minimizing the cost of quantum computations is by unitarily transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations and propose their integration into mixed quantum-classical dynamics, allowing this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta of the classical degrees of freedom are combined into a set of complex-valued coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets.

A 2D chiral microcavity based on apparent circular dichroism.

Engineering asymmetric transmission between left-handed and right-handed circularly polarized light in planar Fabry-Pérot (FP) microcavities would enable a variety of chiral light-matter phenomena, with applications in spintronics, polaritonics, and chiral lasing. Such symmetry breaking, however, generally requires Faraday rotators or nanofabricated polarization-preserving mirrors. We present a simple solution requiring no nanofabrication to induce asymmetric transmission in FP microcavities, preserving low mode volumes by embedding organic thin films exhibiting apparent circular dichroism (ACD); an optical phenomenon based on 2D chirality. Importantly, ACD interactions are opposite for counter-propagating light. Consequently, we demonstrated asymmetric transmission of cavity modes over an order of magnitude larger than that of the isolated thin film. Through circular dichroism spectroscopy, Mueller matrix ellipsometry, and simulation using theoretical scattering matrix methods, we characterize the spatial, spectral, and angular chiroptical responses of this 2D chiral microcavity.

Theory predicts 2D chiral polaritons based on achiral Fabry-Pérot cavities using apparent circular dichroism.

Realizing polariton states with high levels of chirality offers exciting prospects for quantum information, sensing, and lasing applications. Such chirality must emanate from either the involved optical resonators or the quantum emitters. Here, we theoretically demonstrate a rare opportunity for realizing polaritons with so-called 2D chirality by strong coupling of the optical modes of (high finesse) achiral Fabry-Pérot cavities with samples exhibiting "apparent circular dichroism" (ACD). ACD is a phenomenon resulting from an interference between linear birefringence and dichroic interactions. By introducing a quantum electrodynamical theory of ACD, we identify the design rules based on which 2D chiral polaritons can be produced, and their chirality can be optimized.

Ehrenfest modeling of cavity vacuum fluctuations and how to achieve emission from a three-level atom.

A much-needed solution for the efficient modeling of strong coupling between matter and optical cavity modes is offered by mean-field mixed quantum-classical dynamics, where a classical cavity field interacts self-consistently with quantum states of matter through Ehrenfest's theorem. We previously introduced a modified mean-field approach, referred to as decoupled mean-field (DC-MF) dynamics, wherein vacuum fluctuations of the cavity field are decoupled from the quantum-mechanical ground state as a means to resolve an unphysical drawing of energy from the vacuum fluctuations by a two-level atom. Here, we generalize DC-MF dynamics for an arbitrary number of (nondegenerate) atomic levels and show that it resolves an unphysical lack of emission from a three-level atom predicted by conventional mean-field dynamics. We furthermore show DC-MF to provide an improved description of reabsorption and (resonant) two-photon emission processes.

Theory predicts UV/vis-to-IR photonic down conversion mediated by excited state vibrational polaritons.

This work proposes a photophysical phenomenon whereby ultraviolet/visible (UV/vis) excitation of a molecule involving a Franck-Condon (FC) active vibration yields infrared (IR) emission by strong coupling to an optical cavity. The resulting UV/vis-to-IR photonic down conversion process is mediated by vibrational polaritons in the electronic excited state potential. It is shown that the formation of excited state vibrational polaritons (ESVP) via UV/vis excitation only involve vibrational modes with both a non-zero FC activity and IR activity in the excited state. Density functional theory calculations are used to identify 1-Pyreneacetic acid as a molecule with this property and the dynamics of ESVP are modeled. Overall, this work introduces an avenue of polariton chemistry where excited state dynamics are influenced by the formation of vibrational polaritons. Along with this, the UV/vis-to-IR photonic down conversion is potentially useful in both sensing excited state vibrations and quantum transduction schemes.

Exciton annihilation in molecular aggregates suppressed through quantum interference.

