Autonomous Maxwell's demon in a cavity QED system

We present an autonomous Maxwell's demon scheme. It is first analyzed theoretically in terms of information exchange in a closed system and then implemented experimentally with a single Rydberg atom and a high-quality microwave resonator. The atom simulates both a qubit interacting with the cavity and a demon carrying information on the qubit state. While the cold qubit crosses the hot cavity, the demon prevents energy absorption from the cavity mode, apparently violating the second law of thermodynamics. Taking into account the change of the mutual information between the demon and the qubit-cavity system gives rise to a generalized expression of the second law that we establish and measure. Finally, considering the closed qubit-cavity-demon system, we establish and measure that the generalized second law can be recast into an entropy conservation law, as expected for a unitary evolution.

Figure 1

Autonomous Maxwell's demon. (a) Scheme of the experimental setup with a microwave cavity ($\mathsf{C}$) and flying circular Rydberg atoms (blue toroid for the qubit atom, magenta toroids for probe probes). (b) Scheme of the experimental sequence. The cavity $\mathsf{C}$ is prepared in a thermal state at temperature ${\beta }_{\mathsf{C}}$ using microwave source ${\mathsf{S}}_{\mathsf{C}}$. The three-level atom, initially in state $|g\rangle$, is prepared in a thermal state (temperature ${\beta }_{\mathsf{Q}}$) in the $\{|g\rangle ,|e\rangle \}$ subspace using source ${\mathsf{S}}_{eg}$. The demon $\mathsf{D}$ is realized by source ${\mathsf{S}}_{gf}$ resonant with $|f\rangle -|g\rangle$ transition and applied before $\mathsf{Q}$ enters $\mathsf{C}$. The $\mathsf{Q}\text{−}\mathsf{C}$ energy exchange is induced through adiabatic passage technique ($\mathsf{Q}\text{−}\mathsf{C}$ detuning is controlled by electric field applied by voltage potential $\mathsf{V}$). The atomic state is measured by detector $\mathsf{M}$. The cavity state is reconstructed by the Ramsey interferometer (zones ${\mathsf{R}}_1$ and ${\mathsf{R}}_2$ fed by ${\mathsf{C}}_{\mathsf{R}}$) with a sequence of probe atoms.

Figure 2

Heat exchange vs relative inverse temperature $\delta \tilde{\beta }=1-T_{\mathsf{C}}/T_{\mathsf{Q}}$. Diamonds (circles) are the measured ${\mathcal{Q}}_{\mathsf{C}}$ (${\mathcal{Q}}_{\mathsf{Q}}$). Lines are theoretical. Filled symbols with solid lines (open symbols with dotted lines) are in the presence (absence) of the demon. Vertical error bars are computed from the quantum state tomography. Horizontal error bars result from the finite accuracy of the set atomic temperature, especially for thermal states close to $|g\rangle$ and $|e\rangle$. Inset: the relative heat gain $\varepsilon$ of the cavity due to the demon; see text for details.

Figure 3

Temperature dependence of thermodynamic quantities calculated in natural units of information (nats). Symbols are measured results and lines are the corresponding theoretical evolutions. Filled symbols with solid lines (open symbols with dashed lines) are in the presence (absence) of $\mathsf{D}$. (a) Mutual information. Blue, red, and black colors correspond to ${\mathcal{I}}_{\mathsf{QC}:\mathsf{D}}$ after readout, to ${\mathcal{I}}_{\mathsf{QC}:\mathsf{D}}^{\mathrm{fb}}$ after feedback, and to their difference $\mathrm{\Delta }{\mathcal{I}}_{\mathsf{QC}:\mathsf{D}}$, respectively. (b) Generalized SLT. The entropy production $\mathcal{Q}\delta \beta$ is computed here using the qubit heat ${\mathcal{Q}}_{\mathsf{Q}}$ which has a smaller experimental uncertainty than ${\mathcal{Q}}_{\mathsf{C}}$. (c) Relative entropy. Blue (red) colors correspond to ${\mathcal{D}}_{\mathsf{Q}}$ (${\mathcal{D}}_{\mathsf{C}}$), green to $\mathrm{\Delta }{\mathcal{I}}_{\mathsf{Q}:\mathsf{C}}$, and black to the sum ${\mathcal{D}}_{\mathsf{QC}}$ of these three contributions. (d) Total entropy change of the $\mathsf{QDC}$ system. Points and line are the difference of the corresponding data in plots (b) and (c). All error bars are calculated from the reconstructed states using an original method, developed in Refs. [25, 27, 28]; see also Ref. [20].