Compact ultracold electron source based on a grating magneto optical trap

The ultrafast and ultracold electron source, based on near-threshold photoionisation of a laser-cooled and trapped atomic gas, offers a unique combination of low transverse beam emittance and high bunch charge. Its use is however still limited because of the required cold-atom laser-cooling techniques. Here we present a compact ultracold electron source based on a grating magneto-optical trap (GMOT), which only requires one trapping laser beam that passes through a transparent accelerator module. This makes the technique more widely accessible and increases its applicability. We show the GMOT can be operated with a hole in the center of the grating and with large electric fields applied across the trapping region, which is required for extracting electron bunches. The calculated values of the applied electric field were found to agree well with measured Stark shifts of the laser cooling transition. The electron beams extracted from the GMOT have been characterised. Beam energies up to 10 keV were measured using a time-of-flight method. The normalised root-mean-squared transverse beam emittance was determined using a waist scan method, resulting in $\epsilon = 1.9 \rm{nm}$. The root-mean-squared transverse size of the ionisation volume is $30 \mu\rm{m}$ or larger, implying an electron source temperature in the few-10K range, $2-3$ orders of magnitude lower than conventional electron sources, based on photoemission or thermionic emission from solid state surfaces.

for extracting electron bunches. The calculated values of the applied electric field were found to agree well with measured Stark shifts of the laser cooling transition.
The electron beams extracted from the GMOT have been characterised. Beam energies up to 10 keV were measured using a time-of-flight method. The normalised root-mean-squared transverse beam emittance was determined using a waist scan method, resulting in = 1.9 nm · rad. The root-mean-squared transverse size of the ionisation volume is 30 µm or larger, implying an electron source temperature in the few-10K range, 2 − 3 orders of magnitude lower than conventional electron sources, based on photoemission or thermionic emission from solid state surfaces.

I. INTRODUCTION
In the past decade new tools have emerged that allow investigation of structural dynamics with atomic spatial and temporal resolution, i.e. as small as 0.1 nm and 100 fs: Ultrafast Electron Microscopy 1-4 (UEM), Ultrafast Electron Diffraction 5-8 (UED) and X-ray crystallography using Free Electron Lasers (XFELs) [9][10][11] . This revolution would not have been possible without the spectacular development of ultrafast pulsed electron sources 12 .
By femtosecond photoemission from flat photocathodes in RF photoguns, highly charged electron bunches can be created of sufficient quality to drive XFELs, enabling single-shot, femtosecond X-ray diffraction of protein nanocrystals 9 . Unfortunately XFELs are big and costly facilities with limited access for the average researcher. In an alternative approach the electron bunches that drive the XFELs can also be directly used for single-shot UED 5,8,13 .
Using electrons instead of X-rays has the great advantage of smaller, cheaper setups. However, the beam quality is not sufficient for studying complicated macromolecular structures or for imaging with (sub)nanometer resolution. Higher beam quality is generally provided by sharp-tipped sources, developed for electron microscopy. By sideways femtosecond photoemission from a nanometer-sized field emission tip 14 (or by RF chopping [15][16][17] ) the same beam quality can be achieved as in conventional electron microscopy, enabling imaging with atomic spatial and temporal resolution. However, this results on average in less than one electron per pulse. Increasing the charge per pulse spoils the beam quality and therefore the atomic resolution. A source that offers the combination of high beam quality and high bunch charge is highly desirable.
In the quest for better beam coherence while maintaining a large source size, a new electron source was proposed 18 , the ultracold electron source (UCES). In the UCES the initial transverse angular momentum spread is decreased which results in increased beam coherence for a given source size [19][20][21] . This significantly reduces Coulomb effects at the source which allows extraction of more charge, required for single-shot measurements.
In the UCES high charge electron bunches are created by near threshold photo-ionisation of a cloud of laser-cooled and trapped atoms in a magneto optical trap (MOT) 22 . Previous work showed high quality diffraction patterns 23,24 with these bunches, demonstrating pulsed electron source temperatures as low 19-21 as a few-10 K. Additionally it was shown that it is possible to extract ultracold picosecond electron pulses 25 which can in principle be compressed to ∼ 100fs using well established RF compression techniques 26 .
In this work we present a novel compact ultracold electron source based on a grating magneto-optical trap (GMOT), which only requires one trapping laser beam. This makes the technique more widely accessible and therefore increases its applicability. The paper is organised as follows: In Section II we describe the operating principle of a GMOT. Next, in Section III, we discuss the design of the ultracold electron source, the vacuum system, the accelerator and the electron beamline. In Section IV we will show that it is possible to operate a GMOT with a hole in the center of the grating and with large electric fields applied across the trapping region, which are both required for extracting electron bunches.
We will also show that the calculated values of the applied electric field agree well with measured Stark shifts of the laser cooling transition. Finally, in section V we will discuss the commissioning of the ultracold electron source. The electron beams extracted from the GMOT have been characterised. Beam energies up to 10 keV were measured using a timeof-flight method. The normalised root-mean-squared (rms) transverse beam emittance was determined using a waist scan method, resulting in = 1.9 nm · rad. The rms transverse source size is 30 µm or larger, implying an electron source temperature less than 25 K.

