Antiproton reservoir preparation
The BASE-STEP catching trap is constructed of 15 cylindrical electrodes arranged in a coaxial stack (Extended Data Fig. 1a). Sapphire rings ensure electrical insulation and mechanical alignment. Antiprotons emerging from the degrader foil follow the magnetic field lines (B = 993 mT) into the trap, where three high-voltage electrodes (C01–C03) on the degrader side capture them. These electrodes form a nested axial potential well floated to −142 V with a depth of 16 V (Extended Data Fig. 1b). For capture, we pulse beam-side electrode C01 from 0 V to −158 V in 30 ns using a high-voltage switch. This pulse closes the potential well centred on C02 and traps antiprotons from the low-energy tail of the degraded beam.
After capture, cotrapped electrons—secondary particles forced out of the degrader—sympathetically cool the antiprotons61. We then ramp the C02 voltage to increase the trapping potential to 200 V, which destabilizes most contaminant negative ions while preserving antiproton confinement because of their higher q/m. We subsequently transport the particles to the central region of the catching trap. To this end, we configure electrodes C01–C03 to form a 20-V well and shift the axial potential adiabatically through the stack (typical electrode ramp time: 1 s). Finally, we confine the particles in a compensated, orthogonal five-electrode Penning trap formed by the central ring electrode C08, correction electrodes C07 and C09 and grounded endcaps starting at C06 and C10.
For non-destructive antiproton detection, we remove residual contaminants that would otherwise distort particle motion by means of space-charge effects and prevent formation of a stable axial dip signal. The dominant residual species are electrons and H− ions, which cannot be eliminated by high-voltage cleaning because of their similar or higher q/m.
We remove cotrapped electrons by applying an axial dipolar drive at 9.59 MHz to an endcap electrode (Extended Data Fig. 2a). By reducing the trap depth to 1 V, we tune the electron axial frequency into resonance with the applied drive. We then further reduce the trap depth to 0.5 V, evaporating the excited electrons. We repeat this sequence until no electrons remain. The drive is sufficiently detuned from the motional frequencies of antiprotons and H− ions to avoid unintended excitation. Following injection, we repeat electron cleaning as needed to remove beta-decay-induced electron contamination from activated surfaces (Extended Data Fig. 2b). We then tune the particle cloud into resonance with the axial detector (453 kHz) and apply magnetron sideband cooling. As described in the main text, at thermal equilibrium, the particle–detector interaction produces a characteristic dip in the detector noise spectrum.
Next, we remove heavier residual ions that persist after the initial high-voltage ramp using stored waveform inverse Fourier transform excitation62 applied to the endcap electrode. The drive spans 20–380 kHz, exciting their axial motion. By subsequently reducing the trap depth to 0.5 V and repeating the sequence, we obtain a reservoir containing only antiprotons and H− ions.
Antiprotons and H− ions exhibit nearly identical axial frequencies (separated by about 250 Hz) and indistinguishable dip widths per particle, such that both species contribute to a combined dip signal. At the applied catching parameters, we typically obtain a mixed particle cloud consisting of about 80% antiprotons and 20% H− ions. To discriminate between them, we exploit the difference in modified cyclotron frequency, which amounts to about 16 kHz at B = 993 mT. Using a single trapped proton as a magnetic field probe before injection, we determine
$${\nu }_{+,\bar{p}}=15.140\,{\rm{MHz}}\,,\qquad {\nu }_{+,{H}^{-}}=15.124\,{\rm{MHz}}.$$
(3)
We selectively remove H− ions by applying a radial dipolar radio frequency drive to a segmented correction electrode (Extended Data Fig. 2a). A frequency sweep from 15.130 to 15.120 MHz resonantly excites the H− modified cyclotron motion, increasing its radius until radial confinement is lost while leaving antiprotons unaffected. We verify successful removal by monitoring the dip width before and after excitation (Extended Data Fig. 2b). We repeat the sweep until the dip width no longer decreases (typically after one sweep; at least three are applied for robustness), yielding a clean antiproton reservoir.
Given the procedure described above, we prepare antiproton reservoirs containing about 90 antiprotons per beam injection.
