A Computational Quantum Model for Periodontal Low-Level Laser Therapy: Analytical Prediction of Coherence and Excitation

This study aimed to develop a computational quantum model to evaluate the feasibility of coherent effects in low-level laser therapy (LLLT) for periodontal applications. It sought to quantify excitation dynamics and coherence timescales under conditions reflecting clinical photobiomodulation parameters. A driven-dissipative two-level system (TLS) from open quantum systems theory was extended to include separate relaxation and dephasing channels. The Rabi frequency (Ω, 0.05–0.50 MHz), relaxation rate (γ₁ = 0.001 MHz), and dephasing rates (γ_φ = 0.05–0.20 MHz) were scaled using a characteristic rate (Γ = 1 MHz) for unit conversion, mapping simulation time to microseconds. All results were derived from exact analytical solutions of the extended Lindblad master equation, avoiding numerical fitting. The steady-state excited population, given by P e = Ω 2 / ( γ 1 2 + 2 Ω 2 ) , was approximately 0.5 for all parameters due to the small γ₁. The corresponding quantum jump rate J = γ 1 P e ranged from 5.55 × 10 − 5 to 4.975 × 10 − 4 MHz. Quantum coherence decayed exponentially with a lifetime of τ = 1 / ( γ 1 / 2 + γ ϕ ) , yielding values of approximately 20, 10, and 5 µs for γ_φ = 0.05, 0.10, and 0.20 MHz, respectively. These results represent theoretical upper bounds for coherence under a low-noise regime. This work provides a rigorous theoretical framework for considering quantum effects in periodontal LLLT. It generates testable predictions regarding excitation flux and coherence times, establishing a quantitative foundation for future experimental spectroscopy on laser-exposed tissues. The findings highlight the critical balance between laser parameters and biological noise, informing the design of studies to probe potential non-classical contributions to photobiomodulation mechanisms.