Thermodynamic engine with a quantum degenerate working fluid

Can quantum mechanical thermodynamic engines outperform their classical counterparts? To address one aspect of this question, we experimentally realize and characterize an isentropic thermodynamic engine that uses a Bose-condensed working fluid. In this engine, an interacting quantum degenerate gas of bosonic lithium is subjected to trap compression and relaxation strokes interleaved with strokes strengthening and weakening interparticle interactions. We observe a significant enhancement in efficiency and power when using a Bose-condensed working fluid, compared to the case of a nondegenerate gas. We demonstrate reversibility, and measure power and efficiency as a function of engine parameters including compression ratio and cycle time. Results agree quantitatively with exact interacting finite temperature field-theoretic simulations.

Figure 1

Thermodynamic engine with a quantum degenerate working fluid. (a) Engine cycle in $a_s\text{−}\overline{\omega }$ space. Color shows total energy per particle. (b) Top: BEC images after 12 ms of expansion at each step. Middle: Evolution of trap frequency (dotted) and scattering length (dot dashed). Bottom: measured release energies for quantum degenerate (circles) and thermal (squares) working fluids during one engine cycle, normalized by the step $A$ value. Dotted lines connect data points. Inset shows efficiency for each condensate fraction $f_c$; line indicates theoretical maximum efficiency in the Thomas-Fermi regime. Error bars show standard error in all figures.

Figure 2

Engine reversibility and repeatability. (a): Comparison of the cycle performed in the “forward” $\left(A-B-C-D-A\right)$ and “reverse” $\left(A-D-C-B-A\right)$ directions, indicated by right- and left-pointing markers, respectively. Light blue line shows results of analytic calculations [see Eq. (7)]; black line shows results of isentropic fully interacting numerical simulations in both panels. (b): Measured release energy evolution during four repeated engine cycles. Simulation particle number is set to the mean particle number across each four-step cycle. Error bars are smaller than symbol size.

Figure 3

Efficiency and power vs cycle time. (a): Measured energy transfer efficiency $\eta$ versus cycle time. Line shows theoretical efficiency from Eq. (7). (b): Measured engine power, quoted in quectoWatts $({10}^{-30}$ Watts), versus cycle time. Shaded region shows the theoretical prediction of Eq. (7) for the measured range of atom numbers. The power shown here is taken from release energy measurements; as discussed in the main text, the total power is a factor of 2.5 higher. Inset shows adiabaticity parameter $\mathrm{\Theta }$ versus cycle time.

Figure 4

Varying compression ratio. (a): Measured release energy evolution over one engine cycle for varying $\nu ={\overline{\omega }}_B/{\overline{\omega }}_A$ at a fixed interaction ratio $\kappa =a_s^C/a_s^A=2.4$. Lines show analytical prediction of Eq. (7). (b): Efficiency $\eta$ as a function of compression ratio. Shaded region shows theoretical prediction of Eq. (9) for the measured range of atom numbers.

Figure 5

Varying interaction strength ratio. (a): Measured release energy evolution over one engine cycle for varying interaction strength ratio $\kappa =a_s^C/a_s^A$ at a fixed compression ratio $\nu =1.94$. (b): Power output as a function of $\kappa$. Shaded regions in both panels are theoretical predictions from Eq. (7) for the measured range of atom numbers.

Figure 6

$\mathcal{PV}$ diagram for the thermodynamic engine. ${\mathcal{V}}_A$ and ${\mathcal{P}}_A$ are the harmonic volume and pressure evaluated at step $A$ of the engine cycle. Here $\kappa =10$ and $\nu =1.5$.