Exciton-exciton annihilation (EEA), an important loss channel in optoelectronic devices and photosynthetic complexes, has conventionally been assumed to be an incoherent, diffusion-limited process. Here we challenge this assumption by experimentally demonstrating the ability to control EEA in molecular aggregates using the quantum phase relationships of excitons. We employed time-resolved photoluminescence microscopy to independently determine exciton diffusion constants and annihilation rates in two substituted perylene diimide aggregates featuring contrasting excitonic phase envelopes. Low-temperature EEA rates were found to differ by more than two orders of magnitude for the two compounds, despite comparable diffusion constants. Simulated rates based on a microscopic theory, in excellent agreement with experiments, rationalize this EEA behaviour based on quantum interference arising from the presence or absence of spatial phase oscillations of delocalized excitons. These results offer an approach for designing molecular materials using quantum interference where low annihilation can coexist with high exciton concentrations and mobilities.

Overcoming positivity violations for density matrices in surface hopping.

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question of how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity while yielding improved accuracy throughout much (but not all) of parameter space.

A Mean-Field Treatment of Vacuum Fluctuations in Strong Light-Matter Coupling.

Mean-field mixed quantum-classical dynamics could provide a much-needed means to inexpensively model quantum electrodynamical phenomena by describing the optical field and its vacuum fluctuations classically. However, this approach is known to suffer from an unphysical transfer of energy out of the vacuum fluctuations when the light-matter coupling becomes strong. We highlight this issue for the case of an atom in an optical cavity and resolve it by introducing an additional set of classical coordinates to specifically represent vacuum fluctuations whose light-matter interaction is scaled by the instantaneous ground-state population of the atom. This not only rigorously prevents the aforementioned unphysical energy transfer but is also shown to yield a radically improved accuracy in terms of the atomic population and the optical field dynamics, generating results in excellent agreement with full quantum calculations. As such, the resulting method emerges as an attractive solution for the affordable modeling of strong light-matter coupling phenomena involving macroscopic numbers of optical modes.

Modulating Singlet Fission by Scanning through Vibronic Resonances in Pentacene-Based Blends.

Vibronic coupling has been proposed to play a decisive role in promoting ultrafast singlet fission (SF), the conversion of a singlet exciton into two triplet excitons. Its inherent complexity is challenging to explore, both from a theoretical and an experimental point of view, due to the variety of potentially relevant vibrational modes. Here, we report a study on blends of the prototypical SF chromophore pentacene in which we engineer the polarizability of the molecular environment to scan the energy of the excited singlet state (S1) continuously over a narrow energy range, covering vibrational sublevels of the triplet-pair state (1(TT)). Using femtosecond transient absorption spectroscopy, we probe the dependence of the SF rate on energetic resonance between vibronic states and, by comparison with simulation, identify vibrational modes near 1150 cm-1 as key in facilitating ultrafast SF in pentacene.

A reciprocal-space formulation of surface hopping.

Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping and assess their accuracy against mean-field mixed quantum-classical dynamics and numerically exact results. Having very similar equations of motion, reciprocal-space surface hopping can be straightforwardly incorporated in existing (real-space) surface hopping implementations.

Theory of Apparent Circular Dichroism Reveals the Origin of Inverted and Noninverted Chiroptical Response under Sample Flipping.

Circular dichroism (CD) finds widespread application as an optical probe for the structure of molecules and supramolecular assemblies. Its underlying chiral light-matter interactions effectively couple between photonic spin states and select quantum-mechanical degrees of freedom in a sample, implying an intricate connection with photon-to-matter quantum transduction. However, effective transduction implementations likely require interactions that are antisymmetric with respect to the direction of light propagation through the sample, yielding an inversion of the chiroptical response upon sample flipping, which is uncommon for CD. Recent experiments on organic thin films have demonstrated such chiroptical behavior, which was attributed to "apparent CD" resulting from an interference between the sample's linear birefringence and linear dichroism. However, a theory connecting the underlying optical selection rules to the microscopic electronic structure of the constituent molecules remains to be formulated. Here, we present such a theory based on a combination of Mueller calculus and a Lorentz oscillator model. The theory reaches good agreement with experimental CD spectra and allows for establishing the (supra)molecular design rules for maximizing or minimizing this chiroptical effect. It furthermore highlights that, in addition to antisymmetrically, it can manifest symmetrically such that no chiroptical response inversion occurs, which is a consequence of a helical stacking of molecules in the light propagation direction.

