The zero-field ground-state hyperfine splitting of antihydrogen and the unobserved antiproton spin-flip transition

The first observation of the hyperfine spectrum of antihydrogen (ALPHA, 2017) detected the two positron spin-flip transitions in a magnetic minimum trap and determined the ground-state hyperfine splitting to 400 parts per million, while explicitly deferring several goals: a field-free (zero-magnetic-field) determination using an in-flight antihydrogen beam, and observation of the nuclear-magnetic-resonance-type antiproton spin-flip transition between the two trapped hyperfine sublevels. Later work by the ALPHA collaboration has now resolved the trapped-atom precision core, measuring the splitting to 4 ppm at a 1-T trap field. The surviving open core of the source question is therefore: determine the antihydrogen ground-state hyperfine splitting at essentially zero magnetic field, where it is directly comparable to the hydrogen-maser value known to 7 parts in 10^13, and observe for the first time the antiproton spin-flip ($|c\rangle\leftrightarrow|d\rangle$) transition — the remaining ingredients needed to complete the hyperfine-structure characterization of antihydrogen for CPT and Lorentz-symmetry tests.

Background

Antihydrogen, the bound state of an antiproton and a positron, is the antimatter counterpart of hydrogen and a clean system for testing CPT symmetry (the theorem that the laws of physics are invariant under simultaneous charge conjugation, parity inversion, and time reversal), which predicts identical spectra for hydrogen and antihydrogen. In the ground state, the interaction of the positron spin with the antiproton spin splits the $1S$ level into a hyperfine doublet of total spin $F=0$ and $F=1$, separated by the hyperfine splitting energy $a_{1S}$; in hydrogen this corresponds to the famous 21-cm line, known from the hydrogen maser (the microwave frequency standard locked to this transition) to about 7 parts in $10^{13}$. In a static magnetic field $B$ the levels are further Zeeman-split (through the interaction of the atomic magnetic moments with the field) into four sublevels, conventionally labelled $|a\rangle$, $|b\rangle$, $|c\rangle$, $|d\rangle$ in order of increasing energy; in the high-field limit these correspond to definite spin states $|a\rangle=|\uparrow\Downarrow\rangle$, $|b\rangle=|\uparrow\Uparrow\rangle$, $|c\rangle=|\downarrow\Uparrow\rangle$, $|d\rangle=|\downarrow\Downarrow\rangle$ (positron spin first, antiproton spin second), while at zero field $|b\rangle$, $|c\rangle$, $|d\rangle$ become the degenerate $F=1$ triplet and $|a\rangle$ the $F=0$ singlet. The states $|c\rangle$ and $|d\rangle$ are low-field seekers (their energy increases with field) and can be confined in a magnetic-minimum trap, whereas $|a\rangle$ and $|b\rangle$ are high-field seekers that are expelled and annihilate on the trap wall. The ALPHA experiment at CERN's Antiproton Decelerator (the facility that supplies slow antiprotons) traps antihydrogen in such a minimum-$B$ trap and probes it with microwaves: driving the positron spin-flip transitions $|c\rangle\rightarrow|b\rangle$ or $|d\rangle\rightarrow|a\rangle$ ejects the atom, and the resonant frequencies at the trap's field minimum differ exactly by $a_{1S}/h$, independent of the trap field. In 2017 ALPHA observed both transitions and obtained $a_{1S}/h = 1420.4 \pm 0.5$ MHz (400 ppm) from the difference of the two onset frequencies (Ahmadi et al. 2017). The paper explicitly acknowledged open issues: the in situ microwave magnetic field $B_{\mathrm{MW}}$ that drives the transitions was only estimated from the measured microwave electric field via $B_{\mathrm{MW}} = E_{\mathrm{MW}}/c$, since the Penning-trap electrode stack (the nested cylindrical electrodes used to confine the charged particles electrically) supports a complex mixture of standing and travelling waves; the more gradual onset of the $|d\rangle\rightarrow|a\rangle$ line (attributed to a lower in situ $B_{\mathrm{MW}}$) complicated line-shape interpretation, which the authors deferred; and improved precision would require smaller frequency steps, balanced microwave power (limited by thermal effects in the cryogenic ultrahigh-vacuum system), and better trap-field characterization and stabilization. The paper also stated plans to measure the same quantity in zero magnetic field using a beam of antihydrogen, and noted that the nuclear-magnetic-resonance (NMR)-type transition between $|c\rangle$ and $|d\rangle$ — an antiproton spin flip — was of interest and feasible with improved trapping, but not yet observed. Physically, the hyperfine splitting is sensitive to the internal structure of the (anti)proton through the Zemach correction (the convolution of the charge and magnetization distributions) and nuclear magnetic polarizability, which contribute at the level of about 40 ppm in hydrogen; it is therefore a complementary CPT probe to the parts-per-trillion $1S$–$2S$ comparison, and a target for constraining spin-dependent Lorentz- and CPT-violating coefficients in the Standard-Model Extension (SME), the effective field theory for such violations. The ASACUSA collaboration at CERN pursues the complementary beam approach: a cusp-trap antihydrogen source (a nested charged-particle trap with a cusp-shaped magnetic field that forms antihydrogen and extracts it along the axis as a beam) feeding a Rabi-type microwave spectrometer (the classic atomic-beam method, with spin-state selectors before and after a microwave interaction region, in which a resonance appears as a change in transmitted flux) in a field-free region, validated on hydrogen to a relative precision of $2.7\times10^{-9}$ (Diermaier et al. 2017).

Problem Statement

The 2017 observation of the hyperfine spectrum of antihydrogen established two positron spin-flip transitions in a magnetic-minimum trap and a 400-ppm value of the ground-state hyperfine splitting $a_{1S}$ there, and its stated programme included several goals. The trapped-atom precision goal has since been achieved (4 ppm at a 1-T trap field; Akbari et al. 2026). The surviving, source-faithful open problem is to complete the ground-state hyperfine-structure characterization of antihydrogen, namely: (1) determine $a_{1S}$ of antihydrogen at essentially zero magnetic field, the field-free configuration directly comparable to the hydrogen-maser determination (7 parts in $10^{13}$); (2) observe for the first time the NMR-type antiproton spin-flip transition $|c\rangle\leftrightarrow|d\rangle$ between the two trapped hyperfine sublevels, including a means of detecting the flip given that both states remain trapped; and (3) quantify and control the associated systematics, in particular the in situ microwave magnetic field driving the transitions, which remains 'not well understood' inside the trap electrode structure, and trap-field drifts. These components jointly support one objective: extend the hydrogen–antihydrogen hyperfine comparison, including the field-free splitting and eventually detailed line shapes, to the precision at which antiproton internal-structure contributions (Zemach radius and magnetic polarizability, ~40 ppm scale) and spin-dependent CPT- or Lorentz-violating effects can be resolved or bounded.

References

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