A nonequilibrium quantum Otto engine enhanced via multi-parameter control

TL;DR

The paper investigates nonequilibrium quantum Otto engines under simultaneous multi-parameter sudden quenches, establishing a universal framework where the total work decomposes into contributions from each quenched parameter. By applying this to a harmonically trapped 1D Bose gas with tunable interaction strength g and trap frequency ω, the authors derive a general inequality showing that the two-parameter cycle can exceed the sum of its single-parameter counterparts, thereby enhancing engine performance and refrigerator CoP. They validate the enhancement analytically in the zero-temperature Thomas-Fermi regime, and numerically via thermodynamic Bethe Ansatz for finite-temperature quasicondensates and in the Tonks-Girardeau limit, consistently observing substantial gains in net work and efficiency. The results demonstrate a broadly applicable principle: rapid, coordinated control over multiple system parameters can significantly boost the performance of quantum thermal machines in realistic many-body settings, with direct relevance to ultracold atoms and trapped-ion experiments.

Abstract

Advances in experimental control of interacting quantum many-body systems with multiple tunable parameters--such as ultracold atomic gases and trapped ions--are driving rapid progress in quantum thermodynamics and enabling the design of quantum thermal machines. In this work, we utilize a sudden quench approximation as a means to investigate the operation of a quantum thermodynamic Otto cycle in which multiple parameters are simultaneously controllable. The method applies universally to many-body systems where such control is available, and therefore provides general principles for investigating their operation as a working medium in quantum thermal machines. We investigate application of this multi-parameter quench protocol in an experimentally realistic one-dimensional Bose gas as the working fluid, with control over both the frequency of an external harmonic trap and the interparticle interaction strength. We derive a general inequality for the net work of this two-parameter Otto cycle, demonstrating that this protocol out-performs its constituent single-parameter Otto cycles when operating as an engine, and additionally implying an enhancement to the coefficient of performance when operating as a refrigerator. Further, we demonstrate that multi-parameter control can exhibit dramatically improved performance of the Otto engine when compared not only to single-parameter constituent quenches but also to the combined effect of its constituent engine cycles.

Figures (7)

• Figure 1: Total system energy ($\langle \hat{H}\rangle_{(g,\omega)}$) diagram for the sudden quench Otto cycle with a harmonically trapped 1D Bose gas as the working fluid. Here, control is over both the interaction strength, $g$, and the external harmonic trapping frequency, $\omega$, given on the horizontal and vertical axes, respectively, for realistic experimental values expt_values. Beginning in the low energy equilibrium state, given by $(g_l,\omega_l)$, one may consider a single-parameter Otto cycle where either interaction strength is suddenly quenched, $(g_l,\omega_l)\!\to\!(g_h,\omega_l)$, corresponding to an interaction-driven Otto cycle, or the harmonic trapping frequency is quenched, $(g_l,\omega_l)\!\to\!(g_l,\omega_h)$, corresponding to a volumetric Otto cycle. In contrast, the two-parameter Otto cycle consists of quenching both parameters, $(g_l,\omega_l) \!\to\!(g_h,\omega_h)$, resulting in an enhanced performance (see text) over the sum of the single-parameter Otto cycles.
• Figure 2: Performance of the two-parameter sudden quench quantum Otto engine cycle in the weakly interacting ground state of the 1D Bose gas using the Thomas-Fermi approximation. Panels (a) and (b) demonstrate the net work ($W$) and efficiency ($\eta$), respectively, as a function of both the interaction strength ratio, $g_h/g_l$, along the horizontal axis, and harmonic trapping frequency ratio, $\omega_h^2/\omega_l^2$, along the vertical axis. The net work is represented in harmonic oscillator units defined by the longitudinal frequency in the low energy equilibrium state, $\omega_l$. The low energy equilibrium state ($l$) is parameterized by $N\!=\!2000$ total particles at dimensionless interaction strength $\gamma_0\!=\!4.9\times 10^{-2}$. $\Delta N\!=\!200$ particles are exchanged with the reservoirs while in contact.
• Figure 3: Comparison of the two-parameter sudden quench quantum Otto engine cycle against the single-parameter Otto engine cycles. In panel (a), we demonstrate the net work of the single-parameter Otto engine cycles as a function of their quenched parameter; the interaction-driven cycle, $W_g$, is shown as the solid blue line, whereas the volumetric cycle, $W_\omega$, as the solid red line. The value of the quenched parameter ratio is denoted 'ratio'. This is contrasted with the maximum net work of the two-parameter Otto engine cycle, denoted $W^{\mathrm{max}}$ and shown as the solid yellow line. The maximum net work of both single-parameter Otto cycles are given by the blue and red dashed lines for the interaction-driven and volumetric cycles, respectively, with their sum shown as the black dashed line. In contrast, the maximum net work of the two-parameter Otto engine cycle is greater than this sum by more than an order of magnitude. Panel (b) demonstrates the efficiency of the single-parameter Otto engine cycles, with colors corresponding to those shown in panel (a). The efficiency at maximum net work of the two-parameter Otto cycle is shown as the solid yellow line, and clearly out-performs both single-parameter cycles both in terms of magnitude and breadth of operation.
• Figure 4: Performance of the two-parameter sudden quench thermo-chemical quantum Otto engine cycle in the finite temperature quasicondensate regime, evaluated via numerically exact TBA methods. Panels (a) and (b) demonstrate the net work and efficiency, respectively, as a function of the ratio of both quenched parameters. The parameter values for the low energy equilibrium state are chosen to match those used in Fig. \ref{['fig:GP_T0']}, but at a finite dimensionless temperature of $\tau_0\!=\!1.2\!\times\!10^{-2}$ (see text). Further, we utilize a fixed temperature ratio between the high and low energy equilibrium states of $T_h/T_l\!=\!1.33$, making this a thermo-chemical quantum Otto cycle. We observe a maximum net work of $-W/\hbar \omega_l \!\simeq \!1.1\!\times\! 10^4$, corresponding to $-W/N_l\hbar \omega_l \!\simeq \!5.5$, and an efficiency at maximum net work of $\eta \!\simeq\!0.04$. Panels (c) and (d) display a comparison between the maximum net work and efficiency at maximum net work of the two parameter Otto cycle, respectively, against the single-parameter Otto cycles, as previously shown for the zero temperature quasicondensate system in Fig. \ref{['fig:GP_T0_compare']}.
• Figure 5: Performance of the two-parameter sudden quench Otto engine cycle for a harmonically trapped 1D Bose gas in the strongly interacting Tonks-Girardeau regime, calculated via numerically exact TBA methods. All panels are presented in the same form as in Fig. \ref{['fig:GP_Performance_thermochem']}. The low energy equilibrium state is fixed by $N_l\!=\!20$, $\tau_0\!\simeq\!0.18$, and $\gamma_0\!\simeq\!8.5$. The high energy equilibrium state has $N_h\!=\!22$, and $T_h/T_l\!=\!2$. We observe a maximum net work of $-W/\hbar \omega_l \!\simeq \!1.1$, corresponding to $-W/N_l\hbar \omega_l \!\simeq \!5.5\times 10^{-2}$, and an efficiency at maximum net work of $\eta \!\simeq\!0.02$.