Combining energy efficiency and quantum advantage in cyclic machines

Abstract

Energy efficiency and quantum advantage are two important features of quantum devices. We here report an experimental realization that combines both features in a quantum engine coupled to a quantum battery that stores the produced work, using a single ion in a linear Paul trap. We begin by establishing the quantum nature of the device by observing nonclassical work oscillations with the number of cycles as verified by energy measurements of the battery. We moreover apply shortcut-to-adiabaticity techniques to suppress quantum friction and improve work production. While the average energy cost of the shortcut protocol is only about 3%, the work output is enhanced by up to approximately 33%, making the machine significantly more energy efficient. We additionally show that the quantum engine consistently outperforms its classical counterpart in this regime. Our results pave the way for energy efficient machines with quantum-enhanced performance.

Fig. 1. Quantum engine.

a A single ion trapped in a harmonic potential is subjected to control laser fields to realize the quantum machine. b A qubit engine cyclically operates between cold and hot coherent baths, and stores the produced work in a quantum harmonic oscillator battery, whose energy is measured after a number of cycles. c The cycle consists of four consecutive steps: isochoric expansion, coherent heating, isochoric compression and coherent cooling.

Fig. 2. Quantum signature in the engine work output.

The mean phonon number ${\overline{n}}_{NA}\left(N\right)$ determined by an energy measurement of the quantum battery after N cycles exhibits quantum oscillations (orange dots). For a classical engine, the work output scales linearly with N (orange dashed line). With counterdiabatic driving, quantum friction is suppressed and the work output ${\overline{n}}_{STA}\left(N\right)$ is increased (green triangles) above the classical limit (green dashed line). In both cases, good agreement with numerical simulations (solid lines) is obtained. The inset shows the corresponding standard deviations, σ_NA(N) (orange squares) and σ_STA(N) (green inverted triangles). Parameters are v₀ = ω = 2π × 0.075MHz and τ = 119 μs. Error bars correspond to one standard deviation.

Fig. 3. Energy efficient quantum machine.

The relative increase of work output, $\mathrm{\Delta }{\overline{n}}_{STA}/{\overline{n}}_{NA}$, in the presence of counterdiabatic driving is between 8.2(19.8)% and 27.9(19.5)% (pink squares), depending on the cycle number N. By contrast, the average energetic cost of the shortcut protocol, $\mathrm{\Delta }{\overline{\mathrm{\Omega }}}_{STA}/{\overline{\mathrm{\Omega }}}_{NA}$, is only about 2.6(0.2)% (green line whose width indicates the experimental error). Available resources are therefore more efficiently used. The inset shows the relative increase of the standard deviation Δσ_STA/σ_NA (blue diamonds), which is equal to 6.46(14.54)% on average. Solid lines show numerical simulations in both cases. Error bars correspond to one standard deviation.

Fig. 4. Shortcut enhanced power output.

Power output of the quantum engine, $P=\overline{n}/\left(N\tau \right)$, for various cycle times and fixed cycle number N = 15 without counterdiabatic driving (orange dots) and with counterdiabatic driving (green triangles). The power output increases when quantum dissipation is suppressed by the shortcut-to-adiabaticity protocol. Good agreement is obtained with numerical simulations (solid lines). Error bars correspond to one standard deviation.

Fig. 5. Energy efficient quantum machine.

The relative increase of power output, ΔP_STA/P_NA, with counterdiabatic driving is between 7.4(17.5)% and 33.2(20.0)% (pink squares), depending on the cycle time τ. By contrast, the average energetic cost of the shortcut protocol, $\mathrm{\Delta }{\overline{\mathrm{\Omega }}}_{STA}/{\overline{\mathrm{\Omega }}}_{NA}$, varies between 2.7(0.2)% and 2.9(0.2)% (green line whose width indicates the experimental error). Available resources are thus more efficiently used. Solid lines show numerical simulations. Error bars correspond to one standard deviation.