We report the development of an efficient many-body algorithm for simulating open quantum system dynamics that utilizes a time-dependent variational principle for matrix product states to evolve large system-environment states. Capturing all system-environment correlations, we reproduce the non-perturbative, quantum-critical dynamics of the zero temperature spin-boson model, and then exploit the many-body information to visualize the complete time-frequency spectrum of the environmental excitations. Our 'environmental spectra' reveal correlated vibrational motion in polaronic modes which preserve their vibrational coherence during incoherent spin relaxation, demonstrating how environment information could yield valuable insights into complex quantum dissipative processes.

The simulation of open quantum dynamics is a critical tool for understanding how the non-classical properties of matter might be functionalised in future devices. However, unlocking the enormous potential of molecular quantum processes is highly challenging due to the very strong and non-Markovian coupling of ‘environmental’ molecular vibrations to the electronic ‘system’ degrees of freedom. Here, we present an advanced but general computational strategy that allows tensor network methods to effectively compute the non-perturbative, real-time dynamics of exponentially large vibronic wave functions of real molecules. We demonstrate how ab initio modelling, machine learning and entanglement analysis can enable simulations which provide real-time insight and direct visualisation of dissipative photophysics, and illustrate this with an example based on the ultrafast process known as singlet fission.

The process of photosynthesis, the main source of energy in the living world, converts sunlight into chemical energy. The high efficiency of this process is believed to be enabled by an interplay between the quantum nature of molecular structures in photosynthetic complexes and their interaction with the environment. Investigating these effects in biological samples is challenging due to their complex and disordered structure. Here we experimentally demonstrate a technique for studying photosynthetic models based on superconducting quantum circuits, which complements existing experimental, theoretical, and computational approaches. We demonstrate a high degree of freedom in design and experimental control of our approach based on a simplified three-site model of a pigment protein complex with realistic parameters scaled down in energy by a factor of 105. We show that the excitation transport between quantum-coherent sites disordered in energy can be enabled through the interaction with environmental noise. We also show that the efficiency of the process is maximized for structured noise resembling intramolecular phononic environments found in photosynthetic complexes.

The complex dynamics of ultrafast photoinduced reactions are governed by their evolution along vibronically coupled potential energy surfaces. It is now often possible to identify such processes, but a detailed depiction of the crucial nuclear degrees of freedom involved typically remains elusive. Here, combining excited-state time-domain Raman spectroscopy and tree-tensor network state simulations, we construct the full 108-atom molecular movie of ultrafast singlet fission in a pentacene dimer, explicitly treating 252 vibrational modes on 5 electronic states. We assign the tuning and coupling modes, quantifying their relative intensities and contributions, and demonstrate how these modes coherently synchronise to drive the reaction. Our combined experimental and theoretical approach reveals the atomic-scale singlet fission mechanism and can be generalized to other ultrafast photoinduced reactions in complex systems. This will enable mechanistic insight on a detailed structural level, with the ultimate aim to rationally design molecules to maximise the efficiency of photoinduced reactions.

We calculate the exact many-body time dynamics of polaritonic states supported by an optical cavity filled with organic molecules. Optical, vibrational and radiative processes are treated on an equal footing employing the Time-Dependent Variational Matrix Product States algorithm. We demonstrate signatures of non-Markovian vibronic dynamics and its fingerprints in the far-field photon emission spectrum at arbitrary light-matter interaction scales, ranging from the weak to the strong coupling regimes. We analyze both the single and many-molecule cases, showing the crucial role played by the collective motion of molecular nuclei and dark states in determining the polariton dynamics and the subsequent photon emission.

