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Chinese Physics B

Population dynamics of excited atoms in non-Markovian environments at zero and finite temperature

Hong‐Mei Zou, Mao-Fa Fang

Published Aug 1, 2015• 4 citations
Publisher

Abstract

The population dynamics of a two-atom system, which is in two independent Lorentzian reservoirs or in two independent Ohmic reservoirs respectively, where the reservoirs are at zero temperature or finite temperature, is studied by using the time-convolutionless master-equation method. The influences of the characteristics and temperature of a non-Markovian environment on the population of the excited atoms are analyzed. We find that the population trapping of the excited atoms is related to the characteristics and the temperature of the non-Markovian environment. The results show that, at zero temperature, the two atoms can be effectively trapped in the excited state both in the Lorentzian reservoirs and in the Ohmic reservoirs. At finite temperature, the population of the excited atoms will quickly decay to a nonzero value.

DOI
10.1088/1674-1056/24/8/080304

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The population dynamics of a two-atom system, which is in two independent Lorentzian reservoirs or in two independent Ohmic reservoirs respectively, where the reservoirs are at zero temperature or finite temperature, is studied by using the time-convolutionless master-equation method. The influences of the characteristics and temperature of a non-Markovian environment on the population of the excited atoms are analyzed. We find that the population trapping of the excited atoms is related to the characteristics and the temperature of the non-Markovian environment. The results show that, at zero temperature, the two atoms can be effectively trapped in the excited state both in the Lorentzian reservoirs and in the Ohmic reservoirs. At finite temperature, the population of the excited atoms will quickly decay to a nonzero value.
The quantum discord of the two-atom system, which is in two independent Lorentzian reservoirs and in two independent Ohmic reservoirs with the Lorentz–Drude cutoff function, respectively, and the reservoirs are at zero temperature, is studied by applying the time-convolutionless master-equation method. We find that the quantum discord of the two-atom system is dependent on the characteristics of non-Markovian environments. The results show that the quantum discord can be effectively protected not only in Lorentzian reservoirs, but also in ohmic reservoirs with the Lorentz–Drude cutoff function. Finally, the physical interpretations for these results are given via the correlation function.
The dynamic evolutions of the discord and entanglement of two atoms immersed in two independent Lorentzian reservoirs at zero and finite temperatures have been investigated by using the time-convolutionless master-equation method. Our results show that, nonzero temperature can induce the entanglement sudden death and accelerate the decays of discord and entanglement. The discord and the entanglement have different robustness for different initial states and their robustness may change under certain conditions. When both the non-Markovian effect and detuning are present simultaneously, due to the memory and feedback effect of non-Markovian reservoirs, the discord and entanglement can be effectively protected even at nonzero temperature by increasing the non-Markovian effect and the detuning.
The squeezing dynamics of two independent two-level atoms off-resonantly coupled to two non-Markovian reservoirs is studied by the time-convolutionless master-equation approach. We find that the squeezing of two atoms is dependent on both detuning and the non-Markovian effect. Our results show that, in the non-Markovian regime, the bigger the detuning and the stronger the non-Markovian effect are, the larger the strength of the squeezing is. And the squeezing of two atoms can be effectively protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the detuning not only can promote the feedback of information from the environment into the atomic system but also can greatly suppress the atomic decay in the non-Markovian regime.
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.
The dynamics of a three-level Λ-atom coupled to a structured reservoir has been investigated. Comparing the Lorentzian time-dependent decay rate and population dynamics for the weak coupling regime with those for the strong coupling regime, we note that non-Markovian features exist in both regimes, but population dynamics shows fairly different behaviors. Moreover, the different positions of the two transition frequencies with respect to the structured reservoir reduces the influence of non-Markovian effects on population dynamics. Based on the non-Markovianity, we give an intuitive interpretation of the result that the non-Markovian effects have little influence on population dynamics in the weak coupling regime, but have an obvious influence in the strong coupling regime.