Effect of atom-oscillator interaction on the aging transition in coupled oscillators

Abstract

Oscillators are often employed as a model of radiation fields, which may couple to an atom and play an important role for creating and manipulating nonclassical states in quantum metrology, quantum simulation, and quantum information. Aging transitions in coupled oscillators have been studied extensively in both the classical and quantum contexts. It is well known that the onset of aging transitions can be modulated by the dissipative coupling between oscillators. In this study, we propose an alternative way to modulate the aging transition through coherent couplings between a two-level atom and the oscillators. Our findings reveal that, compared to atom-free systems in both classical and quantum regimes, the atom-oscillator coherent interaction reduces the inactive-to-total oscillator ratio required for aging transitions. Analytical results of the transition for both the classical oscillators and quantum oscillators suggest that the decay rate of the atom and the atom-oscillator coupling strength jointly change the aging transition point. The physics behind the observation is also elucidated in this article. Our research introduces a readily implementable strategy for manipulating aging transitions in more intricate systems, thereby advancing the control and understanding of these critical transitions in quantum technologies.

Figures (8)

• Figure 1: The normalized order parameter $Q_c$ as a function of the ratio of the inactive oscillators to the total oscillators $p$ for different values of atom-oscillator coupling strength $g$. For active oscillators $\gamma_n=a=80\kappa$ and for inactive oscillators $\gamma_n=b=40\kappa$. The other parameters are $N=100, J=300\kappa, V=300\kappa$.
• Figure 2: Time evolution of the complex amplitude $\alpha$ for the active and inactive oscillators in the phase space in the Schr$\ddot{\text{o}}$dinger picture under the initial condition (a)-(b) $A_0=I_0=0.01$ (marked by S). (c)-(d) $A_0=I_0=1$. The atom is initially in the excited state. $p=0.59, g=3.6\kappa$. Other parameters are the same as in Fig. \ref{['fig1']}.
• Figure 3: The dependence of the threshold $p_\text{cmin}$ on the atom-oscillator coupling strength $g$ and decay rate of the atom $J$. Other parameters chosen are the same as in Fig. \ref{['fig1']}.
• Figure 4: (a) Quantum aging transition: Dependence of order parameter $Q_q$ on $p$ for different atom-oscillator coupling strength $g$. (b) The dependence of $p_c$ on atom-oscillator coupling strengths $g$ with $J=7.5\kappa$. (c) The dependence of $p_c$ on atom decay rates $J$ with $g=0.03\kappa$. For active oscillators $\gamma_n=a=0.5\kappa$ and for inactive oscillators $\gamma_n=b=0.375\kappa$. The other parameters chosen are $N=100, J=7.5\kappa, V=3.75\kappa$.
• Figure 5: Population of boson numbers $n_0$, $\mathcal{P}(n_0)$ for active (upper row) and inactive (lower row) oscillators for different inactive-active oscillator ratio $p$ in the absence and presence of the atom-oscillator interaction. [(a), (d)] $p = 0.1$, [(b), (e)] $p = 0.2$. [(c), (f)] $p = 0.34$. Other parameters chosen are the same as in Fig. \ref{['fig4']}.