Symplectic split-operator method for the time-dependent unitary Tavis-Cummings model

TL;DR

This paper introduces a fast, memory-efficient numerical method for simulating the time-dependent Tavis-Cummings model, preserving unitarity and applicable to systems with time-varying parameters.

Contribution

The authors develop a symplectic split-operator method that efficiently handles non-tridiagonal Hamiltonians by basis re-indexing, enabling scalable simulations of complex quantum systems.

Findings

Method is linear in system dimension for time and memory.

Can simulate systems beyond the rotating-wave approximation.

Applicable to any closed quantum system with tri-diagonalizable Hamiltonians.

Abstract

We present a fast, memory-efficient, unitarity-preserving numerical method beyond the rotating-wave approximation for the closed Tavis-Cummings model in which a multilevel spin system interacts with a cavity mode. This model can describe the interaction of an ensemble of spins with a cavity mode in which the spin frequency and other parameters are time-dependent. The method exploits the fact that, while the Tavis-Cummings model is not tri-diagonal, it can be brought into tri-diagonal form by a change of basis that can be implemented purely by re-indexing (permuting basis elements), which is a fast operation. By truncating the Fock basis of the cavity mode, the computational complexity of the method is linear in the total dimension of the coupled system, both in time and memory. The method can be employed to simulate any closed quantum system whose Hamiltonian terms can be brought into tri-diagonal form.