Characterization of the 1S-2S transition in antihydrogen

Abstract

In 1928, Dirac published an equation ¹ that combined quantum mechanics and special relativity. Negative-energy solutions to this equation, rather than being unphysical as initially thought, represented a class of hitherto unobserved and unimagined particles-antimatter. The existence of particles of antimatter was confirmed with the discovery of the positron ² (or anti-electron) by Anderson in 1932, but it is still unknown why matter, rather than antimatter, survived after the Big Bang. As a result, experimental studies of antimatter^3-7, including tests of fundamental symmetries such as charge-parity and charge-parity-time, and searches for evidence of primordial antimatter, such as antihelium nuclei, have high priority in contemporary physics research. The fundamental role of the hydrogen atom in the evolution of the Universe and in the historical development of our understanding of quantum physics makes its antimatter counterpart-the antihydrogen atom-of particular interest. Current standard-model physics requires that hydrogen and antihydrogen have the same energy levels and spectral lines. The laser-driven 1S-2S transition was recently observed ⁸ in antihydrogen. Here we characterize one of the hyperfine components of this transition using magnetically trapped atoms of antihydrogen and compare it to model calculations for hydrogen in our apparatus. We find that the shape of the spectral line agrees very well with that expected for hydrogen and that the resonance frequency agrees with that in hydrogen to about 5 kilohertz out of 2.5 × 10¹⁵ hertz. This is consistent with charge-parity-time invariance at a relative precision of 2 × 10^-12-two orders of magnitude more precise than the previous determination ⁸ -corresponding to an absolute energy sensitivity of 2 × 10^-20 GeV.

Fig. 1. The ALPHA-2 central apparatus and magnetic field profile.

a, b, Penning traps, comprising stacks of cylindrical electrodes immersed in a uniform axial magnetic field generated by an external solenoid (not shown), are used to confine and manipulate antiprotons ($\overline{p}$) and positrons (e⁺) to produce antihydrogen. Cold (less that 0.5 K) anti-atoms can be trapped radially by the octupole field and axially by the magnetic well that is formed by the five mirror coils and plotted in b. The 243-nm laser light is injected from the antiproton side (left in a) and is aligned and position-stabilized on the fixed optical cavity axis. The laser beam crosses the trap axis at an angle of 2.3°. The piezoelectric actuator behind the output coupler is used to modulate the cavity length to lock the cavity to the laser frequency. The axial scale in a and b is the same; the radial extent of the annihilation detector is larger than illustrated. The vacuum window and photo-diode are further to the right (by about 1 m) than illustrated. The brown-shaded electrodes are used to apply blocking potentials during the experimental trials to ensure that antiprotons that result from ionization are confined to annihilate in the active volume of the detector.

Fig. 2. Hydrogenic energy levels.

Calculated energies (E; for hydrogen) of the hyperfine sublevels of the 1 S (bottom) and 2 S (top) states are plotted against magnetic field strength. The centroid energy difference E_1S–2S = 2.4661 × 10¹⁵ Hz has been suppressed on the vertical axis. The vertical black arrow indicates the two-photon laser transition probed here (frequency f_d–d); the red arrow illustrates the microwave transition used to remove the 1S_c state atoms (frequency f_c–b).

Fig. 3. Spectral line of antihydrogen.

a, The complete dataset, scaled as described in the text. The simulated curve (not a fit, drawn for qualitative comparison only) is for a stored cavity power of 1 W and is scaled to the data at zero detuning. ‘Appearance’ refers to annihilations that are detected during laser irradiation; ‘disappearance’ refers to atoms that are apparently missing from the surviving sample. The error bars are 1-s.d. counting uncertainties. b, Three simulated line shapes (for hydrogen) are depicted for different cavity powers to illustrate the effect of power on the size and the frequency at the peak. The width of the simulated line (FWHM) as a function of laser power is plotted in the inset.

Extended Data Fig. 1. Time evolution of the dataset.

The integrated number of atoms is plotted against the trial number for the four detunings D (−200 kHz, −100 kHz, 0 kHz and 100 kHz) in set 1. The error bars are 1-s.d. counting uncertainties.

Extended Data Fig. 2. Simulation fitting functions.

The points (crosses) from the numerical simulation are plotted for various cavity powers. The solid lines represent fits to the simulation by a piecewise-analytic function. The coloured surface represents the interpolation used to fit the experimental data.