Observation of the effect of gravity on the motion of antimatter

Abstract

Einstein's general theory of relativity from 1915¹ remains the most successful description of gravitation. From the 1919 solar eclipse² to the observation of gravitational waves³, the theory has passed many crucial experimental tests. However, the evolving concepts of dark matter and dark energy illustrate that there is much to be learned about the gravitating content of the universe. Singularities in the general theory of relativity and the lack of a quantum theory of gravity suggest that our picture is incomplete. It is thus prudent to explore gravity in exotic physical systems. Antimatter was unknown to Einstein in 1915. Dirac's theory⁴ appeared in 1928; the positron was observed⁵ in 1932. There has since been much speculation about gravity and antimatter. The theoretical consensus is that any laboratory mass must be attracted⁶ by the Earth, although some authors have considered the cosmological consequences if antimatter should be repelled by matter^7-10. In the general theory of relativity, the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure. Here we show that antihydrogen atoms, released from magnetic confinement in the ALPHA-g apparatus, behave in a way consistent with gravitational attraction to the Earth. Repulsive 'antigravity' is ruled out in this case. This experiment paves the way for precision studies of the magnitude of the gravitational acceleration between anti-atoms and the Earth to test the WEP.

Fig. 1. ALPHA-g apparatus.

a, Cross section of the ALPHA-g apparatus. The full device comprises three antihydrogen trapping regions; only the bottom one is employed here. The MCP detectors are used to image charged particles (e⁻, e⁺, $\overline{\mathrm{p}}$) extracted from the Penning traps for diagnostic purposes. b, Expanded view of the bottom antihydrogen trap (the dashed rectangle in a) illustrating the Penning trap for antihydrogen production and the superconducting coils that form the neutral atom trap. The on-axis, axial field profile at full current is shown on the right. Note that the rTPC, the barrel scintillator and the main solenoid are not drawn to scale here; see Fig. 1a for a scaled image. The mirror coils B–F, the analysis coil, the mini-octupole, the transfer coil and the background coil are not utilized here. The capture solenoid is used for charged particle transfer and manipulations and is de-energized for gravity measurements. The LOc coils (dark blue in the figure) extend past the trapping region used here and constitute part of two additional antihydrogen traps intended for future use.

Fig. 2. Illustrations of the magnetic bias.

a, Expanded view of the end-of-ramp mirror coil peak regions for a bias of −1g (note the discontinuous abscissa). The square points represent offline ECR measurements carried out to determine the field profile and to find the peak field location. The points with red circles indicate the axial locations at which ECR measurements were made at the beginning and end of the mirror coil ramp-down for each gravity trial. b, Calculated on-axis final well shapes (after ramp-down) for the positive bias trials. The features at |z| > 20 cm are due to the OcB (Fig. 1) end turn windings. The vertical dashed lines represent the physical axial midpoints of mirrors A and G.

Fig. 3. Escape histograms.

The raw event z-distributions are displayed as histograms for each of the bias values, including the ±10g calibration runs. These are uncorrected for background or detector relative efficiency. The time window represented here is 10 s to 20 s of the magnet ramp-down. The z-cut regions are indicated by the solid, diagonal lines. Explicitly, the acceptance regions in z are [−32.8, −12.8] and [12.8, 32.8] cm for the ‘down’ and ‘up’ regions, respectively.

Fig. 4. Time structure of the annihilation events from escaped antihydrogen.

The number of detected events (left ordinate) is plotted as a function of time as the magnets are ramped down. This figure represents the sum of the seven trials having bias 0g. The dashed line (right ordinate) illustrates the calculated axial well depth during the magnet ramp-down. The excluded events fail the time cut.

Fig. 5. Escape curve and simulations.

The derived P_dn values are plotted versus bias for the experimental data and for simulations of the experiment for three values of the gravitational acceleration $a_{\overline{g}}$: 1g (normal gravity, orange), 0g (no gravity, green) and −1g (repulsive gravity, violet). See the text for the definitions of the uncertainties. The right ordinate is the down-up asymmetry A = 2P_dn− 1. The confidence intervals on the no- and repulsive gravity simulations are comparable to those for the normal gravity simulation and have been omitted for clarity.

Extended Data Fig. 1. Simulated escape curves for various values of ag¯.

We illustrate the escape curves resulting from assuming several different values of the gravitational acceleration, $a_{\overline{g}}$, of antimatter due to the Earth. See the legend for details. The simulations are otherwise identical to that used for the 20 s release experiment and normal gravity (Fig. 5). The solid blue curve represents expectations for normal gravity.

