Non-Markovian quantum Mpemba effect in strongly correlated quantum dots

Abstract

Harnessing non-Markovian effects has emerged as a resource for quantum control, where a structured environment can act as a quantum memory. We investigate the quench dynamics from specific initial states to equilibrium steady states in strongly correlated quantum dot systems. The distance between quantum states is quantified using the Bures metric, which endows the space of reduced density matrices with a Riemannian geometric structure. Using the numerically exact hierarchical equations of motion (HEOM) method, we demonstrate a quantum Mpemba effect arising from non-Markovianity. This effect is characterized by a relaxation slowdown due to information backflow from the bath to the system, which induces a pronounced memory effect. We show that the emergence of the non-Markovian quantum Mpemba effect on the approach to a strongly correlated steady state is determined by the interplay between the initial-state-dependent non-Markovianity and the initial geometric distance between states. Our results underscore the critical role of memory effects in quantum quench dynamics and suggest new pathways for controlling anomalous relaxation in open quantum systems.

Figures (5)

• Figure 1: Time-evolution of von Neumann entropy (a) and (b), trace distance (c) and (d), and geodesic distance (e) and (f) for initial states $\left| \uparrow\downarrow \right>\left< \downarrow\uparrow \right|$ and $\frac{1}{2}(\left| \uparrow \right>\left< \uparrow \right| + \left| \downarrow \right>\left< \downarrow \right|)$. For (a), (c), (e) the temperature is $\tilde{T}=0.1$ while for (b), (d), (f) $\tilde{T}=1$. The inset in (e) is the spectral functions. Other parameters are set as $\epsilon_{d} = -0.7$, $U=1$, $\Gamma=0.2$, $W=2$, in unit of meV.
• Figure 2: (a)-(e) Geodesic distance evolution from initial states $\left| \uparrow\downarrow \right>\left< \downarrow\uparrow \right|$ and $\frac{1}{2}(\left| \uparrow \right>\left< \uparrow \right| + \left| \downarrow \right>\left< \downarrow \right|)$ for different single electron energy level $\epsilon_d$. The inset of (d) show the asymptotic behavior for long-time evolution. (f) The geodesic distance polarization $\chi$ versus time $t$ and $\epsilon_d$. For (a)-(f) temperature is set as $\tilde{T}=0.02$, other parameters are same as that in Fig. \ref{['fig1']}.
• Figure 3: (a)-(d) Evolution trajectories of $\rho_{\text{db}}(t)$ (black solid line) and $\rho_{\text{sm}}(t)$ (red solid line) for different $\epsilon_d$, where the initial states are marked by circles and the ESSs are marked by squares. The dashed lines are the geodesics connecting the initial state and ESS. (e)-(h) The evolution of residue distances and geodesic distances corresponding to (a)-(d). Parameters are same as that in Fig. \ref{['fig2']}.
• Figure 4: (a) and (d) Trace distance, (b) and (e) quantum relative entropy, (c) and (f) geodesic distance evolution for different initial states. Temperature for the left (right) panel is $\tilde{T}=0.1$ ($\tilde{T}=1$). The single electron energy level is $\epsilon_d = -3U/4$, other parameters are same as that in Fig. \ref{['fig1']}.
• Figure 5: (a)-(d) Evolution trajectories of $\rho_{\text{db}}(t)$ (black solid line) and $\rho_{\text{sm}}(t)$ (red solid line) for different $\epsilon_d$ in generalized Bloch space, where the initial states are marked by circles and the ESSs are marked by squares. The dashed lines are the geodesics connecting the initial and equilibrium states. The corners of the tetrahedron are the four pure Fock sates. (e)-(h) The evolution of residue distances and geodesic distances corresponding to (a)-(d). Spin splitting is set as $\Delta_s/\Gamma = 1$, other parameters are same as that in Fig. \ref{['fig3']}.