II. THE PRINCIPLE OF A GRATING MOT BASED UCES
In a conventional magneto-optical trap (MOT) atoms are laser cooled using three pairs of orthogonal laser beams whose frequency is red shifted with respect to the atomic laser cooling transition. The atoms are trapped using a quadrupole magnetic field which creates position-dependent resonance conditions 22 for the atomic transition through the Zeeman effect, and thus a restoring force and stable trapping. A recent development in the field of laser cooling and trapping is the Grating MOT 27 which requires only one input laser beam instead of the six for a conventional MOT.

A. Grating MOT
The GMOT, developed at University of Strathclyde, Glasgow, is based on an optical grating that diffracts a single incoming circularly polarised laser beam. The MOT is formed inside the overlap volume which is spanned by the incoming beam, the zeroth order back reflection and three first order diffracted beams [27][28][29][30] . The grating chip consists of three identical linear gratings, lying in a plane with 120 • relative orientations, see Figure 1a).
Each grating diffracts the incoming laser beam according to Bragg's law, with d g the grating period, (n = ±1) the diffraction order and λ = 780 nm the Rubidium trapping laser wavelength. We have used two gratings with periods d g = 892 nm and d g = 1560 nm which result in first order diffraction angles θ = 61 • and θ = 30 • respectively.
The diffraction angle is defined as the angle between the grating normal and the diffracted beam, see Figure 1d and e. Figure 1b   which is collimated using a lens and subsequently circularly polarised using a quarter wave plate. Figure 1d shows that when the center of the beam is aligned with the center of the grating three first order diffracted beams are created which span the overlap volume With the above mentioned beam parameters we calculate the overlap volume V 61 ≈ atoms using a grating MOT with an overlap volume of V ≈ 570 mm 3 . Using the scaling law we expect to be able to trap N 61 ≈ 10 6 and N 30 ≈ 3 · 10 7 atoms in our experiment.
B. Ultracold electron source Figure 2 shows a schematic representation of the electron gun. First the MOT is loaded with 85-rubidium atoms, then the trapping beam is switched off for a few µs so that all atoms relax back to the ground state. During these few µs a small cylinder (60 µm waist) of atoms is excited using a cw excitation laser beam ( ). The excitation laser beam is intersected by a pulsed 480 nm ionisation laser beam at right angles which is focused down to a 60 µm waist. This results in an approximately Gaussian spherical ionization volume with a root-mean-square (rms) radius σ x = 30 µm. The wavelength λ ion of the ionisation laser is tuned close to the ionisation threshold to minimise the excess energy E exc gained by the electron. The Stark shifted excess energy is given by

III. DETAILED EXPERIMENTAL DESIGN
We have designed a modular compact turn-key ultracold electron source that offers maximum optical accessibility. To keep the design simple we decided to have both the MOT coils and the high-voltage (HV) outside the vacuum, avoiding vacuum feed-throughs. A breakout cross-section of the vacuum system is depicted in Figure 3. The main body of the electron gun consists of a CF100 cube. The left flange is a re-entrant flange which allows the accelerator module to be mounted close to the grating. The grating is embedded in a holder which is connected to the re-entrant flange.
The right flange is a reducer flange which couples the cube to the electron beamline.
The bottom, front and back of the cube are sealed with CF100 UV grade viewports. The top flange is a CF100 to CF63 reducer which houses the rubidium dispensers providing a rubidium background pressure of ∼ 2.5·10 −9 mbar. The base pressure of the vacuum system is < 1 · 10 −9 mbar. The two coils generate the magnetic quadrupole field that is required to trap the rubidium atoms.

A. Quadrupole field
The magnetic field coils are asymmetrically driven to compensate for the fact that the trapped gas cloud is not in the center of the CF100 cube (D 2 > D 1 ), see Figure 3. Due to the large coil radius and the large distance from the coils to the trapped gas we need ∼ 2500 Ampere turns to provide the desired axial magnetic field gradient of ∼ 0.15 T/m. Both coils have 196 turns and a radius R coil = 91 mm. The distance from the first coil to the grating surface is D 1 = 79 mm and the distance from the second coil to the grating surface D 2 = 100 mm. The distance D M between the gas cloud and the grating surface determines the ratio between the coil currents: with I 1 and I 2 the currents running through the first coil and second coil, respectively.        detector assembly consists of a micro-channel plate (MCP) and a phosphor screen which is imaged onto a CCD camera.