Extended Data Fig. 2. Escape curve for 130 s ramp-down.

The P_dn values are plotted versus bias for the three trial sets having biases 0 g, −1 g, and −2 g. These biases were chosen after the 20 s ramp results had been examined. Apart from the slower ramp, the experimental and analysis procedures were identical to those for the 20 s protocol. The 20 s data and simulations for both ramp times are also shown for comparison. Note that the simulated escape curve for the 130 s ramp has a steeper transition region than for the 20 s ramp, and the balance point (P_dn = 0.5) is not at a bias of precisely −1 g, as described in the text.

Extended Data Fig. 3. Escape curve for atoms escaping after 20 s.

The escape curve (green points) for the time period (20–80 s) after the mirrors A and G have stopped ramping down and are held at constant current while the ECR measurement is prepared. The main (10–20 s) data set (blue points) is shown for comparison. Note that the bias values and their uncertainties for the green points are assumed to be the same as for the blue points. This assumption should be valid within the uncertainties. The vertical error bars are obtained by following the same procedure described in the text. The blue (green) curve is based on 1,722 (621) total events as defined in Table 1.

Extended Data Fig. 4. rTPC resolution: a measured z-distribution of annihilation vertices from antiprotons held in a Penning trap.

An approximately point-like source of events is obtained from antiprotons annihilating on residual gas while being held for 2000 s in a short Penning trap. The reconstructed vertex distribution in z (points with error bars) is fitted with two Gaussians and a flat background. The two distributions have standard deviation 1.5 cm (Gaussian 1; ~70% of the counts) and 4.2 cm (Gaussian 2, ~24% of the counts). Both widths are significantly smaller than the distance between mirrors A and G (25.6 cm, magnet centres illustrated by the green vertical lines).

Extended Data Fig. 5. Laser based rTPC calibration and comparison with Garfield++ simulation predictions.

a The green bars denote the measured drift times of laser-induced photoelectrons released from nine aluminium strips on the inner cathode surface of the rTPC (Methods). The green dashed line is the predicted drift time from the Garfield++ model used in the detector physics analysis. Each green bar denotes the range of drift times measured during the period of the physics measurement campaign, while the dash in each bar denotes the average drift time over those measurements. Vertical dashed lines indicate the axial midpoints of mirrors A and G. b The red circles denote measurements, at five z-locations, of the Lorentz displacement, i.e., the azimuthal displacement of the radially drifted photoelectrons at the location of the anode wires (r = 18.2 cm). The error bars are due to the fit error and are smaller than the plotting symbols except at the vertical position 0 cm. The two points for each z are measured at different initial azimuthal positions. The red dashed line denotes the prediction from the same Garfield++ simulation model. Note that vertical scales are magnified for both figures.

Extended Data Fig. 6. Decay of persistent fields (offline measurements).

The on-axis fields at the axial midpoint (Fig. 2a) of mirrors A and G, as measured by the rapid cycle ECR technique (Methods) to study the decay of persistent fields after the end of the 20 s ramp. The solid lines are fits using two exponential decay times per curve; see Methods. The three plots are for the extreme biases ±3 g and 0 g. The red points represent the extracted systematic error in the magnetic field difference between mirror A and mirror G at each bias, and they are plotted at the approximate time of the ECR resonance in the actual gravity trials. ‘Offline’ refers to measurements taken independently of the release experiments.

Extended Data Fig. 7. Magnetic field measurements via the magnetron frequency.

Magnetic field measured using the magnetron frequency of electron clouds in the centre of mirror A versus time during the magnet ramp-down. a Raw measurements (blue) are compared to the expected linear ramp (green line). b The difference between the measurements and the expected linear ramp is plotted versus time. c Measurements after accounting for the three corrections described in Methods. The 1–2 s gaps in the data are due to a memory limitation in the FPGA that controls the electrode voltages. New voltage instructions are loaded in this time.

Extended Data Fig. 8. Time dependence of the bias.

The solid curve represents the modelled deviation of the bias from the nominal value (in this case 0 g) as a function of time during the mirror ramp-down. The histogram shows the number of events detected as a function of time for the 0 g trials, as in Fig. 4. The red point shows the derived bias and its uncertainty. Note that the bias deviation during the time data are collected is less than 0.1 g. See Methods.

Extended Data Fig. 9. Schematic diagram of the circuit for energizing mirrors A and G (MAG) in series and supplying the differential current (MGDiff) to mirror G only.

The power supplies are described in Methods and Extended Data Table 1. QPU stands for ‘quench protection unit’.