Aging of coupled qubits

Abstract

The aging transition refers to the shift from an oscillatory state to a globally ceased state due to some forms of deterioration in classical physics. Similar behavior has also been observed in quantum oscillators. Although it has received extensive attention in coupled oscillator systems, it has not yet been studied in coupled qubits. In this manuscript, we explore the aging transition in a network of coupled qubits. Our model describes {numerous} qubits driven by a laser, with both dissipative and coherent qubit-qubit couplings. The ratio of inactive qubits to total qubits and the population in the excited state of the qubits are employed to characterize the aging transition. We find a transition where the population in the excited states suddenly drops when the ratio exceeds a threshold. This behavior is intriguing and contrasts with coupled oscillators, where no sudden drop is observed. Additionally, we demonstrate how the couplings and driving laser influence the threshold. The underlying physics of the sudden drop is elucidated. The region where the aging transition occurs is determined based on stability analysis theory.

Figures (8)

• Figure 1: Fixed points of $\overline{n}$ as a function of the ratio of the inactive qubits $p$. The figure is divided into three regions. In regions I and III, $\overline{n}$ has only one fixed point $\overline{n}_1$ since $(\frac{m}{2})^2+(\frac{n}{3})^3>0$. In region II, there are three fixed points $\overline{n}_1, \overline{n}_2$, and $\overline{n}_3$ since $(\frac{m}{2})^2+(\frac{n}{3})^3<0$. The parameters chosen are $V$=0.2$\kappa$, $N$=100, $\Delta$=3$\kappa$, $g$=0.04$\kappa$, and $\Omega$=3.2$\kappa$.
• Figure 2: (a) The mean excited-state population versus the ratio of inactive qubits for different dissipative coupling strengths $V$ in the two methods. There are 6 lines (except the inset) in figure (a) in 3 different color. $V$ = 0, 0.2$\kappa$, 0.4$\kappa$ are for the green, red, and blue lines, respectively. The dashed lines are plotted by the mean-field theory and the circle lines are plotted by solving the equations of collective motion. $\mathcal{M}$ marks the critical point $p_c$ given by the mean-field theory, while $\mathcal{C}$ the critical point $p_c$ given by the equation of collective motion. (b) $\overline{n}$ as a function of $g$ and $p$ with $\Omega=3.2\kappa$. (c) $\overline{n}$ versus $\Omega$ and $p$ with $g=0.04\kappa$. The initial conditions for $\langle Q\rangle$, $\langle A\rangle$, and ${{{\langle A\rangle}}^\ast}$ are denoted by $\langle Q\rangle_0$=0.5 and ${\langle A\rangle}_0={{{\langle A\rangle}_0}^\ast}=0.5$. Other parameters chosen are the same as in FIG. \ref{['aqbpic1']}.
• Figure 3: The stable regions of the fixed points $\overline{n}_{1,2}$ versus ${\langle Q\rangle}_0$ and ${\langle A\rangle}_0$. $p$ is chosen in the bistable region (i.e., $p$ ranging from 0.71 to 0.88). Figure (a), (b), and (c) correspond to different $p$. (a) $p$ = 0.71, (b) $p$ = 0.8, and (c) $p$=0.88. Other parameters chosen are the same as FIG. \ref{['aqbpic1']}.
• Figure 4: (a) The interval [$p_{\text{cmin}}$, $p_{\text{cmax}}$] for various dissipative coupling strength $V$ with $\Omega$=3.2$\kappa$. (b) The interval [$p_{\text{cmin}}$, $p_{\text{cmax}}$] for various laser driving strength $\Omega$ with $V$=0.2$\kappa$. Other parameters chosen are the same as FIG. \ref{['aqbpic1']}.
• Figure 5: The parameter versus the total number of qubits $N$ for several fixed $p$. $p$=0.3, 0.4, 0.6 from the top to down. ${\langle Q\rangle}_0$=0.5 and ${\langle A\rangle}_0$=${{\langle A\rangle}_0}^\ast$=0.5. Other parameters are chosen as the same as in FIG. \ref{['aqbpic1']}.