Controllable diatomic molecular quantum thermodynamic machines

TL;DR

This work investigates quantum heat engines that use a diatomic molecule described by a $q$-deformed Morse potential as the working medium. By deriving analytic expressions for work and efficiency, the authors analyze both quantum Carnot and Otto cycles and show that engine performance can be tuned via the deformation parameter $q$ and other potential parameters $(\mathcal{D}_e, \alpha, r_e)$, across various thermodynamic regimes. The quantum Carnot cycle achieves the ideal efficiency $\eta^{QC} = 1 - \frac{T_c}{T_h}$ (e.g., about 0.8 in their examples), while the quantum Otto cycle exhibits tunable, $q$-dependent performance with positive work output over wide parameter ranges. These results highlight how anharmonicity encoded in the $q$-deformed Morse potential can shape quantum thermal machines and suggest experimental routes using anharmonic traps or trapped ions to realize tunable quantum heat engines.

Abstract

We present quantum heat machines using a diatomic molecule modelled by a $q$-deformed potential as a working medium. We analyze the effect of the deformation parameter and other potential parameters on the work output and efficiency of the quantum Otto and quantum Carnot heat cycles. Furthermore, we derive the analytical expressions of work and efficiency as a function of these parameters. Interestingly, our system operates as a quantum heat engine across the range of parameters considered. In addition, the efficiency of the quantum Otto heat engine is seen to be tunable by the deformation parameter. Our findings provide useful insight for understanding the impact of anharmonicity on the design of quantum thermal machines.

Figures (7)

• Figure 1: Plot of the q-deformed Morse potential for $q\!\in\!\{0.4, ~0.5,~ 1\}$, where $q\rightarrow1$ corresponds to the standard Morse potential. Parameters used: $\mathcal{D}_{\text{e}}\!=\!10$, and $\alpha\!=\!2$.
• Figure 2: A pictorial representation of a Carnot thermal machine using a $q$-deformed Morse oscillator as a working substance. The engine cycle consists of two adiabatic strokes ($B \to C$ and $D \to A$) and two isothermal strokes, $A \to B$ at $T_{\text{h}}$ and $C \to D$ at $T_{\text{c}}$, with $T_{\text{h}} > T_{\text{c}}$.
• Figure 3: Quantum Carnot engine: (a) The heat exchanges of the working substance with the hot reservoir, $\mathcal{Q}_{\text{h}}$ vs $\mathcal{D}_{e}$ and $q$ (b) The heat exchanges of the working substance with the cold reservoir, $\mathcal{Q}_{\text{c}}$ vs $\mathcal{D}_{e}$ and $q$. (c) The Work output $\mathcal{W}$ vs $\mathcal{D}_{e}$ and $q$. Parameters used: $\alpha_h = 2.236$, $\alpha_c = 1$, $T_c\!=\!2$ and $T_h = 10$
• Figure 4: A pictorial illustration of an Otto machine The engine cycle consists of two adiabatic strokes ($B \to C$ and $D \to A$) where it is decoupled from the thermal baths and two isochoric strokes ($A \to B$ and $C \to D$) where the engine is coupled to two thermal baths at temperatures $T_{\text{h}}$ and $T_{\text{c}}$, with $T_{\text{h}} > T_{\text{c}}$.
• Figure 5: Quantum Otto engine with changing width of the potential well: (a) Heat exchange with the hot reservoir, $\mathcal{Q}_{\text{h}}$, (b) Heat exchange with the cold reservoir, $\mathcal{Q}_{\text{c}}$ (c) Work output, $\mathcal{W}$, and (d) Efficiency, $\eta$ as a function of $\mathcal{D}_{e}$ and $q$. Parameters used: $\alpha_h\!=\!2.236$, $\alpha_c\!=\!1$, $T_c\!=\!2$ and $T_h\!=\!10$.