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Based-Ohmic-Reservoir non-Markovianity and Quantum Speed Limit Time

Hong‐Mei Zou, Rongfang Liu, D. Stephen Long, Jianhe Yang, Danping Lin

Published Mar 22, 2020• 0 citations
OpenAlex

Abstract

The non-Markovianity and the quantum speed limit time (QSLT) are investigated in Jaynes-Cummings model coupling with the Ohmic reservoir at zero temperature when when $t=0$ and $N=1$. We obtain the non-Markovianity expressed by using the decoherence rate in the time-local master equation. We find that the non-Markovianity in the dynamics process can be witnessed by both of the negative decoherence rate and the positive derivative of the trace distance. The atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the quantum speed-up process of the atom, which the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. We also provide the physical interpretation.

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The non-Markovianity and the quantum speed limit time (QSLT) are investigated in Jaynes-Cummings model coupling with the Ohmic reservoir at zero temperature when when t=0t=0t=0 and N=1N=1N=1. We obtain the non-Markovianity expressed by using the decoherence rate in the time-local master equation. We find that the non-Markovianity in the dynamics process can be witnessed by both of the negative decoherence rate and the positive derivative of the trace distance. The atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the quantum speed-up process of the atom, which the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. We also provide the physical interpretation.
Abstract We study the non-Markovianity and quantum speedup of a two-level atom (quantum system of interest) in a dissipative Jaynes-Cumming model, where the atom is embedded in a single-mode cavity, which is leaky being coupled to an external reservoir with Ohmic spectral density. We obtain the non-Markovianity characterized by using the probability of the atomic excited state and the negative decoherence rate in the time-local master equation. We also calculate the quantum speed limit time (QSLT) of the evolution process of the atom. The results show that, the atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the transition from no speedup to speedup process, and the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. Finally, the physical interpretation is provided.
Abstract In this work, we obtain an analytical representation of the density operator of an atom in a dissipative cavity when the reservoir is at zero temperature and the total number of excitations is N = 1. We also investigated the quantum speed limit time (QSLT) of the atom and the non-Markovianity in the dynamics process. The results show that the QSLT and the non-Markovianity can be effectively manipulated by the atom–cavity coupling and the reservoir parameters. Both of the atom–cavity coupling and the detuning can induce a sudden transition from Markovian to non-Markovian dynamics, and this transition is the main physical reason of the quantum speed-up process. The critical value of the sudden transition from no speed-up to speed-up the atom–cavity coupling and the reservoir parameters. The corresponding physical explanation is also provided for our results.
The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [ Phys. Rev. Lett . 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s . We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.
In this work, we provide a model of a moving-qubit interacting with the multimode cavity, where the qubit is driven by the classical field. We obtain the analytic solution of the density operator of the qubit, then investigate the quantum speed limit time(QSLT) and the non-Markovianity based on the classical field and the moving-velocity. The results show that the transition from Markovian to non-Markovian dynamics is the intrinsic physical reason of the quantum speed-up process, both of the driving field and the strong coupling can enhance the non-Markovianity in the dynamics process and speed up the evolution of the qubit, but the moving velocity of the qubit can decrease the non-Markovianity in dynamics process and delay the evolution of qubit. To some extent, the classical field can reduce the effect of the moving velocity of the qubit on the quantum evolution process.
The minimal time a system needs to evolve from an initial state to its one orthogonal state is defined as the quantum speed limit time, which can be used to characterize the maximal speed of evolution of a quantum system. This is a fundamental question of quantum physics. We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, when the system starts from the excited state, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.
We explore signatures of the non-Markovianity in the time-resolved energy transfer processes for quantum open systems. Focusing on typical systems such as the exact solvable damped Jaynes-Cummings model and the general spin-boson model, we establish quantitative links between the time-resolved energy current and the symmetric logarithmic derivative quantum Fisher information (SLD-QFI) flow, one of measures quantifying the non-Markovianity, within the framework of non-Markovian master equations in time-local forms. From the relationships, we find in the damped Jaynes-Cummings model that the SLD-QFI backflow from the reservoir to the system always correlates with an energy backflow, thus we can directly witness the non-Markovianity from the dynamics of the energy current. In the spin-boson model, the relation is built on the rotating-wave approximation, calibrated against exact numerical results, and proven reliable in the weak coupling regime. We demonstrate that whether the non-Markovianity guarantees the occurrence of an energy backflow depends on the bath spectral function. For the Ohmic and sub-Ohmic cases, we show that no energy backflow occurs and the energy current always flow out of the system even in the non-Markovian regime. While in the super-Ohmic case, we observe that the non-Markovian dynamics can induce an energy backflow.