Particle-number calibration
The particle number N, as shown in equation (1), is determined from the linear dependence of the axial resonator dip width Δνz on the number of trapped particles. The relation can be simplified to
$$\Delta {\nu }_{z}=\Delta {\nu }_{z,1}N,$$
(4)
where Δνz,1 denotes the single-particle dip width. This proportionality enables extraction of N from measured spectra once a calibration of Δνz,1 has been established. Calibration measurements use proton and antiproton clouds of different sizes. We prepare clouds containing about 20 particles in the catching trap, as larger particle numbers require longer averaging times for precise counting. The clouds are then reduced stepwise to a single particle by controlled evaporation. At each step, we record the spectra and fit the dip line shape21 to determine Δνz. The final single-particle signal provides a reference for Δνz,1, allowing assignment of particle numbers to intermediate cloud sizes. Linear fits of Δνz(N) yield the calibration functions. Proton and antiproton data are treated equivalently, as their Δνz,1 values are identical. The dip width depends on the magnetic field, as the effective parallel resistance Rp of the superconducting resonator varies with field strength. Following a magnetic-field ramp from 136 to 993 mT, we observe a reduction in dip width (Extended Data Fig. 3a), consistent with a decrease in Rp at higher magnetic fields63. The single-particle dip width scales linearly with Rp:
$$\Delta {\nu }_{z,1}=\frac{1}{2\pi }\frac{{q}^{2}}{m{D}_{z}^{2}}{R}_{{\rm{p}}}.$$
(5)
We therefore perform separate calibration measurements for each magnetic field. Linear fits of Δνz(N) for 136 and 993 mT (Extended Data Fig. 3b) yield
$$\begin{array}{c}\Delta {\nu }_{z}(993\,\mathrm{mT})=3.004(24)\,\mathrm{Hz}\,\cdot N\,+\,0.129(166)\,\mathrm{Hz},\\ \Delta {\nu }_{z}(136\,\mathrm{mT})=3.633(16)\,\mathrm{Hz}\,\cdot N\,-\,0.017(105)\,\mathrm{Hz},\end{array}$$
(6)
where the intercepts are consistent with zero within uncertainty. The calibration data shown were obtained from a proton cloud with N = 21 and an antiproton cloud with N = 18. The low-particle-number region is particularly important for the calibration, as uncertainties in the single-particle reference directly affect the assignment of particle numbers. The inset in Extended Data Fig. 3b highlights this region and demonstrates the agreement of the particle number assignment with the linear calibration model.
For 880 mT, where no direct calibration measurement is available, the dip width per particle is inferred from the measured detector Rp. Using the proportionality Δνz,1 ∝ Rp and comparison to calibrated field settings, we obtain Δνz,1(880 mT) ≈ 3.07(4) Hz.
To monitor the antiproton number in the transport reservoir over time, we implement an automated measurement sequence recording image-current spectra with an averaging time of 64 s. The stored antiproton cloud undergoes slow radial expansion, an effect that has been observed and studied in detail in other traps54,64. In general, cylinder-symmetry breaking components of the electric field apply a torque to the trapped ion cloud driving the radial expansion. Here these arise potentially from a small tilt between the electric and magnetic field axes, patch potentials or leakage currents on the segmented electrodes. The radial expansion results in a shift of the axial frequency and also in an increased dip width due to the residual potential imperfections in the trap (Extended Data Fig. 4). Compared to our proton tests, during which radial expansion has not been observable on a time scale of 4 h (ref. 10), the present antiproton measurements exhibit a faster radial expansion, indicating a larger torque acting on the stored cloud. The origin of this increased torque has not been identified, and the trap configuration has remained unchanged since the proton measurements. Nevertheless, the observed behaviour is consistent with a torque-driven radial expansion, as the frequency shift can be reset by applying a magnetron cooling drive64. Regular magnetron cooling cycles are therefore required to reset the radial expansion and enable an accurate particle number extraction.
