Excitation of molecules by incident incoherent electromagnetic radiation, such as sunlight, is described in detail and contrasted with the effect of coherent (e.g. laser) light. The nature of the quantum coherences induced by the former, relevant to
transport processes in nature and in technology, is emphasized. Both equilibrium and steady state scenarios are discussed, Three examples: simple models, calcium excitation in polarized light, and the isomerization of retinal in rhodopsin are used to expose the underlying qualitative nature of the established coherences.
We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The generalized
adiabatic theorems show that a sufficiently slow modulation conserves the dynamical modes of time dependent reference Hamiltonians. In the limiting case of modulations of static fields, the standard adiabatic theorems are recovered. Applying these results to periodic fields shows that they remain in Floquet states rather than in energy eigenstates. More generally, these adiabatic theorems can be applied to transformations of arbitrary time-dependent fields, by accounting for the rapidly varying part of the field through the dynamical normal modes, and treating the slow modulation adiabatically. As examples, we apply the generalized theorem to (a) predict the dynamics of a two level system driven by a frequency modulated resonant oscillation, a pathological situation beyond the applicability of earlier results, and (b) to show that open quantum systems driven by slowly turned-on incoherent light, such as biomolecules under natural illumination conditions, can only display coherences that survive in the steady state.
We explore the properties of steady-state Fano coherences generated in a three-level V-system continuously pumped by polarized incoherent light in the absence of coherent driving. The ratio of the stationary coherences to excited-state populations $m
athcal{C} = (1+frac{Delta^2}{gamma(r+gamma)} )^{-1}$ is maximized when the excited-state splitting $Delta$ is small compared to either the spontaneous decay rate $gamma$ or the incoherent pumping rate $r$. We demonstrate that an intriguing regime exists where the $mathcal{C}$ ratio displays a maximum as a function of the dephasing rate $gamma_d$. 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 identify the imaginary Fano coherence with the non-equilibrium flux across a pair of qubits coupled to two independent thermal baths, unraveling a direct connection between the seemingly unrelated phenomena of incoherent driving of multilevel quantum systems and non-equilibrium quantum transport in qubit networks. 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. 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 vs. isotropic incoherent light. Our analysis paves the way toward further theoretical and experimental studies of non-equilibrium coherent steady states in thermally driven atomic and molecular systems, and for the exploration of their potential role in biological processes.
We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by pro
bability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouvilles theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that are shown to be consistent with the derived analytical results.
Two different Master Equation approaches have been formally derived to address the dynamics of open quantum systems interacting with a thermal environment (such as sunlight). They have led to two different physical results: non-secular equations that
show noise-induced (Fano) coherences and secular equations that do not. An experimental test for the appearance of non-secular terms is proposed using Ca atoms in magnetic fields excited by broadband incoherent radiation. Significantly different patterns of fluorescence are predicted, allowing for a clear test for the validity of the secular and non-secular approach and for the observation of Fano coherences.
Light induced processes in nature occur by irradiation with slowly turned-on incoherent light. The general case of time-dependent incoherent excitation is solved here analytically for V-type systems using a newly developed master equation method. Cle
ar evidence emerges for the disappearance of radiatively induced coherence as turn-on times of the radiation exceed characteristic system times. The latter is the case, in nature, for all relevant dynamical time scales for other than nearly degenerate energy levels. We estimate that, in the absence of non-radiative relaxation and decoherence, turn-on times slower than 1 ms (still short by natural standards) induce Fano coherences between energy eigenstates that are separated by less than 0.9 cm$^{-1}$.
We present 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. 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 $zeta=frac{1}{2}(gamma_1+gamma_2)/Delta_p$, where $gamma_i$ are the radiative decay rates of the excited levels $i=1,2$, and $Delta_p=sqrt{Delta^2 + (1-p^2)gamma_1gamma_2}$ depends on the excited-state level splitting $Delta>0$ and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit ($zetagg1$), approach a long-lived quasi-steady state in the overdamped limit ($zetall 1$), and display an intermediate behavior at critical damping ($zeta= 1$). The sudden incoherent turn-on generates a mixture of excited eigenstates $|e_1rangle$ and $|e_2rangle$ and their in-phase coherent superposition $|phi_+rangle = frac{1}{sqrt{2bar{r}}}(sqrt{r_1} |e_1rangle + sqrt{r_2}|e_2rangle)$, which is remarkably long-lived in the overdamped limit (where $r_1$ and $r_2$ are the incoherent pumping rates). Formation of this coherent superposition {it 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, we identify additional asymptotic quasistationary coherences, 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 $r_1=r_2$ and the transition dipole moments are fully aligned.
We study Landau-Zener transitions between two states with the addition of a shared discretized continuum. The continuum allows for population decay from the initial state as well as indirect transitions between the two states. The probability of nona
diabatic transition in this multichannel model preserves the standard Landau-Zener functional form except for a shift in the usual exponential factor, reflecting population transfer into the continuum. We provide an intuitive explanation for this behavior assuming independent individual transitions between pairs of states. In contrast, the probability of survival in the ground state at long time shows a novel, non-monotonic, functional form, with an oscillatory behavior in the sweep rate at low sweep rate values. We contrast the behavior of this open-multistate model to other generalized Landau-Zener models incorporating an environment: the stochastic Landau-Zener model and the dissipative case, where energy dissipation and thermal excitations affect the adiabatic region. Finally, we present evidence that the continuum of states may act to shield the two-state Landau-Zener transition probability from the effect of noise.
