In 1934, Pavel Cherenkov discovered that when charged particles surpass the speed of light in matter, they generate an electromagnetic shockwave. A well-known analogue for this phenomenon is a sonic boom – shockwaves of sound generated when jet planes surpass the speed of sound in air. This new understanding of light–matter interactions led Cherenkov to share the 1958 Nobel Prize in Physics with Ilya Frank and Igor Tamm for his experiment and their theory. The Vavilov–Cherenkov effect has been studied extensively since then and besides being of fundamental science importance, it has led to applications in particle identification, medical imaging, quantum cascade lasers, optical frequency combs, laser-driven particle acceleration, and other areas of nonlinear optics and nanophotonics

In 2020, our paper in Nature Physics demonstrated an experimental signature of a quantum Cherenkov effect. In this post, we take you behind the scenes of our experiment.

The quantum Cherenkov effect

The Cherenkov interaction and analogous effects were mainly studied in the context of classical physics; however, some scientists were interested in their quantum description. The first to study the quantum nature of the Cherenkov effect were Ginzburg and Sokolov in 1940. The conclusion from their work was that quantum corrections to the Cherenkov effect are negligible and irrelevant. In a later paper from 1996, Ginzburg even states that “…In 1940, L D Landau told about my work stated that it was of no interest. It follows from the above, that he was fully justified in drawing this conclusion, and his comment hit the mark as was usual with his criticism”. For many years, this statement and related beliefs created a conception that kept scientists away from studying the quantum Cherenkov effect.

A series of theoretical papers from the past 5 years revisited the quantum Cherenkov effect and ignited a new interest in its consequences, starting with our theoretical paper from 2016. These papers predicted interesting consequences for a quantum treatment of Cherenkov-type effects and envisioned that modern experimental capabilities and advances in electron microscopy and in quantum optics could lead to the demonstration of quantum Cherenkov-type phenomena.

Over the last couple of years, other scientists began to predict similar theoretical features in related effects, such as the Smith-Purcell effect (see work by Talebi, Gover, Arie, Polman, and Garcia de Abajo). All these effects can be considered as Cherenkov-type because they all share the same underlying principle: an enhanced interaction between a charged particle and light that occurs when the velocity of the particle matched the phase velocity of light – also termed phase-matched particle–light interaction. These theoretical findings increased the general interest in building an experiment to test these theoretical predictions.

There exist three types of quantum effects that can occur in phase-matched particle–light interactions.

1. Recoil corrections due to the quantization of the electromagnetic field. The emission occurs in quantized packets, creating a deviation from classical theories of radiation emission. This effect was first analyzed in 1940 by Ginzburg and Sokolov, in the context of the Cherenkov effect.
2. Intrinsic changes to both the charge dynamics and the emission properties due to higher-order processes in QED. These effects include photon re-absorption that causes an electron mass correction (analogous to Lamb shift in renormalization theory), all being effects that cannot be explained classically.
3. Phenomena due to the quantum wave nature of the charged particle, with features that cannot be explained by a classical point-charge description, such as the emergence of discrete energy peaks in the electron energy distribution. This is what we measured in 2020.

Our paper

In our recent work, we measured the third type of the quantum effects described above. To demonstrate the Cherenkov-type interaction, we launched a laser pulse through an optical medium (see prism, below) to synchronize its velocity with a highly-collimated electron beam passing nearby. Using a very accurate electron energy spectrometer (as used in the EELS technique), we measured the electron energy distribution and revealed the discrete energy peaks discussed above. The longitudinal profile of the electron wavefunction altered the interaction. Analogous quantum corrections also arise from transverse features in the electron wavefunction, as its orbital angular momentum (OAM) or its transverse spatial profile.

Our experiment demonstrated a Cherenkov-type interaction between light waves and an electron wavefunction: the Cherenkov conditions are satisfied between an electron pulse and an incoming laser pulse that stimulates the interaction. This stimulated-Cherenkov effect is also known as the inverse-Cherenkov effect. The excitation laser pulse interacts with the electron at the Cherenkov angle (the same angle at which the radiation is emitted in the Cherenkov effect), resulting in a phase-matching between the electron and the laser light that leads to their strong interaction – causing both energy gain and energy loss – occurring simultaneously by each individual electron. In our experiment, this interaction is sustained over hundreds of wavelengths, causing the electron to become a coherent superposition of hundreds of energy levels.

Our setup is based on the ultrafast transmission electron microscope (UTEM), which utilizes femtosecond lasers for pump probe experiments. The microscope offers several degrees of freedom to measure the interactions between light and free electrons: controlling the delay between the light (“pump”) and the electron (“probe”), in addition to the light wavelength and polarization. The microscope allows us to control the electron wavefunction in space and time through its interaction with the laser.

Our Cherenkov experiment required a unique configuration that has never been achieved in a UTEM system, or in any transmission electron microscope: we needed to align the electron beam to graze the surface of our prism over 500 microns, while remaining at a distance of just 100 nanometers from the surface. To understand how complex this achievement is, consider that even samples that are 10,000 times thinner (nanometer scale, about the size of the corona virus or a couple of DNA strands) are considered quite thick in transmission electron microscopy.

To explain our results, we used the theory that was originally developed for a technique called photon-induced nearfield electron microscopy (PINEM), and extended it to describe our grazing-angle interaction. While all previous PINEM experiments dealt with localized interactions (in w

hich the electron-light interaction spans over a single light wavelength or much below), our grazing angle experiment enabled the electron-light interaction to extend over hundreds of field cycles and hundreds of wavelengths. By satisfying energy–momentum matching over a long interaction distance and a prolonged interaction duration, the interactions become stronger by orders of magnitude compared to localized interactions – this opens the way to creating strong and ultrastrong coupling phenomena with free electrons.

Going back to the types of quantum effects that can arise in electron-light interactions, the PINEM interactions (see work by Carbone, Ropers and others) can be seen as an occurrence of the quantum effect of the third type – since it depends on the electron wavefunction. However, PINEM interactions before our work did not reach the Cherenkov-type interaction because they relied on localized fields (interestingly, even the acronym PINEM includes the word “nearfield”, although other types of fields can also create the effect).

The Cherenkov effect is only one example of phased-matched particle–light interactions. The energy–momentum phase-matching condition that is famously found in the Cherenkov effect also occurs in the Smith-Purcell effect, their inverse effects and a wide range of electron–light interactions that satisfy similar phase-matching conditions.

Looking Ahead

In another recent study by our group in 2020, published in Nature, we measured the interaction of free electrons with light captured inside a photonic cavity (also measured at the same time here). Looking ahead, we envision combining the Cherenkov phase-matched interaction with an elongated photonic cavity as a route to achieving efficient electron-photon interactions. The cavity will channel emitted photons that can then be resonantly reabsorbed by the elongated electron, creating a strongly-coupled electron–photon hybrid. This hybrid will enable the exploration of extreme conditions such as single-electron–single-photon interactions, which can serve as a novel mechanism for number-resolved single photons detection.

Reaching this regime of physics would open previously unknown processes like free-electron Lamb shifts, controllable free-electron mass renormalizations, and potentially even cavity-mediated Cooper pairs of free electrons. These exciting prospects rely on the quantum interaction of free electrons with photons that are dressed by their optical environment – which enables the Cherenkov effect and many other future ideas.