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.
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.
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.
In a multi-level quantum system Fano coherences stand for the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. In this paper we propose a V-type three-level quantum system on which we certify the presence of genuinely quantum traits underlying the generation of Fano coherences. We do this by determining work conditions that allows for the loss of positivity of the Kirkwood-Dirac quasiprobability distribution of the stochastic energy changes within the discrete system. We also show the existence of nonequilibrium regimes where the generation of Fano coherences leads to a non-negligible excess energy given by the amount of energy that is left over with respect to the energy of the system at the beginning of the transformation. Excess energy is attained provided the initial state of the discrete system is in a superposition of the energy eigenbasis. We conclude the paper by studying the thermodynamic efficiency of the whole process.
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.
Abstract Whether genuine quantum effects, particularly quantum coherences, can offer an advantage to quantum devices is a topic of much interest. Here, we study a minimal model, the three-level V system coupled to two heat baths, and investigate the role of quantum coherences in heat transport in both the transient regime and in the nonequilibrium steady-state. In our model, energy is exchanged between the baths through two parallel pathways, which can be made distinct through the nondegeneracy of excited levels (energy splitting Δ) and a control parameter α , which adjusts the strength of one of the arms. Using a nonsecular quantum master equation of Redfield form, we succeed in deriving closed-form expressions for the quantum coherences and the heat current in the steady state limit for closely degenerate excited levels. By including three ingredients in our analysis: nonequilibrium baths, nondegeneracy of levels, and asymmetry of pathways, we show that quantum coherences are generated and sustained in the V model in the steady-state limit if three conditions, conjoining thermal and coherent effects are simultaneously met: (i) the two baths are held at different temperatures. (ii) Bath-induced pathways do not interfere destructively. (iii) Thermal rates do not mingle with the control parameter α to destroy interference through an effective local equilibrium condition. Particularly, we find that coherences are maximized when the heat current is suppressed. Although we mainly focus on analytical results in the steady state limit, numerical simulations reveal that the transient behavior of coherences contrasts the steady-state limit: large long-lived transient coherences vanish at steady state, while weak short-lived transient coherences survive, suggesting that different mechanisms are at play in these two regimes. Enhancing either the lifetime of transient coherences or their magnitude at steady state thus requires the control and optimization of different physical parameters.