Time-Resolved Fluorescence of a Two-Level System Using Time-Dependent Variational Method

Abstract

The time-resolved fluorescence spectrum of a driven two-level system is investigated using a time-dependent variational method. We first establish the transient build-up of the Mollow triplet via the Lindblad master equation under the rotating-wave approximation, providing a complete visualization of the spectral evolution from initial turn-on to steady state. To go beyond the perturbative regime, we employ the multiple Davydov D2 ansatz (multi-D2), which uses the σz eigenstates as the basis and naturally accommodates arbitrary system–bath coupling types and spectral densities. The multi-D2 method converges with M = 4 multiplicities in studied cases, outperforming the multi-D1 ansatz (M = 8) for the σx coupling benchmark. For pure σz (dephasing) coupling under resonant driving, we find that the time-resolved spectrum reveals a distinct fluorescence peak at the Rabi frequency—a signature of dressed-state transitions induced by the dephasing channel that remains hidden in population dynamics. Under mixed σx–σz coupling, the spectrum exhibits combined features of both Mollow triplet and σz-mediated emission. The effects of sub-Ohmic, Ohmic, and super-Ohmic spectral densities are systematically compared. While the resonant spectral weight J(ω0) governs the overall dissipation rate, a controlled comparison at fixed J(ω0) reveals that the super-Ohmic regime exhibits an intrinsic shape-dependent suppression of sideband emission under resonant driving, highlighting an asymmetric role of the spectral density exponent in engineering transient fluorescence. Our work establishes the multi-D2 ansatz as a versatile tool for simulating time-resolved fluorescence in complex bosonic environments.