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.
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.
Quantum coherent dynamics of a Λ-system driven by a thermal environment: Enhancing coherence lifetimes via incoherent driving
We present a theoretical study of quantum coherent dynamics in a three-level Λ system driven by a thermal environment. By solving the 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 dimensionless 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 overdampled regime for p=1, we observe the emergence of coherent quasi-steady states with the lifetime τc=1.34(r/Δ2), which have low von Neumann entropy compared to the conventional thermal states. Our results suggest that thermal excitations can enhance the lifetimes of initially created coherent superpositions, making thermal driving a potentially useful coherence-enhancing tool for quantum information science.
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.
We present a theoretical study of noise-induced quantum coherences in a model three-level V-type system interacting with incoherent radiation, an important prototype for a wide range of physical systems ranging from trapped ions to biomolecules and quantum dots. By solving the quantum optical equations of motion, we obtain analytic expressions for the noise-induced coherences and show that they exhibit an oscillating behavior in the limit of large excited level spacing $\mathrm{\ensuremath{\Delta}}$ ($\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma}\ensuremath{\gg}1$, where $\ensuremath{\gamma}$ is the radiative decay width). Most remarkably, we find that in the opposite limit of small level spacing $\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma}\ensuremath{\ll}1$, appropriate for large molecules, (a) the coherences can survive for an extremely long time $\ensuremath{\tau}=(2/\ensuremath{\gamma})(\mathrm{\ensuremath{\Delta}}/\ensuremath{\gamma}{)}^{\ensuremath{-}2}$ before eventually decaying to zero, and (b) coherences at short times can be substantial. We further show that the long-lived coherences can survive environmental relaxation and decoherence, suggesting implications to the design of quantum heat engines and to incoherent light excitation of biological systems.
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
We explore the properties of steady-state noise-induced (Fano) coherences generated in a three-level V-system continuously pumped by polarized incoherent light in the absence of coherent driving.By solving the nonsecular Bloch-Redfield quantum master equation, we obtain the ratio of the stationary coherences to excited-state populations, C = 1, which quantifies the impact of steady-state coherences on excited-state dynamical observables of the V-system.The ratio is maximized when the excited-state splitting is small compared to either the spontaneous decay rate γ or the incoherent pumping rate r.We demonstrate that while the detrimental effects of a strongly decohering environment generally suppress the coherence-to-population ratio by the factor γ d /γ , an intriguing regime exists where the C ratio displays a maximum as a function of the dephasing rate γ d .We attribute the surprising dephasing-induced enhancement of stationary Fano coherences to the environmental suppression of destructive interference of individual incoherent excitations generated at different times.We clarify the physical basis for the steady-state Fano coherence, whose imaginary part is identified with the nonequilibrium flux across a pair of qubits coupled to two independent thermal baths or, equivalently, the spontaneous emission flux from the right qubit to the right bath, unraveling a direct connection between the seemingly unrelated phenomena of incoherent driving of multilevel quantum systems and nonequilibrium quantum transport in qubit networks.We further establish the equivalence between the two-qubit system and a V-system, each of whose transitions is driven simultaneously by both baths.The real part of the steady-state Fano coherence is found to be proportional to the deviation of excited-state populations from their values in thermodynamic equilibrium, making it possible to observe signatures of steady-state Fano coherences in excited-state populations.Finally, we put forward an experimental proposal for observing steady-state Fano coherences by detecting the total fluorescence signal emitted by Calcium atoms excited by polarized versus isotropic incoherent light.Our analysis paves the way toward further theoretical and experimental studies of nonequilibrium coherent steady states in thermally driven atomic and molecular systems and for the exploration of their potential role in quantum thermodynamics and in biological processes.