Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ=12(γ1+γ2)/Δp, where γi are the radiative decay rates of the excited levels i = 1, 2, and Δp=Δ(2)+(1-p(2))γ1γ2 depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1〉 and |e2〉 and their in-phase coherent superposition |ϕ+〉=1r1+r2(r1|e1〉+r2|e2〉), which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned.
We explore the coherent dynamics of a three-level
V-type system interacting with a thermal bath in the regime where thermal excitation occurs much faster than spontaneous decay. We present analytic solutions of the Bloch-Redfield quantum master equations, which show that strong incoherent pumping can generate long-lived quantum coherences among the excited states of the
V-type system in the overdamped regime defined by the condition $\mathrm{\ensuremath{\Delta}}/(\overline{n}\ensuremath{\gamma})<f(p)$, where $\mathrm{\ensuremath{\Delta}}$ is the excited-state level splitting, $\ensuremath{\gamma}$ is the spontaneous decay rate, $\overline{n}\ensuremath{\gg}1$ is the effective photon occupation number proportional to the pumping intensity, and
f(p) is a universal function of the transition dipole alignment parameter
p. In the limit of nearly parallel transition dipoles ($p\ensuremath{\rightarrow}1$) the coherence lifetime ${\ensuremath{\tau}}_{c}=1.34(\overline{n}/\ensuremath{\gamma}){(\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma})}^{\ensuremath{-}2}$ scales linearly with
n and is enhanced by the factor
0.67n with respect to the weak-pumping limit [Phys. Rev. Lett. 113, 113601 (2014); J. Chem. Phys. 144, 244108 (2016)]. We also establish the existence of long-lived quasistationary states, which occur in the overdamped regime and affect the process of thermalization of the
V-type system with the bath, slowing down the approach to thermal equilibrium. In the case of nonparallel transition dipole moments (
p<1), no quasistationary states are formed and the coherence lifetime decreases sharply. The sharp transition between the different regimes of coherent dynamics is due to an interplay between coherence-generating Fano interference and various coherence-destroying processes (such as stimulated decay). Using a newly developed effective decoherence rate model, we find that in the limit $p\ensuremath{\rightarrow}1$ the rates of coherence generation and decay are almost exactly balanced and the effective decoherence rate is minimized, leading to long coherence lifetimes. Our results reveal new regimes of long-lived quantum coherent dynamics, which could be observed in thermally driven atomic and molecular systems.
The excitation of molecular systems by incoherent light is studied primarily using a V-system model in the Partial Secular Bloch-Redfield formalism. First, the dynamical regimes are characterized for a system irradiated by suddenly turned on light and the relevant timescales are defined in terms of system parameters. Then excitation by slowly turned-on light is studied, showing a decay in the magnitude of noise-induced coherences with increasing turn-on times, leading to their disapearance in the very slow turn-on limit relevant to many natural systems.
We consider incoherent excitation of multilevel quantum systems, e.g., molecules with multiple vibronic states. We show that (1) the geometric constraints of the matter-field coupling operator guarantee that noise-induced coherences will be generated in all systems with four or more incoherent transitions between energy eigenstates and (2) noise-induced coherences can lead to population oscillations due to quantum interference via coherence transfer between pairs of states in the ground and excited manifolds. Our findings facilitate the experimental detection of noise-induced coherent dynamics in complex quantum systems.
We present a theoretical study of quantum coherent dynamics of a three-level Λ-system driven by a thermal environment (such as blackbody radiation), which serves as an essential building block of photosynthetic light-harvesting models and quantum heat engines. By solving nonsecular Bloch–Redfield master equations, we obtain analytical results for the ground-state population and coherence dynamics and classify the dynamical regimes of the incoherently driven Λ-system as underdamped and overdamped depending on whether the ratio Δ/[rf(p)] is greater or less than one, where Δ is the ground-state energy splitting, r is the incoherent pumping rate, and f(p) is a function of the transition dipole alignment parameter p. In the underdamped regime, we observe long-lived coherent dynamics that lasts for τc ≃ 1/r, even though the initial state of the Λ-system contains no coherences in the energy basis. In the overdamped regime for p = 1, we observe the emergence of coherent quasi-steady states with the lifetime τc = 1.34(r/Δ2), which have a low von Neumann entropy compared to conventional thermal states. We propose an experimental scenario for observing noise-induced coherent dynamics in metastable He* atoms driven by x-polarized incoherent light. Our results suggest that thermal excitations can generate experimentally observable long-lived quantum coherent dynamics in the ground-state subspace of atomic and molecular Λ-systems in the absence of coherent driving.