IV. COMMISSIONING GRATING MOT
We have tested the operation of the GMOT under the influence of an applied electric field and with a hole in the center of the grating chip. The measurements were done using the θ = 61 • grating chip. The input laser beam has P t = 22.5 mW at the trapping wavelength and P r = 5.5 mW at the repump wavelength. The trapping beam has a 1/e 2 beam diameter of 15 mm resulting in a trapping beam peak intensity I t = 25.5 mW/cm 2 , which is well above the rubidium saturation intensity 22 . The repump beam peak intensity is I r = 6.2 mW/cm 2 .
The atom numbers were estimated using fluorescence measurements with a saturated atomic scattering rate Γ/2.   is increased. This is due to broadening of the laser cooling transition by breaking of the degeneracy of the m F levels in the 5 2 P 3/2 state 36 . At maximum electric field we still have a steady state atom number N ∞ = 2.4 · 10 6 which is more than sufficient to operate the GMOT as an electron source.

V. COMMISSIONING UCES
In the previous section we showed that ∼ 10 6 atoms are trapped in the presence of a In this section we present measurements of the electron beam energy, using a time-of-flight method, and of the transverse beam quality using a waist scan 19,20 method.

A. Time-of-Flight
The electron beam energy was determined using an electron time-of-flight (TOF) scan 20 .
The arrival time of the electron pulse on the MCP was determined by measuring the charge signal with a trans-impedance amplifier. Figure 10 shows the arrival time of the electron pulse relative to the ionisation time as a function of acceleration voltage V acc .
The resulting TOF data was fit, solid line in Figure 10, using the relativistically correct with c the speed of light, m the electron mass, V 0 an accelerator potential offset and τ 0 an electronics delay. This function was fitted with f , V 0 and τ 0 as fitting parameters, yielding f = 0.51 ± 0.02, V 0 = 83 ± 6V and τ 0 = 2.1 ± 0.1 ns. The electron energy U is given by with e the electron charge. The final electron beam energy U as a function of accelerator voltage V acc calculated using Equation 6 is shown in Figure 10.

B. Beam quality
The transverse electron beam quality is given by the normalized rms transverse emittance which is defined by  Figure 11 shows the rms transverse beam size as measured on the detector as a function of current I sol running through the solenoid. At the focus an rms electron spot size σ ≈ 50 µm was reached which is at the limit of our detector resolution. Detailed charged particle tracking simulations were done, in which the source temperature was varied while the source size σ x was kept fixed. We used realistic fields for the accelerating field, the quadrupole magnetic field of the MOT coils and the field produced by the magnetic solenoid lens.
Coulomb interactions can be neglected 25 because we have used a nanosecond ionization laser pulse. The measured data was fitted with the simulation results 20 which was quadratically added to the detector resolution. The solid black line in figure 11 is the best fit with particle tracing simulations.
The fit results in a beam emittance = 1.9 nm · rad, which corresponds to a source temperature T = 25 K. The grey band in the figure defines an upper and a lower limit (dashed lines) for the source emittance. At the lower limit this results in = 0.4 nm · rad  Figure 11: The electron beam rms spot size σ as measured on the detector as a function of current I sol running through the magnetic solenoid lens. and at the upper limit = 2.8 nm · rad. Using σ x = 30 µm, this translates into a lower temperature limit T − = 1 K and an upper temperature limit T + = 50 K. The inner data points (close to the focus) imply a source temperature even lower than 25 K. The measured source temperature and beam emittance of the GMOT UCES are in line with results reported in earlier work [19][20][21] .

VI. CONCLUSION AND OUTLOOK
We have successfully developed a compact ultracold electron source based on a GMOT.
The unique modular design only requires one input beam that passes through a transparent accelerator module. We show that the GMOT can be operated with a hole in the center of the grating and with large electric fields applied across the trapping region. The electric field was determined by measuring the Stark shifts of the laser cooling transition.
The electron beams extracted from the GMOT have been characterised. Beam energies up to 10 ± 0.4 keV were measured using a time-of-flight method. The normalised root-meansquared transverse beam emittance was determined using a waist scan method, resulting in = 0.4 − 2.8 nm · rad. Since the root-mean-squared transverse size of the ionisation volume is 30 µm or larger, this implies an electron source temperature in the 1 − 50 K range.
We have demonstrated a clear path towards harnessing the great potential of the UCES in a practical setting. Future research will focus on increasing the bunch charge of picosecond electron pulses created by femtosecond photoionisation. These pulses are sufficiently short for RF acceleration and compression, creating intriguing new possibilities. Obviously space charge forces will become a problem at higher bunch charges which can be addressed by shaping of the initial electron distribution.