In the regime of strong coupling between molecular excitons and confined optical modes, the intra-molecular degrees of freedom are profoundly affected, leading to a reduced vibrational dressing of polaritons compared to bare electronically excited states. However, existing models only describe a single vibrational mode in each molecule, while actual molecules possess a large number of vibrational degrees of freedom and additionally interact with a continuous bath of phononic modes in the host medium in typical experiments. In this work, we investigate a small ensemble of molecules with an arbitrary number of vibrational degrees of freedom under strong coupling to a microcavity mode. We demonstrate that reduced vibrational dressing is still present in this case, and show that the influence of the phononic environment on most electronic and photonic observables in the lowest excited state can be predicted from just two collective parameters of the vibrational modes. Besides, we explore vibrational features that can be addressed exclusively by our extended model and could be experimentally tested. Our findings indicate that vibronic coupling is more efficiently suppressed for environments characterised by low-frequency (sub-Ohmic) modes.

next-generation environmental technologies for advanced harvesting of solar energy. The operating principles of DSCs are well documented: a photoanode (working electrode) is covered in mesoporous and nanocrystalline metal oxide (usually TiO 2 ), which is sensitized by a monolayer of dye molecules adsorbed via anchoring groups. [ 2 ] Upon photon absorption, the excited dyes inject an electron into the conduction band of the semiconducting TiO 2 , generating a potential difference with respect to this working electrode and a counter-electrode (a transparent conducting oxide, usually fl uorine-doped tin oxide FTO). Thus, the adsorbed electron is transported to the counter-electrode, i.e., initiating the electrical current in the solar cell. An electrolyte solution between these electrodes acts as a redox couple, taking the electron from the counter-electrode and passing it back to the dye in order to regenerate its ground state, thus completing the electrical circuit. The redox process is catalyzed by platinum, a thin fi lm of which is coated into the counter-electrode. Due to its slow recombination with electrons from TiO 2 , the redox couple typically employed is I − / I 3 − . However, it is worth noting that a Co (II/III) tris(bipyridyl) redox couple is gaining traction as an alternative, given that it has a higher redox potential ( E redox ≈ +0.535 V) compared to I − / I 3 − ( E redox ≈ +0.35 V) and it mitigates better against energy losses in the dye regeneration process. [ 1,3,4 ] As the most effi cient, and hence most commonly used dyes contain the expensive and relatively rare transition metal ruthenium, [ 5,6 ] metal-free organic dyes have become attractive candidates due to their low cost, high molar extinction coeffi cients, and inherent design fl exibility. [ 5,6 ] Most organic dyes are based on donor-(π-bridge)-acceptor ( D -π-A ) architectures, in which a π-conjugated system connects an electron-donating group ( D ) with an electron-accepting group ( A ). Upon photoexcitation, the resulting "push-pull" effect is characterized by anisotropic intramolecular charge transfer (ICT) from the donor to the acceptor, which facilitates electron injection into the semiconductor. Modifi cations to the three main components of the D -π-A architecture allow a fi ne-tuning of the magnitude of this "push-pull" effect, in terms of the molar extinction coeffi cient (ε), the maximum peak absorption wavelength (λ max peak ), tris(bipyridyl) suggests promise for these computationally designed dyes as co-sensitizers for DSC applications.

The theoretical study of open quantum systems strongly coupled to a vibrational environment remains computationally challenging, due to the strongly non-Markovian character of the dynamics. We study this problem in the case of a molecular dimer of the organic semiconductor tetracene, the exciton states of which are strongly coupled to a few hundreds of molecular vibrations. To do so, we employ a previously developed tensor network approach, based on the formalism of matrix product states. By analysing the entanglement structure of the system wavefunction, we can expand it in a tree tensor network state, which allows us to perform a fully quantum mechanical time evolution of the exciton-vibrational system, including the effect of 156 molecular vibrations. We simulate the dynamics of hot states, i.e. states resulting from excess energy photoexcitation, by constructing various initial bath states, and show that the exciton system indeed has a memory of those initial configurations. In particular, the specific pathway of vibrational relaxation is shown to strongly affect the quantum coherence between exciton states in timescales relevant for the ultra-fast dynamics of application-relevant processes such as charge transfer. The preferential excitation of lowfrequency modes leads to a limited number of relaxation pathways, thus 'protecting' quantum coherence, and leading to a significant increase of the charge transfer yield in the dimer structure.