SPIDER for electron wavepackets – published in Science Advances

In our new work published in Science Advances [1], our team presents a new approach to measure the full quantum wavefunction of a free electron wavepacket. The project was lead by Dr. Zhaopin Chen and we worked in collaboration with Dr. Yiming Pan, who is now a faculty member at ShanghaiTech University, and Bin Zhang from Tel Aviv University. We were motivated by the fact that a free-space single electron wavepacket perfectly unites in itself the wave-particle duality of quantum mechanics. It leads to a description of wavefunctions for elementary particles such as electrons, bringing tremendous success to quantum mechanics. However, the measurement-induced collapse of the wave function has long been a challenge for the measurement of free electron quantum wave functions.

Moreover, in the realm of ultrafast phenomena, femtosecond (10-15 s) and attosecond (10-18 s) electron pulses serve as cutting-edge tools that enable the observation of ultrafast coherent quantum dynamics of electrons and holes in molecules and solid materials. These ultrashort electron pulses offer simultaneous ultra-high spatial resolution (in Angstroms) and ultra-high temporal resolution (in femtoseconds and attoseconds). However, due to their extremely short temporal duration, existing equipment faces difficulties in achieving such rapid responses for accurate measurements. In this context, by performing Fourier transforms on the spectral amplitude and phase of electrons, the complete quantum wave function in the time domain can be revealed. While high-resolution electron spectrometer can measure spectral amplitudes, acquiring electron spectral phase in free space remains challenging.

In our paper, we propose the Free Electron Spectral Shearing Interferometry (FESSI) approach for reconstructing the quantum wave function of ultrashort free electrons. We were inspired by SPIDER which is a powerful approach to measure the electric field of ultrashort light pulses [2]. The FESSI setup involves the use of a Wien filter [3] to generate two time-delayed replicas of electron wave packet. Then, by applying an energy shift to one of the paths using a mid-infrared laser-driven light-electron modulator [4], spectral interference forms in the electron spectrometer. By analyzing the resulting spectral fringes, the overall distribution of the electron spectral phase can be deduced. Together with the spectral amplitude, this information enables the reconstruction of the complete temporal wave function of the free electrons with high fidelity.

FESSI proposed in our paper is experimentally feasible and its realization for the reconstruction of quantum wave functions in ultrashort free electrons holds great promise across various scientific fields. It can be employed for characterizing femtosecond and attosecond electron pulses in the photoelectron guns, ultrafast transmission and scanning electron microscopy, and strong-field physics. Furthermore, free electron wavefunction reconstruction can test the foundations of quantum mechanics, which may shed light on many fundamental issues, such as the wavefunction collapse and the measurement problem.

References

1. Z. Chen, B. Zhang, Y. Pan and M. Krüger, Quantum wave function reconstruction by free-electron spectral shearing interferometry, Science Advances 9, eadg8516 (2023).
2. C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
3. M. Nicklaus and F. Hasselbach, Wien filter: A wave-packet-shifting device for restoring longitudinal coherence in charged-matter-wave interferometers. Phys. Rev. A 48, 152 (1993).
4. Y. Pan, B. Zhang and A. Gover, Anomalous Photon-Induced Near-Field Electron Microscopy, Phys. Rev. Lett. 122, 183204 (2019).