Irreversibility of decorrelating processes: an experimental assessment in cavity QED

TL;DR

The work experimentally assesses entropy production in forward-backward cycles with decorrelating processes in a cavity QED system comprising a circular Rydberg atom coupled to a high-$Q$ microwave cavity. Using the two-point measurement framework, irreversibility is quantified via the KL-Umegaki divergence $D(\rho_\tau||\tilde{\rho}_0)$, explored across decoherence, complete decorrelation, and local thermalization channels. A key methodological advance is a Bayesian, full-rank state-estimation approach with Monte Carlo sampling that overcomes divergences associated with rank-deficient density matrices, enabling robust computation of entropy and divergences. The results illuminate the irreversibility of non-thermal processes and underscore the need for careful data-analysis strategies in quantum thermodynamics experiments.

Abstract

Entropy production quantifies the amount of irreversibility of a physical process, leading to fundamental bounds for thermodynamic quantities. Particularly in the quantum realm, considerable research has been carried out in the last decades extending entropy production to nonequilibrium processes. We experimentally investigate the entropy production of forward-backward cycles containing different decorrelating processes realized to erase different types of correlations between two interacting systems, from obliterating solely quantum coherence to completely decorrelating local states. We apply these processes to the entanglement of a two-level atom, realized with a circular Rydberg atom, and a light field of a high-quality microwave cavity. The entropy production is computed from the full quantum-state tomography of the system performed at different stages of the interaction-decorrelation sequence. Due to the quantum nature of the atom-cavity system, we find that, although standard, the maximum likelihood estimation method for the density matrix leads to spurious divergences of the entropy production. We propose and implement an alternative estimator that remedies such divergences. Our work experimentally assesses irreversibility of non-thermal processes and addresses the care that must be taken in handling experimental data to estimate the entropy production.

Figures (6)

• Figure 1: Forward-backward cycle in the presence of an irreversible intermediate process $\mathcal{E}$. In the absence of $\mathcal{E}$, the cycle is completely reversed (dash backward evolution).
• Figure 2: Scheme of the experimental setup. Flying circular Rydberg atoms (toroids), excited in box B, can sequentially interact with two high-quality microwave cavities, C$_\mathrm{x}$ and C. The atom-cavity detuning is controlled by electric field applied by voltage potential V$_\mathrm{x}$ and V, respectively. The atomic state is manipulated by a low-quality cavity R$_1$ and is measured by ionization detector M. The cavity state is reconstructed by the Ramsey interferometer (zones R$_1$ and R$_2$ fed by source S$_{\textsf{R}}$) with a sequence of probe atoms and homodyne microwave field injected by sources S and S$_\mathrm{x}$.
• Figure 3: Reconstructed atom-cavity states. Three columns correspond to initial $\rho_0$, intermediate entangled $\rho_\tau$ and final $\tilde{\rho}_\tau$ states. Upper row: theoretical states based on known experimental imperfections. Lower row: MLE reconstruction. For each atomic state, the cavity photon number is limited by 3 photons. For the sake of clarity, only the absolute values of the density operators are plotted and only up to 2 photons. Red lines on the matrix base delimit the atomic states $e$ and $g$.
• Figure 4: Entropy production for different environments. Simulated results include numerical simulation of both the experimental setup with its known imperfections and the quantum state reconstruction procedure. Red lines indicate the ideal values of 0, 1 and 2 bits of the corresponding environments in the absence of any experimental imperfection and reconstruction noise.
• Figure 5: Schematic representation of the complete decorrelation protocol. First, the auxiliary atom A$_\mathrm{x}$ interacts with the main cavity C. Next, the main atom A interacts with the auxiliary cavity C$_\mathrm{x}$ and then, finally, with the main cavity C.