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arXiv:1805.02145 · Journal of the Optical Society of America B

Quantum evolution speed in the finite-temperature bosonic environment

Jun-Qing Cheng, Guoqing Zhang, Jing‐Bo Xu

Published Aug 20, 2018• 2 citations
arXivHTMLPDF

Abstract

We investigate the quantum evolution speed of a qubit in two kinds of finite-temperature environments. For the first bosonic bath with an ohmic-like spectrum, the high temperature leads to not only the speed-up but also speed-down processes in the weak-coupling regime, which is different from the strong-coupling case, in which only the speed-up process is exhibited. Furthermore, we realize the controllable and stationary quantum evolution speed by applying the bang-bang pulse. For the second nonlinear bath, we study the quantum evolution speed by resorting to the hierarchical equations of a motion method beyond the Born–Markov approximation. It is shown that the quantum evolution speed can be decelerated by the rise of temperature in the strong-coupling regime, which is an anomalous phenomenon and contrary to the common recognition that quantum evolution speed always increases with the temperature.

DOI
10.1364/josab.35.002192

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We investigate the quantum evolution speed of a qubit in two kinds of finite-temperature environments. For the first bosonic bath with an ohmic-like spectrum, the high temperature leads to not only the speed-up but also speed-down processes in the weak-coupling regime, which is different from the strong-coupling case, in which only the speed-up process is exhibited. Furthermore, we realize the controllable and stationary quantum evolution speed by applying the bang-bang pulse. For the second nonlinear bath, we study the quantum evolution speed by resorting to the hierarchical equations of a motion method beyond the Born–Markov approximation. It is shown that the quantum evolution speed can be decelerated by the rise of temperature in the strong-coupling regime, which is an anomalous phenomenon and contrary to the common recognition that quantum evolution speed always increases with the temperature.
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We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak-coupling approximations. It is found that the decoherence of a two-qubit spin-boson model can be reduced by increasing the bath temperature in strong-coupling regimes. For the weak-coupling situation, we find that the bath temperature may enhance the decoherence. This result is contrary to the common recognition that a higher bath temperature always induces a more severe decoherence and suggests that a decoherence dynamical transition occurs in this two-qubit spin-boson model. We also demonstrate that the critical transition point can be characterized by the behavior of the frequency spectrum of the quantum coherence indicator.
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We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the l1l_1l1​-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.
We study entanglement generated between a qubit and a super-ohmic bosonic bath due to their joint evolution which leads to pure dephasing of the qubit. We tune the parameters of the interaction, so that the decoherence is quantitatively independent of the number of bosonic modes taken into account (and corresponds to realistic decoherence seen in small excitonic quantum dots coupled to an environment of phonons) and investigate, how the entanglement generated depends on the size of the environment. A second parameter of interest is the mixedness of the initial state of the environment which is controlled by temperature. We show analytically that for a pure initial state of the environment (zero temperature here), entanglement does not depend on environment size. At finite temperatures (mixed initial state of the environment), the generated entanglement decreases with the increase of environment size. This effect is stronger for larger temperatures, when the environment is initially more mixed, but in the limit of an infinitely large environment, no entanglement is created at any finite temperature.
Quantum theory sets a limit on the minimum time required to transform from an initial state to a target state. It is known as quantum speed limit time. quantum speed limit time can be used to determine the rate of quantum evolution for closed and open quantum systems. Given that in the real world we are dealing with open quantum systems, the study of quantum speed limit time for such systems has particular importance. In this work we consider the topological qubit realized by two Majorana modes. We consider the case in which the topological qubit is influenced by fermionic and bosonic environment. Fermionic and bosonic environments are assumed to have Ohmic-like spectral density. The quantum speed limit time is investigated for various environment with different Ohmic parameter. It is observed that for super-Ohmic environment with increasing Ohmic parameter the quantum speed limit time gradually reaches to a constant value and thus the speed of evolution reaches to a uniform value. The effects of external magnetic field on the evolution rate are also studied. It is observed that with increasing magnitude of magnetic field, the quantum speed limit time decreases