Markovian heat engine boosted by quantum coherence

Abstract

We evaluate the role of quantum coherence as a thermodynamic resource in a noisy, Markovian, one-qubit heat engine. By consuming the coherence of noisy quantum states, we demonstrate that the engine can surpass the classical efficiency limit when operating according to a quantum Otto cycle. The engine's non-classical nature is demonstrated by its violation of the Leggett-Garg's temporal correlations inequality. Amplitude damping increases the extractable work under partial thermalization, thereby increasing the efficiency. In contrast, phase damping increases the extractable work under partial thermalization but reduces the efficiency. We implement the entire Otto cycle in a quantum circuit, simulating realistic amplitude and phase damping channels, as well as gate-level noise. We introduce an operational measure of the circuit's thermodynamic cost to establish a direct link between energy consumption and information processing in quantum heat engines.

Figures (8)

• Figure 1: Schematic of the quantum Otto cycle for the proposed one-qubit heat engine. The working substance is a spin-$\frac{1}{2}$ system and the cycle comprises two isochoric and two adiabatic strokes. The cold and hot reservoirs are denoted by $c$ and $h$, respectively.
• Figure 2: Quantum coherence dynamics of states through the Otto cycle: (a) Production of quantum coherence in the process of energy gap expansion carried out by the Hamiltonian $\mathcal{H}_{\rm exp}(t)$, Eq. \ref{['Hexp']}. (b) Decay of the imaginary part of quantum coherence in a thermal state $\rho_{\rm th}$, with a heat reservoir due to amplitude damping under partial thermalization $\lambda=0.5$ and $p=0$. (c) Effect of thermalization on quantum coherence in the thermal state $\rho_{\rm th}$, with fixed amplitude damping $\gamma=0.8$. (d) Effect of phase damping on coherence of the thermal state $\rho_{\rm th}$, with $\lambda=0.5$ and $\gamma=0.8$. In all cases, the inverse temperatures and frequencies were $\beta_c=1.4$ (peV)$^{-1}$, $\beta_h=0.1$ (peV)$^{-1}$; $\omega_c=1.0$ rad/s, and $\omega_h=1.8$ rad/s.
• Figure 3: Leggett-Garg time correlations for the Otto cycle in the heat engine. Temporal correlation function for (a) unitary evolution for different values of thermalization $\lambda$; $\gamma=0$, $p=0$, (b) amplitude damping without dephasing ($p=0$), $\lambda=0.5$, (c) phase damping without amplitude damping ($\gamma=0$), $\lambda=0.5$. Frequencies and inverse temperatures are the same as in Fig. \ref{['fig:Coherences']}.
• Figure 4: (a) Effect of amplitude damping $\gamma$ on the work dynamics with $p=0$, (b) Effect of phase damping $p$, without amplitude damping. (c) Effect of thermalization $\lambda$, for $p=0$ and $\gamma=0$. (d) Phase diagram of the total work parameters for the heat engine, $p=0$, (e) and (f) operation regime of the heat engine and its variation with respect to power dissipation by amplitude damping; $\gamma=0.2$ and $\gamma=0.8$, respectively. In graphs (a-c), $T_c=0.075\;\mu$K, $T_h=0.45\;\mu$K. In all the graphs, $\omega_c$ and $\omega_h$ are the same as in Fig. \ref{['fig:Coherences']}$, \lambda=0.5$ (except in (c)).
• Figure 5: Effect of thermalization and noise on the efficiency of the heat engine: (a) Effect of amplitude damping $\gamma$ on the efficiency for partial thermalization with the hot reservoir, $\lambda=0.5$ and $p=0$. The inset shows a similar situation with full thermalization, $\lambda=1$. (b) Effect of phase damping $p$, with $\gamma=0$ and $\lambda=0.5$; the inset shows this effect for $\lambda=1$. (c) Combined effects of amplitude and phase damping, $\gamma=0.8$ (main figure), and $\gamma=0.1$ (inset); $\lambda=0.5$. In all cases, the inverse temperatures and frequencies were $\beta_c=1.4$ (peV)$^{-1}$, $\beta_h=0.1$ (peV)$^{-1}$; $\omega_c$ and $\omega_h$ are the same as in Fig. \ref{['fig:Coherences']}. Continuous curves correspond to the efficiency obtained from Eq. \ref{['eq_eta']}, while the dotted curves correspond to the efficiency obtained with Eq. \ref{['eq_efficiency']}.