QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics

The "hierarchical equations of motion" (HEOM) method is a powerful exact numerical approach to solve the dynamics and find the steady-state of a quantum system coupled to a non-Markovian and non-perturbative environment. Originally developed in the context of physical chemistry, it has also been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics. Here we present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both bosonic and fermionic environments. We demonstrate its utility with a series of examples. For the bosonic case, we include demonstrations of fitting arbitrary spectral densities, and an example of the dynamics of energy transfer in the Fenna-Matthews-Olson photosynthetic complex, showing how a suitable non-Markovian environment can protect against pure dephasing. We also demonstrate how the HEOM can be used to benchmark different strategies for dynamical decoupling of a spin from its environment, and show that the Uhrig pulse-spacing scheme is less optimal than equally spaced pulses when the environment's spectral density is very broad. For the fermionic case, we present an integrable single-impurity example, used as a benchmark of the code, and a more complex example of an impurity strongly coupled to a single vibronic mode, with applications to single-molecule electronics.