The Lindblad master equation is a fundamental tool for describing the evolution of open quantum systems, but its computational complexity poses a significant challenge, especially for large systems. This article introduces a stochastic representation of the Lindblad dissipator that addresses this challenge by bundling the Lindblad operators. The stochastic dissipator maintains the Lindblad form, ensuring completely positive and trace-preserving dynamics. We demonstrate the effectiveness of this method by considering a Morse oscillator coupled to a spin bath. Our numerical experiments show that a small number of stochastically bundled operators can accurately capture the system’s dynamics, even when the Hilbert space dimension is large. This method offers a new perspective on open quantum systems and provides a computationally efficient way to simulate their dynamics.

Abstract Simulating mixed-state evolution in open quantum systems is crucial for various chemical physics, quantum optics, and computer science applications. These simulations typically follow the Lindblad master equation dynamics. An alternative approach known as quantum state diffusion unraveling is based on the trajectories of pure states generated by random wave functions, which evolve according to a nonlinear Itô-Schrödinger equation (ISE). This study introduces weak first- and second-order solvers for the ISE based on directly applying the Itô-Taylor expansion with exact derivatives in the interaction picture. We tested the method on free and driven Morse oscillators coupled to a thermal environment and found that both orders allowed practical estimation with a few dozen iterations. The variance was relatively small compared to the linear unraveling and did not grow with time. The second-order solver delivers much higher accuracy and stability with bigger time steps than the first-order scheme, with a small additional workload. However, the second-order algorithm has quadratic complexity with the number of Lindblad operators as opposed to the linear complexity of the first-order algorithm.

The conjecture that, as in bulk semiconductors, hot multiexcitons in nanocrystals cool rapidly to the lowest available energy levels is tested here by recording the effects of a single cold “spectator” exciton on the relaxation dynamics of a subsequently deposited hot counterpart. Results in CdSe/CdS nanodots show that a preexisting cold “spectator exciton” allows only half of the photoexcited electrons to relax directly to the band-edge. The rest are blocked in an excited quantum state due to conflicts in spin orientation. The latter fully relax in this sample only after ∼25 ps as the blocked electrons spins flip, prolonging the temporal window of opportunity for harvesting the retained energy more than 100 fold! Common to all quantum-confined nanocrystals, this process will delay cooling and impact the spectroscopic signatures of hot multiexcitons in all envisioned generation scenarios. How the spin-flipping rate scales with particle size and temperature remains to be determined.