Design and simulation of a linear electron cavity for quantum electron microscopy

Highlights

• Quantum electron microscopy (QEM) could reduce sample radiation damage.

• QEM exploits an interaction-free measurement scheme in an electron cavity.

• A linear electron cavity design is presented and characterized through simulation.

• Approaches to correct spherical aberrations inside the cavity are proposed and validated through simulation.

Abstract

Quantum electron microscopy (QEM) is a measurement approach that could reduce sample radiation damage, which represents the main obstacle to sub-nanometer direct imaging of molecules in conventional electron microscopes. This method is based on the exploitation of interaction-free measurements in an electron resonator. In this work, we present the design of a linear resonant electron cavity, which is at the core of QEM. We assess its stability and optical properties during resonance using ray-tracing electron optical simulations. Moreover, we analyze the issue of spherical aberrations inside the cavity and we propose and verify through simulation two possible approaches to the problem. Finally, we discuss some of the important design parameters and constraints, such as conservation of temporal coherence and effect of alignment fields.

Introduction

In state-of-the-art electron microscopy, radiation damage due to the minimum electron dose necessary to overcome the source and detector shot noise and resolve sub-nanometer features is recognized as the main resolution limit when imaging biological specimens [1], [2], [3], [4]. Williams and Carter refer to this issue as the microscopists’ counterpart of the Heisenberg uncertainty principle [5]. Important progress to solve this problem has been made in recent years thanks to the development of cryo-transmission electron microscopy [6], [7]. In particular, the coupling of this method with data analysis techniques, consisting of merging data coming from tens of thousands of images, [8] allows reaching sub-nanometer resolution [9]. Even though this technique gets around the radiation-damage problem, it does not allow direct imaging of a single target molecule, which would be the ideal solution. Moreover, even though cryo-TEM shows astonishing results, [10], [11] it exhibits some critical issues in terms of effort in preparing several identical samples and complexity of data treatment [8], [12]. Alternative techniques are under investigation, such as electron wavefront engineering to verify structural hypotheses [13], entanglement-assisted electron microscopy based on a flux qubit [14], electron holography/ptychography [15], [16], multi-pass transmission electron microscopy [17] and quantum electron microscopy (QEM) [18]. This work develops the QEM approach.

A QEM scheme exploits the concept of interaction-free measurement in a resonant electron cavity, that generates and sustains the resonance of two coupled states of the electron wavefunction in order to form images with reduced damage [19]. Several design schemes for a QEM, including new electron optical elements and design considerations, have been proposed in 2016 [18]. These design schemes are based on both linear and circular types of resonators. The cavity of a linear resonator is mainly defined by two electron mirrors. Instead, the form of a circular resonator is similar to the storage ring in particle accelerators [20], and a miniature storage ring has been developed [21]. However, a resonator with controlled electron trajectories for nanoscale imaging applications has not been designed or demonstrated. Thus, before building a physical apparatus, a detailed electron optical design is necessary with consideration of many parameters such as beam diameter, aberration and alignment precision. Particularly important is the validation of the system performance during resonance, which means that a comprehensive study of the electron trajectory evolution with the number of roundtrips is necessary.

To address these issues, in this work we propose a design for a linear resonant electron cavity with two electron mirrors, and we assess its performance through a ray-tracing simulation of the electron trajectories for several consecutive roundtrips. Particularly important in our electron-optical resonant system is the value of electron optical properties such as first-order chromatic aberration (C_c) and third-order spherical aberration (C_s), because they build-up at every roundtrip progressively, thus, compromising the resolution. Specifically, we propose two possible modifications to our initial scheme in order to correct C_s that appears to be the dominant aberration in our system. The first one consists of the insertion of a quadrupole-octupole corrector inside the cavity. The second one consists in the substitution of the electron gate mirror with a hyperbolic triode mirror equipped with an Einzel lens to correct the aberrations [22], [23], [24]. Finally, we discuss some of the constraints that the peculiarity of our system imposes on the design specifications (e.g the path difference between the two coupled beams) and the alignment precision, such as the conservation of the temporal coherence and the parasitic phase error. We also address the necessity of correcting misalignments in the cavity, designing an alignment unit and analyzing the effect of an alignment field on the stability of the system in terms of loss of beam coherence and beam energy spread.