A recent pedagogical paper by Strauch concretely demonstrated how interaction-mediated entanglement can suppress fringe visibility in a one-dimensional model of the electron double-slit experiment. Here we extend that framework to model actual experimental data from electron biprism interferometry. Kerker et al. showed that the macroscopic QED model of Scheel and Buhmann successfully describes their measured results. We show that this Scheel-Buhmann model can be recovered from Strauch's simplified framework by employing a Markov approximation and including thermal effects. The resulting decoherence rate is expressed in terms of mode-resolved scattering probabilities familiar from electron energy-loss spectroscopy (EELS), directly relating EELS to decoherence. The thermal dependence is significant in its own right, as recent theoretical work suggests that visibility reduction could serve as a non-invasive thermal probe for nanoscale systems. This progression from a toy model, to a quantitative account of real data, to a measurement application offers a case study in how simplified models can be made experimentally relevant.
A recent pedagogical paper by Strauch concretely demonstrated how interaction-mediated entanglement can suppress fringe visibility in a one-dimensional model of the electron double-slit experiment. Here we extend that framework to model actual experimental data from electron biprism interferometry. Kerker et al. showed that the macroscopic QED model of Scheel and Buhmann successfully describes their measured results. We show that this Scheel-Buhmann model can be recovered from Strauch's simplified framework by employing a Markov approximation and including thermal effects. The resulting decoherence rate is expressed in terms of mode-resolved scattering probabilities familiar from electron energy-loss spectroscopy (EELS), directly relating EELS to decoherence. The thermal dependence is significant in its own right, as recent theoretical work suggests that visibility reduction could serve as a non-invasive thermal probe for nanoscale systems. This progression from a toy model, to a quantitative account of real data, to a measurement application offers a case study in how simplified models can be made experimentally relevant.
Electron microscopes provide a powerful platform for exploring physical phenomena with nanoscale resolution, based on the interaction of free electrons with the excitations of a sample such as phonons, excitons, bulk plasmons, and surface plasmons. The interaction usually results in the absorption or emission of such excitations, which can be detected directly through cathodoluminescence or indirectly through electron energy loss spectroscopy (EELS). However, as we show here, the underlying interaction of a free electron and an arbitrary optical excitation goes beyond what was predicted or measured so far, due to the interplay of entanglement and decoherence of the electron-excitation system. The entanglement of electrons and optical excitations can provide new analytical tools in electron microscopy. For example, it can enable measurements of optical coherence, plasmonic lifetimes, and electronic length scales in matter (such as the Bohr radius of an exciton). We show how these can be achieved using common configurations in electron diffraction and EELS, revealing significant changes in the electron’s coherence, as well as in other quantum information theoretic measures such as purity. Specifically, we find that the purity after interaction with nanoparticles can only take discrete values, versus a continuum of values for interactions with surface plasmons. We quantify the post-interaction density matrix of the combined electron-excitation system by developing a framework based on macroscopic quantum electrodynamics. The framework enables a quantitative account of decoherence due to excitations in any general polarizable material (optical environment). This framework is thus applicable beyond electron microscopy. Particularly in electron microscopy, our work enriches analytical capabilities and informs the design of quantum information experiments with free electrons, allowing control over their quantum states and their decoherence by the optical environment.
This paper considers a theoretical model of the double-slit experiment with electrons whose paths are monitored. This monitoring, inspired by a recent text by Maudlin, is performed by the Coulomb scattering of the electron by a proton. A simple quantum mechanical calculation is presented, inspired in part by a recent experimental demonstration of this famous thought experiment. The results illustrate the relationship between entanglement and the loss of coherence in the interference pattern. The tradeoff between the visibility of interference and the information gained by measurement is also explored. This calculation can provide advanced undergraduates insight into decoherence, entanglement, and quantum information.
Abstract The performance of modern quantum devices in communication, metrology or microscopy relies on the quantum–classical interaction which is generally described by the theory of decoherence. Despite the high relevance for long coherence times in quantum electronics, decoherence mechanisms mediated by the Coulomb force are not well understood yet and several competing theoretical models exist. Here, we present an experimental study of the Coulomb-induced decoherence of free electrons in a superposition state in a biprism electron interferometer close to a semiconducting and metallic surface. The decoherence was determined through a contrast loss at different beam path separations, surface distances and conductibilities. To clarify the current literature discussion, four theoretical models were compared to our data. We could rule out three of them and got good agreement with a theory based on macroscopic quantum electrodynamics. The results will enable the determination and minimization of specific decoherence channels in the design of novel quantum instruments.
We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore can be observed. We analyse different trajectories in order to show the dependence of the decoherence factor on the velocity of the particles.
The double‑slit experiment epitomizes the wave–particle duality of quantum mechanics. In standard treatments, the interference pattern follows from superposition, while measurement of “which path” destroys coherence. The precise mechanism that turns a coherent superposition into a localized detection event remains an open question. We propose an operator‑based model within the open‑quantum‑system framework that describes the entire process through seven effective Lindblad generators: fluctuating diffusion (initial wavepacket spreading), cyclic reset (quantum Zeno effect), spatial‑mode splitting (simultaneous excitation of both slits), free evolution (interference formation), liminal projection (threshold‑activated measurement), irreversible loss (detector inefficiency), and subspace mapping (projection onto a definite detection outcome). Unlike standard quantum mechanics, the model introduces a nonlinear decoherence rate that depends on the spatial spread of the wavefunction, capturing environment back‑action through a feedback‑controlled coupling. This dependence leads to a small but testable reduction of fringe visibility with increasing particle flux or wavepacket width, even in the absence of explicit which‑path measurement. The measurement activation is modeled as a smooth threshold function, giving a sharp transition in detection probability as the system reaches the screen. Analytical expressions for visibility and the critical Zeno frequency are derived, and numerical simulations are presented. The predictions are accessible with current experimental technology (weak measurements, controlled decoherence, cavity‑QED systems). The framework suggests that wave–particle duality can be understood as a dissipative phase transition, bridging foundational quantum theory with practical open‑system control.