Terahertz-based attosecond metrology of relativistic electron beams

Photons, electrons, and their interplay are at the heart of photonic devices and modern instruments for ultrafast science [1-10]. Nowadays, electron beams of the highest intensity and brightness are created by photoemission with short laser pulses, and then accelerated and manipulated using GHz radiofrequency electromagnetic fields. The electron beams are utilized to directly map photoinduced dynamics with ultrafast electron scattering techniques, or further engaged for coherent radiation production at up to hard X-ray wavelengths [11-13]. The push towards improved timing precision between the electron beams and pump optical pulses though, has been stalled at the few tens of femtosecond level, due to technical challenges with synchronizing the high power rf fields with optical sources. Here, we demonstrate attosecond electron metrology using laser-generated single-cycle THz radiation, which is intrinsically phase locked to the optical drive pulses, to manipulate multi-MeV relativistic electron beams. Control and single-shot characterization of bright electron beams at this unprecedented level open up many new opportunities for atomic visualization.

2 Challenges in capturing the fastest atomic motion with electron probe beams consist of not only creating femtosecond and shorter pulse durations, but also controlling or characterizing the timing of the probe electron beam relative to pump optical pulses with the same or better precision. High power GHz radiofrequency sources and structures developed and perfected in past decades have been the workhorse for manipulating electron beams, ranging from compression of keV electron bunches for table-top ultrafast electron diffraction and imaging [14][15][16][17] to acceleration and temporal characterization of GeV electron beams in kilometer-long X-ray free electron lasers (XFELs). An inherent limitation of the rf approach, however, is associated with the technical challenge to further improve the timing synchronization between high power rf sources and pump lasers. Although rf technology allows generation and characterization of few-femtosecond electron beams [18][19], a viable path to reduce their timing relative to pump optical pulses to below a few tens of femtosecond does not yet exist.
A most promising way to address the timing challenge for pump probe experiments at a fundamental level, is to manipulate the electron beam using electromagnetic radiation intrinsically synchronized with pump lasers. THz radiation generated by optical rectification or other nonlinear processes is locked in time relative to the driving laser pulses with sub-fs accuracy, and thus is an ideal choice. Meanwhile, THz radiation, having ~10 2 -10 3 times higher frequency than rf fields, is much more efficient in shaping the electron beam's temporal characteristics. The manipulations usually involve the introduction of an energy-to-time correlation in beam phase space for pulse compression, or a divergence (transverse momentum)-to-time correlation for streaking and bunch length characterization. To obtain the same amount of correlation in beam phase space, the required change of energy or momentum scales inversely proportionally with the radiation frequency.
Laser-generated THz radiation has recently emerged as a new tool for controlling electrons with high temporal precision. For instance, it has been employed for active switching and spectroscopic mapping of photo-emitted electrons from solids, providing rich insight into carrier behavior in strong near-fields [20].
From isolated gas atoms, photoelectrons ionized by XUV to hard X-ray pulses can be streaked by laser-generated THz radiation into an energy spectrum, which allows characterization of the temporal structure and timing jitter of those ionizing pulses with femtosecond resolution [21][22]. Besides extracting eV-levelenergy photoelectrons from nanotips and atoms through field emission, THz acceleration [23][24][25] and manipulation [26][27] of in-vacuum free electrons with significantly higher kinetic energies will open up a new era for beam physics and ultrafast science. In a few recent demonstrations, sub-relativistic, <100 keV kinetic energy electron beams from DC sources were compressed using laser-generated THz fields to tens of femtoseconds, with their timing jitter stabilized to a few femtoseconds as characterized by THz streaking [28][29].
There is strong incentive to extend THz control to electron beams of significantly higher bunch charge and multi-MeV relativistic kinetic energy and towards the attosecond regime. These beams, featuring extremely high beam brightness, are generated by state-of-the-art high gradient rf sources. High kinetic energy is very effective in suppressing space charge effects for creating and preserving high beam brightness, enabling single-shot measurement of irreversible dynamics in ultrafast diffraction and imaging, as well as studying systems of very low density in the gas phase [30]. However, THz control of bright relativistic electron beams with femtosecond or better precision has not yet been demonstrated, due to the technical challenges of generating and injecting multi-MeV electron beams from an rf gun with pulse durations and timing jitter both significantly smaller than the THz wavelength.
In this Letter, we report on the experimental demonstration of manipulation of bright relativistic electron beams using laser-generated THz radiation, where the timing between the electron beams and the optical pulses can be determined with attosecond accuracy for the first time. The layout of the experiment is illustrated in Fig. 1. A quasi-single-cycle THz pulse (see details in the Methods Section) with up to 10 uJ pulse energy is generated by optical rectification from a LiNbO3 crystal [31][32][33]. The THz radiation is linearly polarized along the vertical direction and focused by a 3-inch-focal-length, 90° off-axis parabolic mirror. A relativistic electron beam with 3.1 MeV kinetic energy, 20 fs rms pulse duration, and 3 fC (2 × 10 % electrons) bunch charge is generated from a photocathode rf gun, injected through an aperture in 4 the parabolic mirror and propagates collinearly with the focused THz pulse. The driving laser pulses for the electron-beam and THz generation are split from a common laser pulse, so that the time delay between the THz and electron beams can be controlled by adjusting the optical path length, leaving the rf-induced timing jitter between THz and electron pulses as the only synchronization uncertainty. The THz and electron beams are adjusted so that they have spatial and temporal overlap at the THz focus where the field strength is maximum and the Lorentz force is strongest. The field of the THz pulse at the focus is measured independently in the time-domain by electro-optical (EO) sampling [34]. 6 The centroid positions of the electron beams provide relative-to-laser timing information with high precision, and the profile of the streaked beams distribution allows single-shot determination of the absolute bunch length with femtosecond resolution. In Fig. 4a  i.e. the time stamp for each single-shot electron scattering images, can be used to resort the images with respect to the pump laser with sub-femtosecond accuracy, and thus significantly improve the overall temporal resolution, similar to the x-ray-optical cross-correlation technique developed at XFELs [35][36].
The absolute bunch length can be further improved by at least one order of magnitude with the addition of an rf [19] or THz compressor.
In summary, we report on an experimental demonstration of streaking relativistic bright electron beams using a laser-generated THz pulse, which allows determination of the electron beam-to-laser timing with unprecedented sub-femtosecond accuracy, and at the same time direct measurement of the bunch length with a resolution approaching single femtosecond. The result is a major advance in manipulating high energy electrons using THz radiation, which is significantly faster than the traditional rf technology and holds tremendous potential in creating and characterizing isolated electron beams into the attosecond regime [37][38][39][40]. Moreover, a distinct advantage of utilizing laser-generated THz is that the manipulation of electron beams is intrinsically synchronized to the driving laser, which essentially eliminates the timingjitter challenge in pump-probe ultrafast electron scattering measurements and external injection in laserdriven accelerators [41][42][43]. Utilizing such dramatically improved temporal resolution, one can explore the intriguing opportunity of bright electron-beam based spatiotemporal mapping of the THz electromagnetic fields in metamaterial devices [44] and optically excited wakefields in plasma and dielectric structures with nanometer and sub-femtosecond resolutions. With stronger THz radiation [32] and more efficient interaction structures [25], THz metrology can be extended to GeV-kinetic-energy electron beams in

