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.
Comment: 20 pages, 15 figures. Updated to describe package inclusion in QuTiP v4.7 (www.qutip.org), new examples (optimal pulse spacing in dynamical decoupling, quantum heat transport), and inclusion of additional contributors in author list. Further updates to expand examples, clarify content and summarize existing packages