Fig. 2: Otto cycles with the isochoric processes executed in the exact- or the broken-phase.
From: Dynamical control of quantum heat engines using exceptional points
A and D Time evolution of the population in the excited state \(\left|e\right\rangle\) when both the second (isochoric heating) and the fourth (isochoric cooling) strokes are in the exact (strong drive and oscillatory dynamics)- and broken (weak drive and non-oscillatory dynamics) phases, respectively. The red solid curves are obtained by simulating the master equation. The circles and the error bars, respectively, denote the average and standard deviation of 10,000 measurements. Regions with different colors correspond to different strokes of the Otto cycle, with the orange, pink, green, and blue corresponding to the first (adiabatic compression), second (isochoric heating), third (adiabatic expansion), and fourth (isochoric cooling) strokes, respectively. The first (orange) and the third (green) strokes are implemented by up- and down-scanning the detuning Δ between \({\Delta }_{\min }/2\pi=0\) kHz, and \({\Delta }_{\max }/2\pi=10\) kHz, respectively, with constant Ω and γeff. The second (pink) and the fourth (blue) strokes are implemented by rapidly increasing and decreasing Ω/γeff with constant detuning. In (A), we used {Ω/2π = 23 kHz,γeff = 300 kHz}, and {Ω/2π = 24 kHz, γeff = 120 kHz} for the first and third strokes, respectively, and \(\{\Omega /2\pi=82\,{{{{{{{\rm{kHz}}}}}}}},\,{\gamma }_{{{{{{{{\rm{eff}}}}}}}}}=370\,{{{{{{{\rm{kHz}}}}}}}},\,\Delta={\Delta }_{\max }\}\) and \(\{\Omega /2\pi=24\,{{{{{{{\rm{kHz}}}}}}}},\,{\gamma }_{{{{{{{{\rm{eff}}}}}}}}}=299\,{{{{{{{\rm{kHz}}}}}}}},\,\Delta={\Delta }_{\min }\}\) for the second and fourth strokes. In (D), we used {Ω/2π = 25 kHz, γeff = 2500 kHz} and {Ω/2π = 25 kHz, γeff = 970 kHz} for the first and third strokes, respectively, and \(\{\Omega /2\pi=64\,{{{{{{{\rm{kHz}}}}}}}},\,{\gamma }_{{{{{{{{\rm{eff}}}}}}}}}=2500\,{{{{{{{\rm{kHz}}}}}}}},\,\Delta={\Delta }_{\max }\}\) and \(\{\Omega /2\pi=25\,{{{{{{{\rm{kHz}}}}}}}},\,{\gamma }_{{{{{{{{\rm{eff}}}}}}}}}=2500\,{{{{{{{\rm{kHz}}}}}}}},\,\Delta={\Delta }_{\min }\}\) for the second and fourth strokes. B and E The net work and output power, and (C) and (F), the efficiencies ηc and ηq as functions of the second stroke execution time t2 while the execution times of the other strokes are kept fixed. In (C) and (F), the horizontal dashed lines represent the efficiency ηO = 1 of the ideal Otto cycle.
