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Register a new userSecular vs. Non-secular Redfield Dynamics and Fano Coherences in Incoherent Excitation: An Experimental Proposal
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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.
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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 $mathcal{C} = (1+frac{Delta^2}{gamma(r+gamma)} )^{-1}$ 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.
While generic drugs offer a cost-effective alternative to brand name drugs, regulators need a method to assess therapeutic equivalence in a post market setting. We develop such a method in the context of assessing the therapeutic equivalence of immediate release (IM) venlafaxine, based on a large insurance claims dataset provided by OptumLabstextsuperscript{textregistered}. To properly address this question, our methodology must deal with issues of non-adherence, secular trends in health outcomes, and lack of treatment overlap due to sharp uptake of the generic once it becomes available. We define, identify (under assumptions) and estimate (using G-computation) a causal effect for a time-to-event outcome by extending regression discontinuity to survival curves. We do not find evidence for a lack of therapeutic equivalence of brand and generic IM venlafaxine.
Complete positivity of a class of maps generated by master equations derived beyond the secular approximation is discussed. The connection between such class of evolutions and physical properties of the system is analyzed in depth. It is also shown that under suitable hypotheses a Zeno dynamics can be induced because of the high temperature of the bath.
We investigate how correlated fluctuations affect oscillatory features in rephasing and non-rephasing two-dimensional (2D) electronic spectra of a model dimer system. Based on a beating map analysis, we show that non-secular environmental couplings induced by uncorrelated fluctuations lead to oscillations centered at both cross- and diagonal-peaks in rephasing spectra as well as in non-rephasing spectra. Using an analytical approach, we provide a quantitative description of the non-secular effects in terms of the Feynman diagrams and show that the environment-induced mixing of different inter-excitonic coherences leads to oscillations in the rephasing diagonal-peaks and non-rephasing cross-peaks. We demonstrate that as correlations in the noise increase, the lifetime of oscillatory 2D signals is enhanced at rephasing cross-peaks and non-rephasing diagonal-peaks, while the other non-secular oscillatory signals are suppressed. We discuss that the asymmetry of 2D lineshapes in the beating map provides information on the degree of correlations in environmental fluctuations. Finally we investigate how the oscillatory features in 2D spectra are affected by inhomogeneous broadening.
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.
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