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Annalen der Physik

The Influence of Non‐Markovian Characters on Quantum Adiabatic Evolution

Ye‐Xiong Zeng, Tesfay Gebremariam Tesfahannes, Ming‐Song Ding, Chong Li

Published Nov 14, 2018• 6 citations
Publisher

Abstract

Abstract The influence of non‐Markovian characters on the adiabatic evolution is investigated. The adiabatic Raman process is simulated in a three‐level system coupled to two independent environments. The results show that the memory effect of environments can restrain the decoherence effect of the system. Even if the system has strong decay rates in the non‐Markovian environments, the adiabatic population transfer can be still completed efficiently. Moreover, the memory effect can reduce the dependence of the adiabatic evolution on the Rabi frequency. Specifically, the two independent non‐Markovian baths can suppress the decoherence more effectively than a single non‐Markovian bath.

DOI
10.1002/andp.201800234

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Abstract The influence of non‐Markovian characters on the adiabatic evolution is investigated. The adiabatic Raman process is simulated in a three‐level system coupled to two independent environments. The results show that the memory effect of environments can restrain the decoherence effect of the system. Even if the system has strong decay rates in the non‐Markovian environments, the adiabatic population transfer can be still completed efficiently. Moreover, the memory effect can reduce the dependence of the adiabatic evolution on the Rabi frequency. Specifically, the two independent non‐Markovian baths can suppress the decoherence more effectively than a single non‐Markovian bath.
In article number 1800234, Ye-Xiong Zeng, Chong Li, and coworkers investigate the influence of the memory effect of the environments on adiabatic evolution and show that the memory can protect the adiabatic process and decrease the dependence of the classical lasers on adiabatic population transfer. The cover image illustrates an atom ensemble controlled by two classical optical fields in two environments. The yellow and purple straight lines represent two classical optical fields. Furthermore, two multicolor coils are considered as two environments which surround an atom ensemble.
Understanding heat transfer between a quantum system and its environment is of grave importance if reliable quantum devices are to be constructed. Here, the heat transfer between the system and bath in non-Markovian open quantum systems in the process of adiabatic speedup is investigated. Using the quantum state diffusion equation method, the heat current, energy current and the power are calculated during the free evolution and under external control of the system. While the heat current increases with increasing system-bath coupling strength and bath temperature, the non-Markovian nature of the bath can restrict the heat current. Without pulse control, the heat current is nearly equal to energy current. However, with pulse control, the energy current is nearly equal to the power. We show that more non-Markovian baths can be used to better approximate an adiabatic evolution and have a smaller heat current. Our results reveal that the non-Markovian nature of the bath significantly contributes to both the heat transfer rate as well as the effective adiabatic speedup.
Abstract Adiabatic evolution has important applications in quantum information processing. In that context, the system has to be maintained in one of its instantaneous eigenstates. Normally the adiabaticity of the system will be ruined by its surrounding environment. Quantum control has been used widely to speed up the adiabatic process and thus reduces the effect of the environment. In this letter, we investigate the adiabatic speedup and the associated quantum heat current with and without pulse control. The system is immersed in a non-Markovian and finite-temperature heat bath. Our calculation results show that the effective adiabatic speedup can be obtained in a weak system-bath coupling and low-temperature heat bath. Specifically, non-Markovianity from the environment can be beneficial to the enhancement of the adiabatic fidelity. Furthermore, we calculate the quantum heat current between the system and bath in the process of adiabatic speedup. We find that the adiabatic fidelity decreases with increasing heat current. Our investigation paves the way for the design of quantum heat engines and quantum devices.
Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of an infinite number of modes. We show how the non-Markovian character of the system is influenced by the coupling strength between the qubit and cavity and the correlation time of the reservoir. In particular, we found a phenomenon whereby the qubit Markovian and non-Markovian transition exhibits a anomalous pattern in a parameter space depicted by the coupling strength and the correlation time of the reservoir.
We investigate the influence of the environment on the rapid adiabatic passage scheme for optimal population transfer in a two-level system. To cope with strong coupling to an external phonon bath with super-Ohmic spectral density, we are solving the time-dependent Schr\"odinger equation of the extended system, including a finite number of bath modes using the multi-Davydov D2 ansatz. This allows for the treatment of the non-Markovian reduced dynamics of the two-level subsystem. Surprisingly, it is found that strong system-bath coupling stabilizes the transition probability from the lower to the upper level as a function of the area under the laser pulse. This dissipative engineering effect could only be uncovered by a non-Markovian treatment. For strong coupling, the transition probability then becomes a monotonically increasing function of the pulse area at zero temperature of the heat bath. Finite temperatures break the monotonicity in the range of pulse areas that we studied, but not the stability of the observed effect.
The character of evolution of an open quantum system is often encoded in the correlation function of the environment or, equivalently, in the spectral density function of the interaction. When the environment is heterogeneous, e.g., consists of several independent subenvironments with different spectral functions, one of the subenvironments can be considered auxiliary and used to control decoherence of the open quantum system in the remaining part of the environment. The control can be realized, for example, by adjusting the character of interaction with the subenvironment via suitable parameters of its spectral density. We investigate non-Markovian evolution of a two-level system (qubit) under influence of three independent decoherence channels: two of them have classical nature and originate from interaction with a stochastic field, and the third is a quantum channel formed by interaction with a bosonic bath. By modifying spectral densities of the channels, we study their impact on steady states of the two-level system, evolution of its density matrix, and the equilibrium emission spectra. Additionally, we investigate the impact of the rotation-wave approximation applied to the bath channel on accuracy of the results.