Complex Langevin methods for approximation-free simulation of cyclically driven quantum gasses

We numerically simulate an interaction-driven thermodynamic cycle with a Bose-Einstein condensate of ⁷Li as the working fluid in full 1:1 scale and at finite temperature. We use the coherent states field theoretic formulation of the path integral rather than a particle coordinate-based formulation to simulate large, high density systems at finite temperature without simplifying approximations, allowing for in-principle exact calculation of release energy, total energy, and entropy. Complex Langevin sampling enables efficient evaluation of the partition function without a sign problem. This combination allows us to exactly replicate the size, temperature, and density of an experimental realization of a four stroke cycle with over 200,000 atoms that alternates strokes of trap compression/expansion with strokes of scattering length increase/decrease. We demonstrate the accuracy and viability of these methods via direct comparison with experimental measurements.