Cryogenic ⁹Be⁺ Penning trap for precision measurements with (anti-)protons

The magnetic field for trapping ions is supplied by a high homogeneity wet superconducting magnet supplied by Oxford Instruments identical to the one described in [15], but operated at a higher magnetic field of $B_0=5\,\mathrm{T}$. The experiment is placed in the horizontal room temperature bore. The magnet's characterization results were in line with the data in [15] with a spatial homogeneity $\Delta B/B<0.3\cdot10^{-6}$ in a $1\,\mathrm{cm}^3$ volume, less than $4\cdot10^{-5}$ over the trap stacks' extent (about 20 cm) and a temporal stability of $(\Delta B/B)(1/\Delta t)<4\cdot10^{-9}/\mathrm{h}$.

An overview of the vacuum system is shown in figure 2. A horizontal bore magnet was chosen in order to be mechanically compatible with the BASE CERN setup.

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The trap and wiring system form a separate cryogenic system independent from the temperature of the superconducting magnet. This allows for maintenance and upgrades on the experiment while maintaining the carefully shimmed magnetic field. All materials used in the magnet have an extremely low magnetic permeability to keep the field as homogeneous as possible. The main cold stage is cooled by the second stage of a two-stage Gifford-McMahon cryocooler equipped with a helium gas heat exchanger for vibration isolation (ColdEdge Techologies SRDK-415 ULV UHV) between the cold head and experiment. Our group measured an identical cooler to have vibration amplitudes below 25 nm at the cold plate. Homemade flexible braids made from oxygen free high conductivity copper (OFHC) further reduce vibrations transmitted to the cold temperature stages and allow for thermal contraction in the apparatus. An aluminium radiation shield is thermally anchored to the first cooling stage of the cryocooler. It is mechanically fixed to the magnet using a titanium structure and disc-shaped G10CR (a glass fiber filled epoxy for low temperature use) spacers with a maze structure to minimize heat leakage. The calculated conductive heat load is about two percent of the cryocooler's cooling power at 4 K, rendering it negligible. The cryogenic trap system and wiring is mounted to the radiation shield using a similar structure. To improve thermal contact, a vacuum annealed copper rod of $99.999\%$ purity is used for thermal contact between the cooler interface and the trap system. Radiative heat transfer is suppressed using high-reflectivity aluminium foil and multi-layer insulation blankets. Convective heat transfer is minimized by pumping the vacuum system to less than 10⁻⁷ mbar with two turbomolecular pumps before cooling down. With this system, we achieve temperatures of around 5 K near the trap.

Laser beam access is realized using custom in-vacuum mirrors to direct the beam through and out of the vacuum system. All laser beam adjustment is done outside of the vacuum chamber on a dedicated platform.

The current trap system (see figure 3) consists of three cylindrical Penning traps with open endcaps located in a cylindrical OFHC 'trap can'. In order to reach the extreme high vacuum (XHV) regime necessary to prevent antiproton annihilation, the trap can can be hermetically sealed to form its own cryopumped vacuum system [21]. The trap stack is comprised of a 'beryllium trap', a coupling trap and a precision trap. Extra space for additional traps, such as a proton source trap, is currently reserved with a dummy electrode. All trap electrodes are precision-machined from OFHC copper and gold-plated to prevent oxidation and minimize surface charge effects. Electrodes are separated by sapphire rings that also ensure concentric alignment of the assembly.

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The beryllium trap (BT) is a compensated and orthogonal five-electrode Penning trap with laser access and loading capabilities. Single pulses from a 532 nm laser are tightly focused onto a solid beryllium target embedded in an endcap electrode using an in-vacuum off-axis parabolic (OAP) mirror to produce beryllium atoms and ions. Laser beams for photoionization, cooling and repumping are introduced using custom in-vacuum mirrors and at an angle of $45^\circ$ with respect to the trap axis to allow coupling to all motional modes. The laser beam is guided out of the vacuum chamber along a parallel path to facilitate adjustment of the beam and allow for beam position monitoring. A custom-made aspheric lens (numerical aperture NA  =  0.25) collects fluorescence light, which is focused and directed onto either an EMCCD camera (Andor iXon 885) or a photomultiplier tube (Hamamatsu H8259-01) for state detection using a lens outside of the vacuum system.

The coupling trap (CT) is a stack of ten equally sized electrodes that allows for applying a double-well potential suitable for coupling the axial motional modes of two ions. For the first demonstration of the direct motional coupling of two beryllium ions in a double-well potential, we will use a trap geometry with an inner diameter of 8 mm, an inter-ion distance of d₀  =  1 mm and $\omega_0/(2\pi)=100$ kHz, resulting in an exchange time $\tau_{\mathrm{ex}}\approx64$ ms and a coupling rate $\Omega_{\mathrm{ex}}\approx25$ s⁻¹.

