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Laser Physics Letters

Non-Markovian dynamics of a dephasing model in a squeezed thermal bath

Zhi He, Hao‐Sheng Zeng, Yu Chen, Chunmei Yao

Published May 13, 2019• 6 citations
Publisher

Abstract

Abstract The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.

DOI
10.1088/1612-202x/ab1420

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Abstract The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.
We theoretically study the quantum speed limits (QSLs) of a qubit system coupled to a thermal dephasing environment with an Ohmic-like spectral density. Based on the geometric QSLs time bound, which is derived by employing the trace distance to quantify the geodesic between two distinguishable states in dynamical evolution, we study the influences of the temperature and spectral density of the environment on the QSLs time of the dephasing qubit. We also investigate the interplay between the QSLs time, the environmental temperature, and the spectral density of the environment. It has been demonstrated that the QSLs time closely depends on the transition frequency and the dynamical behavior (e.g., coherence trapping) of the dephasing qubit. For a fixed Ohmicity parameter of the environmental spectral density, the increase in environmental temperature can enhance the QSLs time bound. In addition, when the environmental temperature remains constant, the increase in the Ohmicity parameter initially leads to a reduction in the QSLs time bound, which is then followed by an increase in the time bound of QSLs. Our results can help to better understand the QSLs in the dynamics of open quantum systems and have potential application in the modulation of QSLs time in the dephasing qubit by engineering the spectral density of the environment.
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.
The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.
We study the dynamics of a dressed qubit implemented by a spinless fermion hopping between two lattice sites with each site strongly coupled to a bath of phonons. We employ Lang-Firsov transformation to make the problem tractable perturbatively. Applying time-convolutionless master equation within the polaron frame, we investigate decoherence dynamics of the dressed qubit within the singlet-triplet basis of the system for a wide range of bath spectral densities. It is shown that the coherence persists for longer time scales for large coupling values and shows non-monotonic behaviour reflecting the presence of non-Markovianity in the dynamics. Non-Markovianity, characterized by coherence revivals and non-monotonic decay patterns, emerges distinctly depending on the bath spectrum and coupling strengths. Systems coupled to sub-Ohmic baths, whether both or in combination with another type, display pronounced memory effects at relatively small values of couplings. In contrast, combinations involving Ohmic and super-Ohmic baths exhibit noticeable non-Markovianity only at higher couplings.
In this paper, the dynamics of quantum Fisher information of a qubit interacting with a squeezed thermal environment are studied. The optimal initial state of the qubit, the temperature of the environment, and the interaction time, which maximize quantum Fisher information are obtained. Based on the ohmicity of the environment, we compare the dynamics of quantum Fisher information in ohmic, sub-ohmic, and super-ohmic regimes of the environment. Moreover, it is shown that the precise estimation of parameters is robust against squeezing.
We consider a model of non-Markovian quantum Brownian motion that consists of a harmonic oscillator bilinearly coupled to a thermal bath, both via its position and via its momentum operators. We derive the master equation for such a model, and we solve the equations of motion for a generic Gaussian system state. We then investigate the resulting evolution of the first and second moments for both an Ohmic and a super-Ohmic spectral density. In particular, we show that, irrespective of the specific form of the spectral density, the coupling with the momentum enhances the dissipation experienced by the system, accelerating its relaxation to the equilibrium as well as modifying the asymptotic state of the dynamics. Eventually, we characterize explicitly the non-Markovianity of the evolution using a general criterion which relies on the positivity of the master equation coefficients.