Quantum speed limits of a qubit system interacting with a nonequilibrium environment

Abstract

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 qubitinitial 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.

Time-invariant discord and steady-state entanglement in engineered non-equilibrium dephasing environments

“…Here, G x [ ] shows the Euler gamma function. It is important to note that unlike the thermal equilibrium case, this decoherence factor exhibits nonmonotonic decay for all values of Ohmicity parameter n [42,43]. Therefore, the non-equilibrium environment considered in our study has a non-Markovian feature for all kinds of Ohmic spectral densities (i.e., sub-Ohmic, Ohmic, and super-Ohmic).…”

“…Interestingly, in [40] it was shown that decoherence in a single-qubit system interacting with a non-equilibrium environment could be potentially controlled by manipulating the relative initial phases of the terms in the Fourier series (or equivalently relative initial phases of the reservoir's modes). Later, it was demonstrated that such a non-equilibrium dephasing environment with an Ohmic class spectrum has dominant effects on the geometric phase and quantum speed limit [41][42][43]. Remarkably, this engineered non-dissipative non-equilibrium environment exhibits non-Markovian characteristics for all the values of Ohmicity parameter n [42].…”

Dynamical control of population and entanglement for open Λ-type atoms by engineering the environment

“…Many relevant physical systems, such as the quantum optical system, [3] the nanoscale solid-state quantum system, [4,5] quantum chemistry, [6] and the excitation transfer in the biological system, [7] should be treated by quantum non-Markovian processes. Recently, quantum non-Markovian processes have been studied extensively, from the measure of non-Markovianity of the processes [8][9][10][11][12][13][14][15][16][17][18] to the properties [19][20][21][22][23][24][25][26][27][28][29] and applications [30][31][32][33][34][35][36][37] of the dynamical processes.…”

Quantum speed limit time of a two-level atom under different quantum feedback control

“…Since the appearance of definitions for QSLT in open quantum systems, the QSLT of quantum systems interacting with various environments has been widely investigated. [12][13][14] Recently, in order to obtain a faster speed of evolution, a lot of efforts have been made to short the QSLT. It has been suggested that memory environments can speed up quantum evolution and the mechanism of the acceleration in open quantum systems is related not only to the non-Markovianity but also to the population of excited states.…”