A new analytical approach, beyond rotating wave approximation, based on unitary transformations and the non-Markovian master equation for the density operator, is applied to treat the biased spin boson model with a Lorentzian structured bath for arbitrary detunings at zero temperature. Compared to zero bias, we find that the dynamics demonstrates two more damping oscillation frequencies and one additional relaxation frequency for non-zero bias, where one of the damping oscillation frequencies is a new effect. Analytical expressions for the non-Markovian dynamics and the corresponding spectrum, the localized-delocalized transition point, the coherent-incoherent transition point, the analytical ground energy, the renormalized tunneling factor and the susceptibility are determined. The sum rule and the Shiba relation are checked in the coherent regime.
We generalize time-evolving matrix product operators method to nonequilibrium quantum transport problems. The nonequilibrium current is obtained via numerical differentiation of the generating functional which is represented as a tensor network. The approach is numerically exact and the non-Markovian effects are fully taken into account. In the transport process, a part of the heat that flows out from a bath flows into the system and other baths, and the rest is stored in the system-bath coupling part. We take the spin-boson model as a demonstration to show the details of this heat flowing and…
We formulate a quantum theory of electron waiting time distributions for charge transport in nano-structures described by non-Markovian generalized master equations. We illustrate our method by calculating the waiting time distribution of electron transport through a dissipative double quantum dot, where memory effects are present due to a strongly coupled heat bath. We consider the influence of non-Markovian dephasing on the distribution of electron waiting times and discuss how spectral properties of the heat bath may be detected through measurements of the electron waiting time.
The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated projection superoperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated pro…
In this paper, we explore the decoherence dynamics of a probing spin coupled to a spin bath, where the spin bath is given by a controllable 1D transverse-field Ising chain. The 1D transverse-field Ising chain with free-ends boundary condition is equivalent to a modified Kitaev model with non-local Majorana bound states in its topological phase. We find that the probing spin non-Markovian decoherence dynamics can manifest the topological structure of the spin chain. By controlling the external magnetic field on the Ising chain, we find the close relationships between the quantum phase transitio…
We provide a versatile analytical framework for calculating the dynamics of a spin system in contact with a fermionic bath beyond the Markov approximation. The approach is based on a second order expansion of the Nakajima-Zwanzig master equation but systematically includes all quantum coherent memory effects leading to non-Markovian dynamics. Our results describe, for the free induction decay, the full time range from the non-Markovian dynamics at short times, to the well-known exponential thermal decay at long times. We provide full analytic results for the entire time range using a bath of i…
An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessi…
We show that quantum coherence of biomolecular excitons is maintained over exceedingly long times due to the constructive role of their non-Markovian protein-solvent environment. Using a numerically exact approach, we demonstrate that a slow quantum bath helps to sustain quantum entanglement of two pairs of Forster coupled excitons, in contrast to a Markovian environment. We consider the crossover from a fast to a slow bath and from weak to strong dissipation and show that a slow bath can generate robust entanglement. This persists to surprisingly high temperatures, even higher than the excito…
Semiconductor quantum dots (QDs) have been demonstrated to be versatile candidates to study the fundamentals of light-matter interaction [1-3]. In contrast with atom optics, dissipative processes are induced by the inherent coupling to the environment and are typically perceived as a major obstacle towards stable performances in experiments and applications [4]. In this paper we show that this is not necessarily the case. In fact, the memory of the environment can enhance coherent quantum optical effects. In particular, we demonstrate that the non-Markovian coupling to an incoherent phonon bat…
We study the decay process in an open system, emphasizing on the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment)or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the Survival Probability and the Loschmidt Echo. These rates are compared to analyt…
We investigate the current noise of a charge qubit coupled to a phonon bath in different parameter regimes. We find, using the theory of Full Counting Statistics of non-Markovian systems, that the current fluctuations are strongly influenced by memory effects generated from the interplay between quantum coherence and the dynamics of the phonon bath.
An efficient optimal-control theory based on the Krotov method is introduced for a non-Markovian open quantum system with a time-nonlocal master equation in which the control parameter and the bath correlation function are correlated. This optimal-control method is developed via a quantum dissipation formulation that transforms the time-nonlocal master equation to a set of coupled linear time-local equations of motion in an extended auxiliary Liouville space. As an illustration, the optimal-control method is applied to find the control sequences for high-fidelity Z gates and identity gates of …
Scalable simulation of non-Markovian quantum transport by stochastic-phase bath reduction
University of California, Berkeley（加州大学伯克利分校）；Flatiron Institute（平顿研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；California Institute of Technology（加州理工学院）
We discuss whether, and under which conditions, it is possible to realize a heat engine simply by dynamically modulating the couplings between the quantum working medium and thermal reservoirs. For that purpose, we consider the paradigmatic model of a quantum harmonic oscillator, exposed to a minimal modulation, that is, a monochromatic driving of the coupling to only one of the thermal baths. We demonstrate, at any order in the system/bath coupling strength, that in this setup non--Markovianity of the bath is a necessary condition to obtain a heat engine. In addition, we identify suitable str…
Work, moments of work and heat flux are studied for the generic case of a strongly driven twolevel system immersed in a bosonic heat bath in domains of parameter space where perturbative treatments fail. This includes particularly the interplay between non-Markovian dynamics and moderate to strong external driving. Exact data are compared with predictions from weak coupling approaches. Further, the role of system-bath correlations in the initial thermal state and their impact on the heat flux are addressed. The relevance of these results for current experimental activities on solid state devic…
Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider n qubits subject to correlated Markovian dephasing and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry plays a crucial role: broken time-reversal symmetry is required for dissipative entanglement generation. Further, simply having nonzero bath susceptibilities is not enough for the dissi…
We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator techniques, with which we obtain explicit equations of motion for the correlation functions, making only a second order expansion in the system--environment coupling strength, and invoking the Born approximation at a fixed initial time. The results are used to investigate a driven semiconductor quantum dot coupled to an acoustic phonon bath, where we find the …
Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Telecomunicações（电信研究所）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学先进材料研究所（WPI-AIMR））
We provide a general discussion of the Liouvillian spectrum for a system coupled to a non-Markovian bath using Floquet theory. This approach is suitable when the system is described by a time-convolutionless master equation with time-periodic rates. Surprisingly, the periodic nature of rates allow us to have a stroboscopic divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility. We illustrate the general theory for a Schrödinger cat which is roaming inside a non-Markovian bath, and demonstrate the appearance of stroboscopic revival of the cat at later …
