Single-Ion Heat Engine at Maximum Power

We propose an experimental scheme to realize a nanoheat engine with a single ion. An Otto cycle may be implemented by confining the ion in a linear Paul trap with tapered geometry and coupling it to engineered laser reservoirs. The quantum efficiency at maximum power is analytically determined in various regimes. Moreover, Monte Carlo simulations of the engine are performed that demonstrate its feasibility and its ability to operate at a maximum efficiency of 30% under realistic conditions.

Figure 1

(a) Energy-frequency diagram of the Otto cycle for the radial mode of the ion. The continuous line represents the ideal process, while the dots show the results of the Monte Carlo simulations. (b) The pictograms illustrate the four individual strokes of the cycle for the radial state. (c) Geometry of the tapered Paul trap: the rf electrodes have an angle of $\theta =20°$ with the trap axis, the length of the trap is 5 mm, the radial distance of the ion to the rf electrodes is $r_0=1\mathrm{mm}$. The axial and radial frequencies of the trap are ${\omega }_{0,z}/(2\pi )\simeq 6\mathrm{MHz}$ and ${\omega }_{0,x}/(2\pi )={\omega }_{0,y}/(2\pi )\simeq 35\mathrm{kHz}$.

Figure 2

Efficiency at maximum power of the Otto engine as a function of the temperature ratio. (a) shows the Carnot efficiency with zero power. (b) corresponds to the theoretical adiabatic process, Eq. (9), while (c) corresponds to the sudden frequency switch, Eq. (11). The black points denote the results of the numerical simulations with realistic trap parameters, and demonstrate that the engine can run at maximum efficiency at maximum power. The horizontal bars indicate estimated upper bounds at ${\omega }_2=1.5{\omega }_1$.

Figure 3

Phase-space distribution of the motional state of the ion during an engine cycle: (a) The radial modes perform the full Otto cycle $ABCD$. (b) Coherent oscillations (with typical displacement of $\alpha ={10}^3$ wave packets) of the axial mode used to store the produced work.