Polaron effects on the information backflow in Jaynes-Cummings model

Abstract

We investigate the influence of phonon degrees of freedom on the qubit dynamics in Jaynes-Cummings (JC) model. A strong qubit-phonon coupling is considered giving rise to Jaynes-Cummings-Holstein (JCH) model. Under anti-adiabatic conditions, we perform a unitary transformation to make the underlying problem tractable through Redfield-type non-Markovian master equation. Analytical expression for the time-dependent coherence is obtained, incorporating both cavity-induced dissipation and phonon-induced dressing effects. The dynamics of JC model is highly non-Markovian for a narrow spectral width and finite detuning. However, a non-zero phonon coupling suppresses these non-Markovian features by effectively reducing the qubit-cavity interaction strength. {It is observed that polaronic dressing effectively supresses the detuning effects. Furthermore, the coherence-based non-Markovianity measure shows an order-of-magnitude suppression in the JCH model, indicating a new dynamical regime, while memory effects extend over a wider range of spectral densities than in the JC model.

Figures (3)

• Figure 1: Time evolution of coherence $C_{l_1}(t)$ for different values of parameters. The plots from (a) to (c) represent coherence in absence of phonons i.e. $g_p=0$. The non-zero effect of phonons (i.e. $g_p=2 \ne 0$) are taken into plots from (d) to (f). The values for detuning parameter $\Delta$ are taken as $0$, $1$ and $10$. Inset in various plots show the behaviour of coherence for short time scale. During short time evolution, coherence oscillates near the maximum value and finally saturates to maximum value in long time limit. Notably, plots (d)-(f) show that, in the presence of phonon-induced dressing, the coherence dynamics becomes largely insensitive to detuning, indicating that phonon renormalization dominates over detuning effects in this regime.
• Figure 2: Non-Markovianity $\mathcal{N}$ plotted as a function of detuning $\Delta$ and bath spectral width $\lambda$. Figure (a) corresponds to the case without phonon coupling ($g_p=0$), where pronounced non-Markovian behavior is observed across a range of parameters due to memory effects from the structured photonic environment. In contrast, Figure (b) shows that when phonon coupling is introduced ($g_p \neq 0$), non-Markovian features are significantly suppressed, as the phonon-induced dressing effectively inhibits coherence backflow and reduces memory effects.
• Figure 3: Non-Markovianity $\mathcal{N}$ as a function of the bath spectral width $\lambda$ and the qubit–phonon coupling strength $g_p$ for different detuning ($\Delta$) values. Figure (a) corresponds to $\Delta = 0$, where $\mathcal{N}$ remains finite within a narrow range of $g_p$. Figure (b) represents moderate detuning ($\Delta = 1$), where non-Markovianity becomes localized for smaller values of $\lambda$ and $g_p$, while figure (c) shows the large-detuning case ($\Delta = 10$), where $\mathcal{N}$ increases with $\lambda$ for weak phonon coupling ($g_p < 1$).