To suppress this systematic effect, we apply magnetron sideband cooling in 6-min intervals, which keeps the cloud centred in the trap. The residual drift corresponds to a particle-number offset of only 0.1(2) antiprotons for a cloud of N = 92. Further systematic increases of the dip width occur if the tuning ratio and frequency detuning between particles and resonator deviate from their optimum values. However, these have been optimized so that their contribution to the particle number is not significant. For substantially larger clouds containing more than 1,000 antiprotons, however, we expect these effects to introduce significant uncertainties. In this regime, the application of a rotating-wall drive becomes desirable for reliable particle-number determination.
Over a period of 33 d, we acquired more than 26,000 spectra and extracted the dip width from each spectrum by fitting the appropriate line shape21. For our evaluation, we average the dip width over 24-h intervals, apply the magnetic-field-dependent calibration functions and round to the next integer number to determine the particle number. In this way, the statistical deviation from the integer number is small and systematic shifts of order 0.1 particle numbers do not affect the extracted particle number.
During the first 4 days, non-optimized trap parameters resulted in dip-width broadening, leading to a systematic overestimation of the particle number. Therefore, these data required a further correction. After determining the particle number with optimized settings, we repeated measurements at 136 and 993 mT under identical non-optimized conditions and compared them to spectra recorded with optimized settings. For these settings, we obtained correction factors of k = Δνz,true/Δνz,measured:
$$\begin{array}{l}k(993\,\,{\rm{mT}})=0.9779(11),\\ k(136\,\,{\rm{mT}})=0.99395(54).\end{array}$$
(7)
The evaluation procedure in this section yields the time evolution of the antiproton number shown in Fig. 3 of the main text.
Storage time and trap vacuum pressure
As noted in the main text, only a single antiproton was lost over the full 33-day storage period. The loss occurred during voltage ramp sequences applied to the reservoir as part of manipulation studies. Because these ramp sequences permitted only intermittent monitoring of the reservoir, the exact time of particle loss cannot be determined precisely. On the basis of the available spectrum data, we assigned an uncertainty of 3 h to the loss time.
Using the event timeline in Extended Data Table 1, we obtained a total antiproton storage duration of 32 days, 22 h, 38 min. This corresponds to 26 days, 13 h, 01 min ± 3 h for N = 92 and 6 days, 9 h, 37 min ± 3 h for N = 91. By weighting the storage time with the particle number and summing the contributions for N = 92 and N = 91, we obtained an integrated equivalent single-particle storage time of \({T}_{\bar{{\rm{p}}}}=8.28025(34){\rm{a}}\).
We model antiproton annihilation as a Poisson process, f(n; λ) = λne−λ/n!, with expectation value \(\lambda ={T}_{\bar{{\rm{p}}}}/{\tau }_{\bar{p},{\rm{lower}}}\). Assuming zero observed annihilation events (n = 0), the lower bound on the antiproton lifetime at a given confidence level (CL) is obtained from the probability of observing zero events:
$${\rm{CL}}=1-{\epsilon }=1-f(0;\lambda ),$$
(8)
with
$$f(0;\lambda )=\exp \left(-\frac{{T}_{\bar{{\rm{p}}}}}{{\tau }_{\bar{p},{\rm{lower}}}}\right).$$
(9)
This yields a lower limit on the antiproton storage lifetime under our experimental conditions of \({\tau }_{\bar{p},{\rm{lower}}}=7.27\,{\rm{a}}\) at a 68% confidence level.
The pressure limits reported in the main text are based on following approach: the conversion of the storage lifetime into an upper limit for the partial pressure of one residual gas component is performed by calculating the reaction rate on the basis of the cross-section of the annihilation reaction:
$$R=\frac{1}{\tau }=\frac{{v}_{{\rm{rel}}}}{\lambda }=\sigma {n}_{\text{gas}}{v}_{\mathrm{rel}}$$
(10)
where λ is the mean free path of the particle in the residual gas, vrel is the relative velocity between the particle and the gas molecules, σ is the reaction cross-section and ngas is the density of the residual gas. This density is then converted into the pressure p using the ideal gas law:
$${p}_{\mathrm{gas}}={n}_{\mathrm{gas}}{k}_{B}{T}_{\mathrm{gas}}=\frac{{k}_{B}{T}_{\mathrm{gas}}}{\tau \sigma {v}_{\mathrm{rel}}}.$$
(11)
The temperature of the residual gas inside the trap chamber is measured by the thermometer on the magnet coil body, which has a strong thermal connection to the walls of the trap chamber and is typically at Tgas = 4.3 K. We assume here that the residual gas is composed of only hydrogen molecules and helium atoms and that all other gases freeze out in the differential pumping section or trap chamber before reaching the trap centre. Because the residual gas composition is not known, the upper limit on the total pressure in the trap chamber is set by the highest partial pressure limit and the assumption that this component makes up 100 % of the residual gas pressure.
