Thermal effects on coherence and excitation transfer

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.

Figure 1

Top: Coherence vs time at $\tau =0$ and $\tau =2$. Bottom: Probability of having an excitation at qubit $l\ne k$, which is initially in the ground state vs time for $\tau =0$ and $\tau =2$. In both figures, the initial state is incoherent with the single excitation at qubit $k$ and $N=7$.

Figure 2

Top: Coherence vs bath mean photon number $\tau$. Bottom: Probability of having qubit $l\ne k$ in the excited state which is initially in the ground state vs bath mean photon number $\tau$. In both figures, the initial state is the incoherent state with the single excitation at qubit $k$, time is fixed at $t=1.8$, and $N=7$.

Figure 3

Coherence of the steady state vs system size $N$ for $\tau =0.1,\tau =1$, and $\tau =4$, from bottom to top. The initial state is the incoherent state with single excitation at qubit $k$ and $N=7$.

Figure 4

Top: Coherence vs time. Bottom: Probability of finding an arbitrary qubit in the excited state vs time. In both figures, the initial state is the coherent state, $N=7$, and $\tau =0,0.3,1.4$, and 2, from bottom to top.

Figure 5

Critical value of bath mean photon number vs system size $N$ when the initial state is coherent.

Figure 6

(a) Coherence in the steady state vs bath mean photon number for the incoherent initial state (dashed red line) and coherent initial state (solid blue line). (b) Probability of finding a qubit in an excited state when the system is in a steady state vs bath mean photon number for the incoherent initial state (dashed red line) and coherent initial state (solid blue line). System size is $N=7$.