Simulating ultracold quantum chemistry at conical intersections

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Computing the electronic structure and dynamics of molecules is a central challenge in the field of modern quantum chemistry. As the computational cost grows exponentially with the size of the molecule, solving the electronic structure problems in a classical computer becomes a formidable task. However, nowadays quantum computation and simulation become increasingly available to understand and characterise intricate many-body quantum states and the dynamics of molecules. Using quantum computers developed at, e.g., IBM and Google, electronic structures in low-lying states have been successfully determined. Nevertheless, challenging tasks remain, with one being the investigation of electronic dynamics when two close-lying electronic potential energy surfaces cross in high dimensional coordinate space. Such exceptional point forms a conical intersection, where intriguing chemical processes governed by topological effects and non-adiabatic transitions occur. Conical intersections also play critical roles in many photochemical and photobiological reactions, such as vision and stability of DNA. However, directly observing the resulting non-adiabatic dynamics is difficult, as it takes place on a femtosecond time scale and on length scales of a few Angstroms. As a result, any measurement will excite a vast number of vibrational states of the molecule, which inevitably leads to heating. This not only prevents the observation of quantum and topological effects, but also causes obstacles in interpreting the experiment theoretically. Furthermore, commonly used approaches, such as the Born-Oppenheimer approximation, fail near conical intersections. In order to address this challenge, we will conduct a research programme that introduces an analogue quantum simulation platform - consisting of a pair of interacting trapped Rydberg ions - to engineer conical intersections and to investigate their ensuing dynamics at length and time scales of the order of nanometres and microseconds, respectively. In an ion trap, the vibrational states of the ions can be laser cooled to nearly zero temperature, allowing the study of fully coherent processes in the vicinity of a conical intersection. This paves a new route towards simulating and probing ultracold quantum chemistry in real time via direct spectroscopic measurements in state-of-the-art trapped ion setup. Building on our initial work, the aim of this proposal is also to uncover novel many-body non-equilibrium and topological phenomena which are enabled by conical intersections but have no immediate counterpart in molecules. This will be enabled by the unprecedented level of controllability over the dimension, size, electron-vibration couplings offered by the Rydberg ion quantum simulator. The expected outputs will be of high relevance not only for the related academic community, but also for the ongoing development of quantum technologies. We will establish a comprehensive theoretical framework for simulating quantum chemistry with trapped Rydberg ions, and by working closely with the internationally pioneering experimental group, we will design protocols to probe coherent dynamics and effects. Our interdisciplinary research will create connections between the UK and the international trapped ion and Rydberg physics communities and thereby strengthen the UK's world-leading position in the area of quantum simulation and quantum computation.