The remaining task is now to insert the annihilation cross-section and the relative velocity. The frequently used cross-section formulas for the annihilation reaction with hydrogen30,40,46,47 trace back to studies about protonium formation51,65,66,67 and approximate the reaction as being with atomic hydrogen. We use the cross-section derived in ref. 66 as
$$\sigma =3\pi {a}_{0}^{2}\sqrt{{E}_{0}/E}=6\pi {a}_{0}^{2}\sqrt{\frac{{E}_{0}}{{m}_{\bar{p}}}}\frac{1}{{v}_{\mathrm{rel}}},$$
(12)
where a0 is the Bohr radius and E0 = 27.2 eV, twice the binding energy of the hydrogen atom. Notably, the 1/vrel scaling makes the reaction rate and consequently the pressure limits independent of vrel and therefore also of the effective noise-temperature of the detection circuit that defines the trapped particle velocity. The same applies for the annihilation cross-section of helium, where the Langevin cross-section is used51, so that a determination of vrel becomes unnecessary to report the pressure limits in the main text.
We also consider a conservative scenario in which the antiproton loss is attributed to annihilation with residual gas rather than to the voltage ramps applied during separation and merging. Under this assumption, a likelihood analysis yields a lower bound on the storage lifetime of \({\tau }_{\bar{p},{\rm{lower}}}=3.6{\rm{a}}\) at the 68% confidence level, with a maximum likelihood estimate of 8.3a. The corresponding pressure constraint relaxes to an upper limit of 4.4 × 10−18 mbar, with a maximum likelihood value of 1.9 × 10−18 mbar, which remains below the upper limit quoted in the main text under the assumption of no annihilation events. Even this conservative bound of 4.4 × 10−18 mbar represents, to our knowledge, the lowest pressure reported for an open cryogenic Penning-trap system and exceeds the minimum operational requirements by more than an order of magnitude. However, given the temporal coincidence of the loss event with the ramp sequence, together with comparable loss behaviour observed for other antiproton clouds under similar manipulation conditions in the same apparatus, a chance annihilation event due to residual gas is highly unlikely.
Inlet valve and vacuum interface
The injection beamline is operated at local pressures from 6 × 10−9 to 3 × 10−8 mbar, determined by the outgassing, conductance and pumping speed along the line. The inlet-chamber pressure is held below 1 × 10−9 mbar using a non-evaporative getter (NEG) pump during trap operation and transport and also a turbomolecular pump while the valves to the injection beamline are open. The differential pumping section is described in ref. 5 and connects the vacuum of the inlet chamber and the trap chamber for the antiproton transfer with a conductance of 0.16 l s−1. It also manages the thermal conductance of the vacuum chamber from room temperature to 4 K by means of a set of concentric tubes. The inlet valve located at the entrance of the differential pumping channel is connected through a copper tube to the 50 K heatshield of the magnet. It is supposed to be opened only for the antiproton transfer and closed during storage and transport operations. This reduces the residual gas flow into the trap chamber and increases the monolayer formation time. The inlet valve used in refs. 5,10 has been exchanged for a newly developed version shown in Extended Data Fig. 5. It improves the sealing, mechanics and heat load compared to the previous version. In particular, the valve head presses on a polytetrafluoroethylene gasket when closing and is supposed to have a lower leak rate than the previously installed metal-on-metal sealed version.
