Semiclassical mapping to analyse the dynamics of the Jaynes-Cummings Hamiltonian.
Duration : Sept 2021 - Aug 2022
Supervisor : Dr. Aaron Kelly
Institute : Max Planck Institute of the Structue and Dynamics of Matter, Hamburg
Abstract: Semiclassical mapping methods provide a framework for reducing the unfavorable computational cost of fully quantum simulations by mapping discrete quantum degrees of freedom onto classical phase space variables, thereby enabling ensemble propagation of independent trajectories. In the context of nonadiabatic and open-system dynamics, a number of such approaches have been developed, including the partially linearized density matrix (PLDM) method [1] based on the Meyer–Miller–Stock–Thoss mapping [2]. Partially linearized methods preserve separate forward and backward propagation of mapping variables, allowing improved treatment of quantum coherence relative to fully linearized schemes. The spin partially linearized density matrix (spin-PLDM) approach extends this class by using a spin mapping and Stratonovich–Weyl transform to constrain the mapping variables to the physical subspace and rigorously include zero-point contributions, improving the computation of correlation functions compared to standard-PLDM [3] and fully linearized spin mapping [4].
In this work, we assess the performance of spin-PLDM for modeling dissipation dynamics in a two-level atomic subsystem coupled to a cavity-modified electromagnetic field, a prototypical open quantum system [5, 6]. Our simulations indicate that spin-PLDM captures key characteristics of polaritonic dissipation with reasonable fidelity while enabling tractable inclusion of several hundred photonic modes. However, the method exhibits systematic deviations from exact benchmarks, including unphysical energy loss and attenuated polariton intensities, consistent with limitations observed in semiclassical mapping approaches when extended beyond simple models. We highlight both the potential of spin-PLDM for scalable semiclassical simulation and the need for further refinement in its treatment of classical variable representing environmental degrees of freedom.
References:
J. R. Mannouch, J. O. Richardson, Partially linearized spin-mapping approach for nonadiabatic dynamics, J. Chem. Phys. 153, 194110 (2020)
G. Stock, M. Thoss Semiclassical description of nonadiabatic quantum dynamics Physical review letters, 1997
P. Huo, D. F. Coker Communication: Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution The Journal of chemical physics 135 (20) 2011
J. E. Runeson, J. O. Richardson Generalized spin mapping for quantum-classical dynamics The Journal of Chemical Physics 2020
NM Hoffmann, C Schäfer, A Rubio, A Kelly, H Appel Capturing vacuum fluctuations and photon correlations in cavity quantum electrodynamics with multitrajectory Ehrenfest dynamics Physical Review A 99 (6), 063819
NM Hoffmann, C Schäfer, N Säkkinen, A Rubio, H Appel, A Kelly Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference The Journal of chemical physics 151 (24), 244113
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