Quantum Szilard Engine with Attractively Interacting Bosons

We show that a quantum Szilard engine containing many bosons with attractive interactions enhances the conversion between information and work. Using an ab initio approach to the full quantum-mechanical many-body problem, we find that the average work output increases significantly for a larger number of bosons. The highest overshoot occurs at a finite temperature, demonstrating how thermal and quantum effects conspire to enhance the conversion between information and work. The predicted effects occur over a broad range of interaction strengths and temperatures.

Figure 1

Szilard engine harboring many interacting bosons in one dimension. (a) Illustration of one possible single Szilard cycle. (b) For $N=4$ bosons the optimal work output $W$ (in units of the classical single-particle work $W_1=k_{B}T\ln 2$, with its magnitude illustrated by the color bar to the right) is found for attractive interactions $g$ (upper panel) at a finite temperature and around a symmetric insertion position of the barrier. The optimal work output exceeds the case of noninteracting (middle panel) and repulsive bosons (lowest panel). (c) Work output for $N=3$ as a function of temperature for different strengths of the attractive interaction. For large $T$, all curves converge into the classical limit. (d) The maximal work output $W/W_1$ increases dramatically with the particle number for bosons with attractive interactions with $g=-0.01g_0$ (red) compared with the case for noninteracting bosons (orange) and classical particles (blue). In each case, the temperature is chosen to maximize the relative work output. Optimal insertion and removal positions of the wall are used to maximize $W/W_1$.

Figure 2

Work output per cycle for the two-particle Szilard engine. For a symmetric insertion of the barrier the work output depends solely on the probability $p_0$ to find all particles on the right side. For $T\to \infty$, $p_0=1/4$. In the limit of low temperature, $p_0$ differs for bosons with different interactions. It moves from the red to the blue cross with increasing $T$. The insets show the ground state degeneracies for noninteracting (middle), repulsive (left), and attractive bosons (right).

Figure 3

Probability distributions. Work can be extracted in all cycles with insertion of the wall at the midpoint, except for the case with an equal number of particles on either side. Shown are the probability distributions assigned to the different measurement outcomes at the temperature of the maximal relative work output for $N=4$ ($k_{B}T/E_1\approx 0.243$, left panel) and $N=8$ ($k_{B}T/E_1\approx 0.0500$, right panel) bosons with weak attraction, $g=-0.01g_0$.