Vacancy control in acene blends links exothermic singlet fission to coherence.

The fission of singlet excitons into triplet pairs in organic materials holds great technological promise, but the rational application of this phenomenon is hampered by a lack of understanding of its complex photophysics. Here, we use the controlled introduction of vacancies by means of spacer molecules in tetracene and pentacene thin films as a tuning parameter complementing experimental observables to identify the operating principles of different singlet fission pathways. Time-resolved spectroscopic measurements in combination with microscopic modelling enables us to demonstrate distinct scenarios, resulting from different singlet-to-triplet pair energy alignments. For pentacene, where fission is exothermic, coherent mixing between the photoexcited singlet and triplet-pair states is promoted by vibronic resonances, which drives the fission process with little sensitivity to the vacancy concentration. Such vibronic resonances do not occur for endothermic materials such as tetracene, for which we find fission to be fully incoherent; a process that is shown to slow down with increasing vacancy concentration.

A reciprocal-space formulation of mixed quantum-classical dynamics.

We derive a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. Taking these variables as a Fourier series then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space. To illustrate the advantage of the reciprocal-space formulation, we present a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons using a truncated reciprocal-space basis, which is not possible within a real-space formulation.

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles.

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble's ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

Quantum biology revisited.

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.

Charge-transfer biexciton annihilation in a donor-acceptor co-crystal yields high-energy long-lived charge carriers.

Organic donor-acceptor (D-A) co-crystals have attracted much interest due to their important optical and electronic properties. Co-crystals having ⋯DADA⋯ π-stacked morphologies are especially interesting because photoexcitation produces a charge-transfer (CT) exciton, D˙+-A˙-, between adjacent D-A molecules. Although several studies have reported on the steady-state optical properties of this type of CT exciton, very few have measured the dynamics of its formation and decay in a single D-A co-crystal. We have co-crystallized a peri-xanthenoxanthene (PXX) donor with a N,N-bis(3-pentyl)-2,5,8,11-tetraphenylperylene-3,4:9,10-bis(dicarboximide) (Ph4PDI) acceptor to give an orthorhombic PXX-Ph4PDI ⋯DADA⋯ π-stacked co-crystal with a CT transition dipole moment that is perpendicular to the transition moments for S n ← S0 excitation of PXX and Ph4PDI. Using polarized, broadband, femtosecond pump-probe microscopy, we have determined that selective photoexcitation of Ph4PDI in the single co-crystal results in CT exciton formation within the 300 fs instrument response time. At early times (0.3 ≤ t ≤ 500 ps), the CT excitons decay with a t -1/2 dependence, which is attributed to CT biexciton annihilation within the one-dimensional ⋯DADA⋯ π-stacks producing high-energy, long-lived (>8 ns) electron-hole pairs in the crystal. These energetic charge carriers may prove useful in applications ranging from photovoltaics and opto-electronics to photocatalysis.

Multiset Matrix Product State Calculations Reveal Mobile Franck-Condon Excitations Under Strong Holstein-Type Coupling.

We show that the dynamics of (vertical) Franck-Condon excitations in the regime where Holstein-coupled vibrational modes mix strongly with electronic degrees of freedom sharply contrasts with the known self-localized behavior of vibrationally relaxed excitations. Instead, the strongly coupled modes are found to periodically induce resonances between interacting electronic sites, during which effective excitation transfer occurs, allowing Franck-Condon excitations to attain substantial mean square displacements under conditions where relaxed excitations are essentially trapped to a single site. In demonstrating this behavior, we employ a multiset matrix product state formalism. We find this tensor network state method to be a remarkably efficient and accurate approach for the notoriously difficult problem posed by the Holstein model in the regime where the electronic coupling, the vibrational quantum, and the vibrational reorganization energy are comparable in magnitude.