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Register a new userZeno Dynamics and High-Temperature Master Equations Beyond Secular Approximation
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Benedetto Daniele Militello Dr
Publication date
2013
fields
Physics
and research's language is
English
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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.
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We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps, randomly distributed in time and described by a quantum channel. The state of the open system is shown to obey a closed evolution equation, given by a master equation with a memory kernel and a inhomogeneous term. The non-Markovianity of the obtained dynamics is explicitly assessed studying the behavior of the distinguishability of two different initial systems states with elapsing time.
The effect of the anti-rotating terms on the short-time evolution and the quantum Zeno (QZE) and anti-Zeno (AQZE) effects is studied for a two-level system coupled to a bosonic environment. A unitary transformation and perturbation theory are used to obtain the electron self-energy, energy shift and the enhanced QZE or the AQZE, simultaneously. The calculated Zeno time depends on the atomic transition frequency sensitively. When the atomic transition frequency is smaller than the central frequency of the spectrum of boson environment, the Zeno time is prolonged and the anti-rotating terms enhance the QZE; when it is larger than that the Zeno time is reduced and the anti-rotating terms enhance the AQZE.
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes, and puts into evidence the non uniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows to phenomenologically construct a large class of non-Markovian evolutions taking as starting point collections of time dependent maps and instantaneous transformations describing the microscopic interaction dynamics.
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.
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 inter-system 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 to different Markovian master equations, we find that a smooth crossover of the equations-of-motion between dominant inter-system and system-bath coupling exists -- but requires a non-secular master equation. We predict a singular behaviour of the dynamics, and show that the ultimate failure of non-secular equations of motion is essentially a failure of the Markov approximation. Our findings justify the use of time-local theories throughout the crossover between system-bath dominated and inter-system-coupling dominated dynamics.
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