Transport set-up
Extended Data Fig. 6 summarizes the electronic set-up integrated in the transport frame (Fig. 2a) for autonomous operation. The antiproton cloud is confined within the central ring electrode (C08) of the catching trap. Axial confinement is provided by biasing the ring and adjacent correction electrodes with a high-precision voltage supply. All remaining electrodes are grounded through relays at the room-temperature interface.
The antiproton cloud is monitored by means of the noise spectrum of the image-current detector using a sound-card-based FFT system. The cryogenic amplifier is powered by a precision DC supply, and the room-temperature amplifiers operate from battery power. Magnetron sideband cooling is implemented through a waveform generator connected to the radial excitation line of the catching trap. The transport frame further incorporates a LHe heater element on the LHe tank to increase the gas flow for cooling of the magnet heat shields by heat transfer to the cold gas in heat-exchanger elements on the exhaust line. Before transport, the turbomolecular-pump gate valve on the inlet chamber is closed, whereas the NEG-pump valve remains open to maintain vacuum conditions in the inlet chamber. Consequently, continuous power is supplied to the NEG-pump valve to prevent automatic closure during transport.
All transport electronics except the room-temperature amplifiers are powered by a dedicated UPS; the room-temperature amplifiers are powered by their own batteries (Extended Data Fig. 6). The total transport power consumption of the UPS-supported electronics is about 170 W (Extended Data Table 2). The UPS has a capacity of about 750 Wh, providing around 4.5 h of operation after the BASE-STEP apparatus has been disconnected from external power. All voltage supplies, waveform generators, the sound card, sensor readout devices and a telemetry logger are connected to the transport control PC, a frame-mounted mini-PC. It continuously monitors the particle signal, cryostat temperatures, telemetry sensors, LHe level and vacuum pressures. The PC also controls electrode voltages and radio frequency drives for magnetron sideband cooling during transport. After disconnection from external infrastructure, remote access to the transport control PC is established by means of a wireless network.
Further transport data
With the cryocooler switched off, the magnet temperature (Extended Data Fig. 7a) gradually increases. Once the cryocooler is inactive, the pulse tubes act as a thermal conduction path to the magnet, which remains thermally linked to the cryocooler. Consequently, the magnet temperature increases from 4.3 K to an equilibrium value of about 5.2 K. During the 2-h and 43-min transport sequence, about 11 l of LHe helium evaporated, corresponding to nearly half of the initial LHe buffer reservoir.
The overall temperature evolution during antiproton transport was consistent with that observed during the proton transport rehearsal10. During road transport (1.11–1.52 h), accelerations of the transport frame (Extended Data Fig. 7b), including vibration-induced peaks, generated turbulence in the LHe buffer tank. This enhanced magnet cooling and maintained the temperature near 4.6 K throughout truck transport. Transport was performed using a medium-duty truck equipped with air suspension and an automatic transmission. To reduce mechanical shocks and high-frequency vibrations, a 5-t steel plate was installed in the truck bed to soften the effective suspension response during transport.
Transient temperature spikes were observed at 2.57 and 2.72 h of autonomous operation. The first spike occurred during connection of the cryocooler flexlines. During disconnection, a pressure differential developed between the flexlines and the transport-frame-mounted cooling system, with lower pressure in the flexlines. On reconnection, the helium pressure equilibrated, transiently heating the 4 K stage and causing a temporary increase in magnet temperature. The second spike occurred on cryocooler restart at the end of transport. During inactivity, helium gas within the cryocooler warmed, such that initial compressor operation transferred heat into the 4 K stage before steady-state cooling resumed. Following restart of the cooler, the magnet temperature returned to its initial operating temperature.
Roughly 50% of the UPS battery capacity was consumed during transport. During stationary periods, the UPS was temporarily reconnected to external power to preserve battery capacity. Vacuum conditions remained stable throughout transport. Pressure spikes reaching the 10−7-mbar level were observed in the cryostat vacuum chamber and attributed to gas release from the multilayer insulation surrounding the thermal stages of the magnet. In contrast, the inlet-chamber pressure remained below the gauge detection threshold of 1 × 10−9 mbar, with only occasional vibration-induced outgassing spikes below 3 × 10−9 mbar.