The precision trap (PT) is a compensated, orthogonal five-electrode trap [15] that can be used for high-precision radio-frequency spectroscopy of protons. All endcap electrodes are segmented into multiple segments to allow for adiabatic transport between traps. Traps are connected with transport electrodes and the segments between the coupling electrodes and the other traps are tapered. In the context of radio-frequency Paul traps, high-fidelity transport of trapped-ion qubit essentially without affecting the temperature has been demonstrated [22], even through complicated junctions [23]. Since the axial degree of motion of the Penning trap is purely electrostatic, we expect transport along that axis to not be too different from transport along the axis of a linear Paul trap. Note that adiabatic transport is already employed in multi-trap methods for g-factor measurements [5, 24].

Trap voltages are supplied by a homebuilt voltage source [25] and amplifiers (APEX PA98). They are connected to the electrodes using low-pass filters on all three temperature stages to reduce noise and ensure thermalization of the lines. The DC voltage source used is capable of a 50 MHz update rate and limited by low-pass filters with a total cut-off frequency of 3.1 kHz outside the vacuum chamber and on the cryogenic stages. Additional coaxial lines allow for axial excitation using an endcap electrode and radial excitation using a segmented correction electrode. The system is prepared to be upgraded with image current detection systems consisting of tank circuits and ultra-low noise amplifiers to enable resistive cooling and motional frequency measurements on protons [26].

The laser setup is shown in figure 4. It is comprised of an ablation laser for ablation of atoms and ions, a photoionization (PI) laser for resonantly enhanced photoionization in neutral ⁹Be, a Doppler cooling and a repumping laser.

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The PI laser adresses the $\left|^1\mathrm{S}_0,\,m_J=0\right\rangle\rightarrow\,\left|^1\mathrm{P}_1,\;m_J=0\right\rangle$ transition near 235 nm. The Doppler and repumper lasers are tuned to the $\renewcommand{\ket}[1]{|#1\rangle} \ket{^2\mathrm{S}_{\frac{1}{2}},\,m_J=\frac{1}{2},\,m_I=\frac{3}{2}}\rightarrow\;\ket{^2\mathrm{P}_{\frac{3}{2}},\,m_J=\frac{3}{2},\,m_I=\frac{3}{2}}$ and $\renewcommand{\ket}[1]{|#1\rangle} \ket{^2\mathrm{S}_{\frac{1}{2}},\,m_J=-\frac{1}{2},\,m_I=\frac{3}{2}}\rightarrow\;\ket{^2\mathrm{P}_{\frac{3}{2}},\,m_J=\frac{1}{2},\,m_I=\frac{3}{2}}$ transitions, both close to 313 nm. The ablation laser is a commercial ns-pulsed, frequency doubled Nd:YAG laser near 532 nm (Continuum Minilite). The photoionization laser is a 940 nm master oscillator power amplfifier (MOPA) system (TOPTICA TA pro) that is frequency-quadrupled in two doubling stages following [27–29]. The Doppler and repumping laser beams are generated by sum frequency generation (SFG) and subsequent second harmonic generation (SHG) using the output of fiber laser systems with an ytterbium doped fiber amplifier (YDFA) close to 1050 nm and two erbium doped fiber amplifiers (EDFA) close to 1550 nm (NKT Photonics Koheras Adjustik & Boostik), also following the general layout of [27, 28], using the cavities described in [29]. The 313 nm laser light and the intermediate 470 nm light for the 235 nm source are guided from an optical table to a laser platform near the experiment using polarization-maintaining photonic crystal fibers (NKT LMA-PM-10, prepared as described in [30, 31]). The final frequency doubling stage 470 nm$\,\rightarrow$ 235 nm, the ablation laser source and beam shaping optics are located on that same platform. See figure 4 for a schematic layout of the laser setup. All laser sources but the ablation laser are frequency stabilised by a wavelength meter (High Finesse WSU-2) that is referenced to a calibrated HeNe laser source. We measured the accuracy of the wavemeter stabilisation to be better than 2 MHz over a six-hour period by beating a 626 nm laser with another one that was locked on an iodine reference via frequency modulation (FM) spectroscopy.

Figure 5(a) shows the fluorescence image of a cloud of $^9\mathrm{Be}^+$ ions loaded by applying single pulses of the ablation laser with energies of around 500 ${\rm \mu}$J, using an axial trap frequency $\nu_z\approx 550~{\rm kHz}$. The ablation laser focus diameter on the beryllium target is estimated to be on the order of 60 ${\rm \mu}$m. Exact determination of the waist diameter is difficult because the laser has a multimode profile and focussing with a parabolic mirror highly depends on beam quality. Direct creation of ions by ablation from a metallic target has been reported before [32, 33]. We found that pulse energies of 40–80 ${\rm \mu}$J are sufficient to load the trap reliably. This corresponds to a peak intensity of about 0.5 to 1 GW cm⁻² at the beryllium target's position. Below a threshold of about 30, no loading is observed.

