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arXiv:1708.03382 · Physical Review A

Thermal effects on coherence and excitation transfer

Laleh Memarzadeh, Azam Mani

Published Oct 13, 2017• 8 citations
arXivHTMLPDF

Abstract

To control and utilize quantum features in small scale for practical applications such as quantum transport, it is crucial to gain a deep understanding of the quantum characteristics of states such as coherence. Here by introducing a technique that simplifies solving the dynamical equation, we study the dynamics of coherence in a system of qubits interacting with each other through a common bath at nonzero temperature. Our results demonstrate that depending on the initial state, the environment temperature affects coherence and excitation transfer in different ways. We show that when the initial state is incoherent, as time goes on, coherence and the probability of excitation transfer increase. But for a coherent initial state, we find a critical value of temperature below which the system loses its coherence in time, which diminishes the probability of excitation transfer. Hence, in order to achieve a higher value of coherence and also a higher probability of excitation transfer, the temperature of the bath should go beyond that critical value. Stationary coherence and the probability of finding excited qubits in a steady state are discussed. We also elaborate on the dependence of the critical value of the bath temperature on system size.

DOI
10.1103/physreva.96.042318

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To control and utilize quantum features in small scale for practical applications such as quantum transport, it is crucial to gain a deep understanding of the quantum characteristics of states such as coherence. Here by introducing a technique that simplifies solving the dynamical equation, we study the dynamics of coherence in a system of qubits interacting with each other through a common bath at nonzero temperature. Our results demonstrate that depending on the initial state, the environment temperature affects coherence and excitation transfer in different ways. We show that when the initial state is incoherent, as time goes on, coherence and the probability of excitation transfer increase. But for a coherent initial state, we find a critical value of temperature below which the system loses its coherence in time, which diminishes the probability of excitation transfer. Hence, in order to achieve a higher value of coherence and also a higher probability of excitation transfer, the temperature of the bath should go beyond that critical value. Stationary coherence and the probability of finding excited qubits in a steady state are discussed. We also elaborate on the dependence of the critical value of the bath temperature on system size.
We analyze the role of bath temperature, coherence and entanglement on excitation transfer in a spin chain induced by the environment. In Markovian regime, we show that coherence and entanglement are very sensitive to bath temperature and vanish in time in contrary to the case of having zero-temperature bath. That is while, finding the last qubit of the chain in excited state increases by increasing the bath temperature. The obtained results show the destructive role of temperature on coherence and entanglement and confirm that these quantum mechanical features cannot affect probability of finding the last qubit in excited state.
We investigate the transient dynamics of quantum coherence for a system of two central spins in a spin-star environment by employing a numerical procedure based on a Laguerre polynomial expansion scheme. The dynamics of the total, local, and global coherence are calculated for different values of the anisotropy parameter, the system-bath interaction strengths, and temperature for different initial bipartite states. Significant dynamical features of quantum coherence are found as follows: (i) an XXX state can only have global coherence; (ii) a state with only initial local coherence gains global coherence during the course of evolution by the induced correlations between the two-qubit system and the common bath; (iii) an incoherent state gains coherence by interacting with an external bath. We find there are two primary ways to gain coherence for an incoherent state: one is by interacting with the external quantum bath and the other is through interconversion of other quantum properties such as purity into coherence. Finally, we demonstrate that our results for the system in an infinite bath also hold qualitatively when the system is in contact with a finite bath.
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 consider a system consisting of two interacting qubits that are individually coupled to separate heat baths at different temperatures. The quantum effects in heat transport are investigated in a numerically rigorous manner with a hierarchial equations of motion (HEOM) approach for non-perturbative and non-Markovian system-bath coupling cases under non-equilibrium steady-state conditions. For a weak interqubit interaction, the total system is regarded as two individually thermostatted systems, whereas for a strong interqubit interaction, the two-qubit system is regarded as a single system coupled to two baths. The roles of quantum coherence (or entanglement) between the two qubits (q-q coherence) and between the qubit and bath (q-b coherence) are studied through the heat current calculated for various strengths of the system-bath coupling and interqubit coupling for high and low temperatures. The same current is also studied using the time convolutionless (TCL) Redfield equation and using an expression derived from the Fermi golden rule (FGR). We find that the HEOM results exhibit turnover behavior of the heat current as a function of the system-bath coupling strength for all values of the interqubit coupling strength, while the results obtained with the TCL and FGR approaches do not exhibit such behavior, because they do not possess the capability of treating the q-b and q-q coherences. The maximum current is obtained in the case that the q-q coherence and q-b coherence are balanced in such a manner that coherence of the entire heat transport process is realized. We also find that the heat current does not follow Fourier's law when the temperature difference is very large, due to the non-perturbative system-bath interactions.
In the long-time limit, an open quantum system coupled to a dissipative environment is believed to lose its coherence without driving or measurement. Counterintuitively, we provide a necessary condition on trapping the coherence of a two-level system entirely with a thermal bath. Based on a time-local master equation, it is found that the residue coherence survives even under a high-temperature bath as long as the long-time Lamb shift is exactly negative to the system transition frequency. This condition is generally met in the strong and even ultrastrong coupling regime that could be relaxed by increasing the environmental temperature. The counter-rotating interactions between system and bath is indispensable to the residue coherence, whose magnitude is affected by the system initial state and the bath structure.
Abstract We study a cascaded system of two subsystems repeatedly interacting with a bath prepared in various non-thermal states. Effects of different types of bath coherence on dynamics of the system heat flux are explored. For a single-qubit bath with the displacement coherence, heat flux of each subsystem is divided into dissipative and coherent parts. In the stationary regime, the dissipative heat fluxes are the same for the two subsystems, but the coherent parts are not due to the cascaded feature. In the transient regime, heat fluxes occur even when the system and the bath have the same temperature and, more surprisingly, heat flow reversal appears when temperatures of the system and the bath differ. For a two-qubit bath we consider two types of coherence: the squeezing and the heat-exchange ones. In the stationary regime, the squeezing coherence establishes correlations between the subsystems, each of which is evolving to its thermal state with a temperature identical to the bath’s. The squeezing coherence slightly influences only the dynamics of the subsystem that interacts with the bath later. As for the heat-exchange coherence, it forces the total system to thermalize to a state with the temperature related to both magnitude and relative phase of the coherence. Particularly, depending on the relative phases, the heat-exchange coherence can amplify or suppress the heat flux during the time evolution.