Photonic Maxwell’s Demon

We report an experimental realization of Maxwell’s demon in a photonic setup. We show that a measurement at the few-photons level followed by a feed-forward operation allows the extraction of work from intense thermal light into an electric circuit. The interpretation of the experiment stimulates the derivation of an equality relating work extraction to information acquired by measurement. We derive a bound using this relation and show that it is in agreement with the experimental results. Our work puts forward photonic systems as a platform for experiments related to information in thermodynamics.

Figure 1

Experimental setup. In analogy with Maxwell’s original thought experiment, the setup uses energy from a thermal system, measurements and feed forward, in order to extract work. Thermal light is produced by collecting laser pulses scattered from a spinning glass diffuser wheel. The demon’s measurement is implemented by high transmittance beam splitters (BS) and highly sensitive avalanche photodiodes (APDs). The two final linear photodiodes are the work extraction mechanism, acting as an electromotive source that charges a capacitor ($C$). A nonzero average voltage across $C$ can be obtained by feed forward of the demons measurement, swapping its polarity according to the APD measurement outcomes.

Figure 2

Measured voltage across the capacitor. (a) Oscilloscope traces showing the voltage created by the photodiodes, filtered by the demon’s measurement outcomes. 4000 traces are sorted according to binary APD signals (click for photon detection). The black dashed line depicted only in quadrant (iv) indicates the time at which the maximum voltage is sampled. (b) Histogram of the maximum voltage. Above, the APD outputs are ignored; below, the sign of the voltage is changed if the measurement outcome is click–no click [quadrant (ii) in (a)]. The dashed vertical lines show the average of each of the two distributions. The number of photon detections per pulse—$p_1=0.702\pm 0.008$ and $p_2=0.311\pm 0.008$—as well as the control strategy, is chosen aiming to optimize the displacement of the mean voltage, as detailed in the Supplemental Material [36].

Figure 3

Extracted work and information. $|⟨U⟩|/\sigma (U)\sim \mathrm{\Delta }⟨W⟩/\sigma (W)$ [see the left-hand side of Eq. (2)], as a function of $p_1$, the number of photon detections per pulse registered by the demon’s measurement on the first mode. The measurement on the second mode yields $0.311\pm 0.008$ detections per pulse. Blue and orange points correspond to two types of feedback: flipping the voltage when the measurement yields click–no click (blue) or no click–click (orange). Error bars are estimated by binning the experimental data. The black line gives the bound established in terms of mutual information [see the right-hand side of Eq. (2)]. Dashed lines give predictions based on the average number difference between the two thermal states after feed forward, modeling states with imperfect autocorrelation, $g^{(2)}(0)=1.9$. The calculations of the photon number difference and the mutual information are detailed in the Supplemental Material [36].