Ring polymer quantization of the photon field in polariton chemistry

Abstract

We use the ring polymer (RP) representation to quantize the radiation field inside an optical cavity to investigate polariton quantum dynamics. Using a charge transfer model coupled to an optical cavity, we demonstrate that the RP quantization of the photon field provides accurate rate constants of the polariton mediated electron transfer reaction compared to Fermi’s golden rule. Because RP quantization uses extended phase space to describe the photon field, it significantly reduces the computational costs compared to the commonly used Fock state description of the radiation field. Compared to the other quasi-classical descriptions of the photon field, such as the classical Wigner based mean-field Ehrenfest model, the RP representation provides a much more accurate description of the polaritonic quantum dynamics because it alleviates the potential quantum distribution leakage problem associated with the photonic degrees of freedom (DOF). This work demonstrates the possibility of using the ring polymer description to treat the quantized radiation field in polariton chemistry, offering an accurate and efficient approach for future investigations in cavity quantum electrodynamics.

Non-Adiabatic Ring Polymer Molecular Dynamics with Spin Mapping Variables

“…Based on our previous experience with the MMST version of NRPMD approach, we conjecture that Hs should be the Hamiltonian for the NRPMD propagation when using the spin mapping variables. This is because the correct equations of motion for the MMST mapping variables 45,62 can be derived based on the partition function 38 through a similar procedure as above, which coincides with the Liouvillian derived from generalized Kubo-transformed TCF with Matsubara approximation and ring polymer approximation 45 We also note that in principle, the partition function in Eq. 45 should generate the same result as the one in Eq.…”

“…Future directions include generalizing the current formalism to multi-electronic states, 53 as well as rigorously derive SM-NRPMD formalism through the recent development of the non-adiabatic Matsubara framework. 45…”

“…In the original NRPMD method, the corresponding equation of motion was first proposed, 36 then recently proved through the non-adiabatic Matsubara dynamics formalism. 45 We envision that the above EOM (Eq. 53a-Eq.…”

“…The NRPMD method 36 was first proposed by Thoss and Richardson as a model dynamics. Recently, it was rigorously derived from the non-adiabatic Matsubara dynamics formalism 45 . It uses the MMST formalism (Eq.…”

“…[36][37][38] In particular, the NRPMD approach has been rigorously derived from the nonadiabatic Matsubara dynamics framework. 45 One potential limitation of these state-dependent RPMD approaches is rooted in the MMST mapping representation. It is well known that the MMST representation has a larger size of Hilbert space than the original electronic subspace, and requires projection back to that subspace to obtain accurate results.…”