Abstract:

Quantum coherences are phase relations between distinct quantum states responsible for quantum interference. Many emerging technologies in computing, metrology, and energy generation, share the goal of exploiting macroscopic control of quantum coherence to design high- efficiency devices. A central issue in quantum technology is sustaining coherence at scale. While accurate quantum dynamics methods are essential to the design of these materials and the nonlinear spectroscopic techniques used to characterize them, exact quantum solutions for these systems are intractable. What is needed instead is a quantum dynamics method which approximates coherences accurately, scales sensibly, and has control over the extent of quantumness assumed in the equations of motion. To address this problem, a new phase space quantum dynamics method is developed.  Working in the Wigner-Moyal representation, exact solutions to the coherence dynamics of a two-state displaced oscillator and model conical intersection are derived using a Thawed Gaussian ansatz. This Thawed Moyal solution corrects the lower order semiclassical approach traditionally used in time-domain spectroscopy. Using the kinematic insights of the Thawed Moyal theory, a new formalism called the Star Coherence Representation is derived. The Star Coherence Representation solves the unitary evolution of a pure state quantum density entirely in terms of its populations and relative phases, with explicit dependence on the off-diagonal coherences eliminated. Instead, this representation constructs quantum coherences on-the-fly in terms of the instantaneous values of the populations and phases. By recasting evolution in terms of population distribution functions, quantum equations of motion to be solved by linearly scaling classical trajectory ensembles which are parallelizable and amenable to statistical estimation through standard techniques of machine learning.