Competing financial interests
The authors declare no competing financial interests.

Additional information
Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to R.K.L. and X.J.W.

Relativistic electron beams
Experiments were conducted at the Accelerator Structure Test Area (ASTA) facility at SLAC National Accelerator Laboratory. A detailed description of the apparatus was reported in Ref [45]. For the measurement reported above, an electron beam was generated by a 2.856 GHz rf photocathode gun operated at 70 MV/m gradient. The electron bunches were generated by UV laser pulses of 100 fs FWHM pulse duration and launched at 5 degrees from the zero-crossing of the rf phase. The beam charge was 3 fC (2 × 10 % electrons) and the beam kinetic energy was 3.1 MeV. The electron beam was collimated by two focusing solenoidal lenses located at 0.19 m and 1.00 m (defined relative to the photocathode at z=0 m), respectively. The THz slit was located at 1.39 m, and the detector screen was at 4.59 m.

THz source and characterization
Quasi-single-cycle THz pulses were generated by optical rectification of 800 nm laser pulses in a LiNbO3 crystal using the tilted pulse front method [31]. The optical pulse energy was 20 mJ and 100 fs FWHM duration. The THz pulse was focused with a 1-inch effective focal length (EFL) parabolic mirror, recollimated using a second, 3-inch diameter, 7-inch EFL parabolic mirror and then transported into the sample vacuum chamber through a polymer window. In vacuum, the THz pulse was focused by a 90 degree off-axis parabolic (OAP) mirror with 3-inch focal length toward the slit structure.

Evaluation of the temporal resolution for the bunch length measurement
The spot size of the electron beams on the detector screen with the THz beam off were 52. 8