Abstract
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.
Highlights
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
While by calculating the quantum speed limit time (QSLT) starting from the time-evolution state at any point in time which is in general a mixed state, it is interesting to find that the QSLT first begins to decrease from the driving time and gradually increases to this driving time in the Markovian dynamics
We demonstrate that the QSLT will be reduced with the starting point in time for Ohmic and sub-Ohmic dephasing model, that is to say, the open system executes a speeded-up dynamics evolution process
Summary
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. 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 apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. 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 (QSLT) The study of it has been focused on both closed and open quantum systems. Let us consider the states of a driven system in the damped Jaynes-Cummings model starting from a certain pure state which corresponds to a special case of our result, one may observe that the QSLT is equal to the driving time in the Markovian regime[18]. We investigate the influence of the relativistic effect on the QSLT for the observer in non-inertial frames in the above two quantum decoherence models
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