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The loading is insensitive to photoionization laser power (or absence thereof). The reason for the insensitivity to the photoionization laser is of concern since ions produced directly by the ablation laser are expected to have much larger magnetron radii than ions that are produced in the trap center. To detect and cool the ions, we shine in laser light with a frequency close to $\nu_0=957.466\,784$ THz to drive the closed cycling transition $\renewcommand{\ket}[1]{|#1\rangle} \ket{^2\mathrm{S}_{\frac{1}{2}},\,m_J=\frac{1}{2},\,m_I=\frac{3}{2}}\rightarrow\;\ket{^2\mathrm{P}_{\frac{3}{2}},\,m_J=\frac{3}{2},\,m_I=\frac{3}{2}}$. We observe a strong fluorescence signal on the EMCCD detector after loading the trap. Figures 5(b) and (c) show images of a large cloud of ions and a single ion after optimization of the imaging system. When continuously laser-cooled, clouds can be trapped for days.

Effective laser cooling in a Penning trap is complicated by the metastable nature of the magnetron motion [34, 35]. The negative energy associated with the magnetron motion makes it hard to cool all three motional modes at the same time. When referring to 'cooling' the magnetron motion, we mean reducing its quantum number, reducing the magnetron radius and hence putting energy into the mode rather than removing it. In contrast to many other experiments, we use a single laser beam that has an inclination of $45^\circ$ with respect to the trap axis, so it interacts with all motional modes.

Upon ramping the cooling laser to the red-detuned side of the resonance, we observe a distinctive change in the fluorescence spectrum over time. Directly after loading, the fluorescence is unaffected by the laser frequency over a tuning range of 1 GHz to the red of the resonance. Assuming Doppler broadening, we estimate a temperature in excess of 1000 K. Initial cooling after loading the trap takes several minutes, while subsequent recooling, e.g. after deliberate excitation, happens on the order of seconds or faster. After cooling with a beam slightly displaced from the geometric trap centre, a clear resonance, as shown in figure 6, with a width (FWHM) of 47 MHz can be extracted from fitting a Voigt profile [36] to the red-detuned side of the spectrum. Heating processes lead to a sharp drop of fluorescence on the blue-detuned side of the resonance frequency.

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Considering that the natural linewidth of the transition is 19.6 MHz [37], we deconvolve the Voigt profile with the corresponding Lorentzian lineshape, and derive a Gaussian FWHM of $\Delta\nu_{\rm D}=35.5$ MHz. Due to the noisy data, this number should be treated as an estimate of the order of magnitude rather than an accurate value. The Gaussian linewidth has contributions from saturation broadening, finite beam waist effects [38] and Doppler broadening. We neglect saturation broadening, as a low-power beam was used. We cannot reliably infer the amount of broadening due to finite beam size due to lack of information about the cloud's rotation frequency. Hence, we attribute the full Gaussian linewidth to Doppler broadening to derive an upper temperature limit of 24 mK using [39]

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle T\leqslant\frac{(\Delta\nu_{\rm D})^2 m c^2}{8\nu_0^2 k_{\rm B}\cdot\ln 2}. \nonumber \end{align} \tag{ 4 }$$

The Doppler limit for the cooling transition used is 0.5 mK, hence further optimization of the cooling parameters, such as beam pointing, should allow to further decrease the temperature of the particle. By moving the laser beam away from the trap center, an intensity gradient over the radial extent of the ion's trajectory is created that allows to cool all three modes simultaneously [34, 35]. We also realized cooling of all three modes by applying a red-detuned laser to cool the axial and cyclotron modes efficiently and simultaneously irradiating a sideband drive with frequency $\nu_\mathrm{z}+\nu_-$ (where $\nu_\mathrm{z}$ is the axial and $\nu_-$ the magnetron frequency) to couple the two modes, thus creating a steady state in which all motional modes are cooled [40]. While clouds appeared smaller when applying sideband excitations, the temperature of the cloud was higher than in the measurement above.

With our current loading scheme, we usually trap a large cloud of ions. Since we plan on using single $^9\mathrm{Be}^+$ ions for motional coupling and subsequent steps, we need to reduce the number of particles. Towards that end, we trap a cloud with a high negative voltage on the ring electrode of around  −80 V. We then decrease the voltage by a factor of 10 to remove the most energetic particles from the trap. After some precooling, we ramp the voltage back to the original value to get a tight confinement of the remaining cloud. We then apply a voltage sequence on the electrodes to adiabatically split the ion cloud and discard a part of it. The remaining cloud is recooled subsequently. After a few of these splitting cycles, we end up with a small cloud. On numerous attempts (see figure 7), we found a smallest increment in the fluorescence signal which we attribute to a single ion. Figure 7(b) shows a linear relation between the number of ions and counts on the EMCCD camera of $5.4 \times 10^{4}$ counts per ion using an exposure time of 0.5 s and an overall gain of 78 (electron multipler gain and preamplifier of the camera). For small numbers of ions, the signal shows occasional drops in the level of fluorescence. We ascribe these to ions jumping to a higher magnetron orbit because of radiation-pressure-gradient changes induced by residual laser-beam position fluctuations. We are examining the possibility of adding an axial laser cooling beam counterpropagating with the direction of fluorescence detection, combined with mode-coupling to address the radial degrees of freedom, which should eliminate this issue.

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