Quantum Otto cycle in the Anderson impurity model

TL;DR

The paper addresses how strong coupling and Coulomb interactions affect the performance of a quantum Otto engine implemented on the Anderson impurity model. It combines the principle of minimal dissipation with numerically exact HEOM to define an internal energy via the effective Hamiltonian $K_{\\rm S}$ and to compute work and heat under non-Markovian dynamics. A key finding is that Coulomb interaction can shift operating regimes and, in certain below-Fermi configurations, enhance efficiency by leveraging interaction-induced level broadening and population asymmetries; in other regimes it reduces efficiency due to increased heat input. The work demonstrates the robustness of these effects across different energetic definitions of work and heat, highlighting the role of many-body correlations in nanoscale quantum engines and providing a pathway to optimize thermodynamic performance in strongly coupled quantum devices.

Abstract

We study the thermodynamic performance of a periodic quantum Otto cycle operating on the single-impurity Anderson model. Using a decomposition of the time-evolution generator based on the principle of minimal dissipation, combined with the numerically exact hierarchical equations of motion (HEOM) method, we analyze the operating regimes of the quantum thermal machine and investigate effects of Coulomb interactions, strong system-reservoir coupling, and energy level alignments. Our results show that Coulomb interaction can change the operating regimes and may lead to an enhancement of the efficiency.

Figures (14)

• Figure 1: Schematic of a periodic quantum Otto cycle.
• Figure 2: Left and center panels: Operating regimes of the quantum Otto cycle as a function of energy levels $\varepsilon_{\rm h}$ (horizontal axis) and $\varepsilon_{\rm c}$ (vertical axis) for Coulomb interactions $U=0$ (left) and $U=2$ (center). The colors indicate different regimes: heat engine (red), refrigerator (blue), accelerator (yellow), and heater (green). The efficiency $\eta_{\rm h}$ is shown for the heat engine regime. Right panel: Difference in efficiency for the heat engine regime, $\Delta \eta_{\rm h} = \eta_{\rm h}(U=2) - \eta_{\rm h}(U=0)$. Parameters, given in units of $\Gamma$, are $k_{\rm B} T_{\rm h} = 10$, $k_{\rm B} T_{\rm c} = 1$.
• Figure 3: Energy-level schemes for the two configurations considered in Sec. \ref{['sec:above']} and Sec. \ref{['sec:below']}. Left: levels above the Fermi energy. Right: levels below the Fermi energy.
• Figure 4: Population of the different states of $\rho_{\rm S}(t)$ as a function of time. Dotted vertical lines indicate the boundaries between strokes of the Otto cycle. Parameters, given in units of $\Gamma$, are $U=0$ (dashed lines), $U=2$ (solid lines), $\varepsilon_{\rm h} =2$, $\varepsilon_{\rm c} =0.6$, $k_{\rm B}T_{\rm h}=10$, $k_{\rm B}T_{\rm c}=1$.
• Figure 5: Work $W_{\rm S}(t)$ and heat $Q_{\rm S}(t)$ as a function of time for the interacting (U=2, solid lines) and the noninteracting (U=0, dashed lines) case. Dotted vertical lines indicate the boundaries between strokes of the Otto cycle. Parameters are $\varepsilon_{\rm h} =2$, $\varepsilon_{\rm c} =0.6$, $k_{\rm B}T_{\rm h}=10$, $k_{\rm B}T_{\rm c}=1$. Parameters and results are given in units of $\Gamma$.