Open quantum systems interacting with a thermal environment are formally treated by secular or nonsecular master equations, with the nonsecular equation predicting distinct dynamics with unobserved noise-induced Fano coherences. The authors propose an experimental test to examine the master-equation applicability and the existence of Fano coherences in an atomic system excited by an incoherent light.
Open quantum systems interacting with a thermal environment are formally treated by secular or nonsecular master equations, with the nonsecular equation predicting distinct dynamics with unobserved noise-induced Fano coherences. The authors propose an experimental test to examine the master-equation applicability and the existence of Fano coherences in an atomic system excited by an incoherent light.
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.
Quantum coherence offers potential for energy conversion technologies. It influences light absorption and emission, affecting energy conversion limits and efficiency. As a result, quantum coherence is being harnessed to boost performance in quantum heat engines, photocells, and photosynthetic-inspired platforms. Of particular interest in this context is the generation of Fano coherences, i.e., the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. We aim to formalize mathematically the possibility of achieving steady-state Fano coherence in a V-type three-level quantum system using polarized incoherent radiation, without requiring the energy difference between the excited levels to tend to zero. We perform this analysis by deriving the Bloch-Redfield equation from first-principles by quantizing the incoherent radiation. The resulting reduced dynamics of the system are analysed, so as to determine the lifetime of Fano coherence and identify the conditions under which it becomes stationary. We characterise distinct dynamical regimes, ranging from weak to strong pumping, in which steady-state Fano coherence emerges, and we quantitatively determine its magnitude. For each regime, we analyse the generation of Fano coherence as a function of both the intensity of the incoherent pumping and the energy splitting between the excited levels. We also assess how obtaining Fano coherence is modified by symmetric or asymmetric decay rates. These findings indicate that a three-level quantum system driven by polarized incoherent light can act as a robust resource for coherence-assisted energy conversion and storage. Finally, we discuss the experimental challenges associated with the implementation of the proposed model using an ensemble of Rubidium atoms.
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.
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.
Finding efficient descriptions of how an environment affects a collection of discrete quantum systems would lead to new insights into many areas of modern physics. Markovian, or time-local, methods work well for individual systems, but for groups a question arises: Does system-bath or intersystem coupling dominate the dissipative dynamics? The answer has profound consequences for the long-time quantum correlations within the system. We consider two bosonic modes coupled to a bath. By comparing an exact solution against different Markovian master equations, we find that a smooth crossover of the equations of motion between dominant intersystem and system-bath coupling exists---but it requires a nonsecular master equation. We predict singular behavior of the dynamics and show that the ultimate failure of nonsecular equations of motion is essentially a failure of the Markov approximation. Our findings support the use of time-local theories throughout the crossover between system-bath-dominated and intersystem-coupling-dominated dynamics.