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arXiv:1510.05772

Quantum speed-up transition in open system dynamics

Xiang Hao, Wenjiong Wu

Published Oct 20, 2015• 0 citations
arXivHTMLPDF

Abstract

The rate of the trace distance is used to evaluate quantum speed-up for arbitrary mixed states. Compared with some present methods, the approach based on trace distance can provide an optimal bound to the speed of the evolution. The dynamical transition from no speed-up region to speed-up region takes on in the spontaneous decay of an two-level atom with detuning. The evolution is characteristic of the alternating behavior between quantum speed-up and speed-down in the strong system-reservoir coupling regime. Under the off-resonance condition, the dynamical evolution can be accelerated for short previous times and then decelerated to a normal process either in the weak or strong coupling regime. From the time-energy uncertainty relation, we demonstrate that the potential capacity for quantum speed-up evolution is closely related to the energy flow-back from the reservoir to the system. The negative decay rate for short time intervals leads to the speed-up process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate becomes positive after a long enough time, which results in the normal evolution with no speed-up potential.

DOI
10.48550/arxiv.1510.05772

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The rate of the trace distance is used to evaluate quantum speed-up for arbitrary mixed states. Compared with some present methods, the approach based on trace distance can provide an optimal bound to the speed of the evolution. The dynamical transition from no speed-up region to speed-up region takes on in the spontaneous decay of an two-level atom with detuning. The evolution is characteristic of the alternating behavior between quantum speed-up and speed-down in the strong system-reservoir coupling regime. Under the off-resonance condition, the dynamical evolution can be accelerated for short previous times and then decelerated to a normal process either in the weak or strong coupling regime. From the time-energy uncertainty relation, we demonstrate that the potential capacity for quantum speed-up evolution is closely related to the energy flow-back from the reservoir to the system. The negative decay rate for short time intervals leads to the speed-up process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate becomes positive after a long enough time, which results in the normal evolution with no speed-up potential.
We put forward a measure for evaluating quantum speed limit for arbitrary mixed states of open systems by means of trace distance. Compared with some present measures, it can provide an optimal bound to the speed of the evolution. The dynamical crossover from no speedup region to speedup region happens during the spontaneous decay of an atom. The evolution is characteristic of the alternating behavior between quantum acceleration and deceleration in the strong coupling case. Under the condition of detuning, the evolution can be initially accelerated and then decelerated to a normal process either in the weak or strong coupling regime. In accordance with the uncertainty relation, we demonstrate that the potential capacity for quantum speedup evolution is closely related to the energy feedback from the reservoir to the system. The negative decay rate for the evolution results in the speedup process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate become positive after a long enough time, which results in the evolution with no speedup potential.
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.
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.
We present a method to accelerate the dynamical evolution of multiqubit open system by employing dynamical decoupling pulses (DDPs) when the qubits are initially in W-type states. It is found that this speed-up evolution can be achieved in both of the weak-coupling regime and the strong-coupling regime. The physical mechanism behind the acceleration evolution is explained as the result of the joint action of the non-Markovianity of reservoirs and the excited-state population of qubits. It is shown that both of the non-Markovianity and the excited-state population can be controlled by DDPs to realize the quantum speed-up.
We investigate the dynamics of a two-level system in the presence of an overall environment composed of two layers. The first layer is just one single-mode cavity that decays to a memoryless reservoir while the second layer is two coupled single-mode cavities that decay to memoryless or memory-keeping reservoirs. We show that, in the weak-coupling regime between the qubit and the first-layer environment, the speed of evolution for the system can be controlled to a speeded-up or speeded-down process by manipulating the coupling strength in a double-layer environment. In particular, we find that multiple dynamics transitions from a not-speeded-up evolution to speeded-up evolution can be realized for the system by increasing the coupling strength in the second-layer environment. These results hold independently of the nature of the reservoirs in the second-layer environment.
Recently, strong coupling between non-Hermitian physical systems of different nature is widely investigated due to it endows them with new properties. In this work, we investigate the energy transport between strongly coupled systems. We use a partial-secular approach for the description of an open quantum system to investigate the system dynamics during the transition from a weak to a strong coupling regime with an increase of coupling between subsystems. On the example of strongly coupled two-level atoms, we show that near the transition point enhancement of energy transport between the system and reservoirs takes place. This manifests in the fact that energy flow normalized to the coupling constant reaches the maximum both in the cases of zero and non-zero frequency detuning. We show that maximization of normalized energy flow can be used for the determination of the transition to the strong coupling regime in the case of non-zero detuning when there is no clear transition point from the weak to strong coupling regime. The suppression of the energy flow at high relaxation is demonstrated.