Quantum heat engine in the optomechanical system with mechanical parametric drive

TL;DR

The paper addresses how to realize and optimize a quantum heat engine where the cavity in an optomechanical system serves as the working fluid and a parametrically driven mechanical mode acts as a quantum fuel generating a non-equilibrium, effectively hot bath. It adopts a quantum Otto-type cycle and employs shortcuts-to-adiabaticity to achieve finite-time, high-power operation while deriving modified thermal efficiencies that include extra heat from optomechanical interactions. The key contributions are the formulation of the heat-flux decomposition, the construction of the Otto cycle under non-equilibrium driving, and the analysis showing simultaneous improvement in thermal and energy-utilization efficiencies, aided by STA and an explicit account of additional heat terms. The results have significance for quantum energy transfer and energy utilization in nano- and quantum-scale devices, suggesting practical routes to enhanced performance in quantum thermal machines.

Abstract

We consider a quantum Otto-type heat engine constructed in an optomechanical system with which the cavity is chosen as the working substance. The cavity can effectively be coupled with hot thermal baths in nonequilibrium steady-states via optomechanical interaction. The mechanical mode with parametric drive fuels the cavity, and the utilization efficiency of energy is discussed. To obtain higher efficiency in finite time evolution, we use the shortcuts-to-adiabaticity method in work generation processes. The modified thermal efficiencies are obtained by numerical simulation. Such a system provides potential applications in quantum heat transfer and energy utilization in quantum devices.

Figures (6)

• Figure 1: (a) Illustration for the heat flux and heat transfer between the cavity(heat engine) and the mechanical oscillator(quantum fuel) in the hot isochoric strokes. The mechanical parametric drive provides an external energy injection, while the optomechanical interaction transforms the energy from the "quantum fuel" to the heat engine. (b) Utilization efficiency and steady-state occupation numbers with parametric drive. Both the $\xi$ and the $\bar{n}_{h}$ are calculated under resonant case $\Delta=\omega_M$. Other parameters are chosen as $G=\kappa$, $\gamma=10^{-2}\kappa$, $\bar{n}_c=0.01$ and $\bar{n}=100$.
• Figure 2: (a) The quantum Otto-type cycle for the cavity by tuning the detuning to produce the extra work output, and turning the parametric drive on and off to "heating" and "cooling" the cavity. (b) An illustration of the amplitude and detuning for the laser drive in an Otto-type cycle. The solid lines indicate detuning while the dashed lines are the corresponding amplitude. The black dashed-dotted line is $|\alpha|^2$, where $\alpha=A/(i\kappa-\Delta)$ is the classical part of the cavity mode. Thus the optomechanical coupling strength $G$ is fixed during the cycle because of $G\propto|\alpha|^2$.
• Figure 3: (a) The non-adiabatic thermal efficiencies (Eq. (\ref{['eq:eta']})). The red, blue, and green lines correspond to the chosen evolution time $\tau = 0.1/\kappa$, $0.15/\kappa$ and $0.5/\kappa$, respectively. The solid lines are the analytical results, while the dots are the numerical simulation results. (b) The adiabatic parameter under different $\tau$. In both plots, $Q^*$ is calculated with the detuning as Eq. (\ref{['eq:delta_t_form']}), other parameters are chosen as $\Delta_h = 20\kappa$, $\Delta_l=\Delta_h/2$, $\omega_M=\Delta_h$, $\bar{n}=100$, $\bar{n}_c=0.01$ and $\gamma=0.01\kappa$.
• Figure 4: Efficiencies for different controlling parameters under fixed $\tau$. (a) Efficiencies for different detunings with a fixed ratio of $\Delta_l/\Delta_h=1/2$, where the mechanical parametric driving strength $\lambda=0.4\kappa$; (b) Efficiencies vs $\lambda$ with the same ratio of $\Delta_l/\Delta_h=1/2$ and fixed $\Delta_h=20\kappa$. In both plots, the evolution time has been chosen as $\kappa \tau = 0.1$. Other parameters for both plots are chosen as $\bar{n}_c=0.01$, $\bar{n}=100$, $G=\kappa$, $\gamma=0.01\kappa$ and $\omega_M=\Delta_h$.
• Figure 5: (a) The minimal $\tau$ in the compression process, which is obtained for $\Omega_t >0$, the white area in the plot means trap inversion occurs. (b) Efficiency at minimal $\tau$ vs $\lambda$. The corresponding $\tau_{\text{min}}$ is obtained numerically. Other parameters are chosen the same as Fig. \ref{['fig:fig4']}.