Observation of the 1S–2P Lyman-α transition in antihydrogen

In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum1,2. The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now know governs the world at the atomic scale. Since then, studies involving the Lyman-α line—the 1S–2P transition at a wavelength of 121.6 nanometres—have played an important part in physics and astronomy, as one of the most fundamental atomic transitions in the Universe. For example, this transition has long been used by astronomers studying the intergalactic medium and testing cosmological models via the so-called ‘Lyman-α forest’3 of absorption lines at different redshifts. Here we report the observation of the Lyman-α transition in the antihydrogen atom, the antimatter counterpart of hydrogen. Using narrow-line-width, nanosecond-pulsed laser radiation, the 1S–2P transition was excited in magnetically trapped antihydrogen. The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 ± 0.12 gigahertz (1σ uncertainty) and agrees with the prediction for hydrogen to a precision of 5 × 10−8. Comparisons of the properties of antihydrogen with those of its well-studied matter equivalent allow precision tests of fundamental symmetries between matter and antimatter. Alongside the ground-state hyperfine4,5 and 1S–2S transitions6,7 recently observed in antihydrogen, the Lyman-α transition will permit laser cooling of antihydrogen8,9, thus providing a cold and dense sample of anti-atoms for precision spectroscopy and gravity measurements10. In addition to the observation of this fundamental transition, this work represents both a decisive technological step towards laser cooling of antihydrogen, and the extension of antimatter spectroscopy to quantum states possessing orbital angular momentum.

In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum 1,2 . The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now know governs the world at the atomic scale. Since then, studies involving the Lyman-α line-the 1S-2P transition at a wavelength of 121.6 nanometres-have played an important part in physics and astronomy, as one of the most fundamental atomic transitions in the Universe. For example, this transition has long been used by astronomers studying the intergalactic medium and testing cosmological models via the so-called 'Lyman-α forest' 3 of absorption lines at different redshifts. Here we report the observation of the Lyman-α transition in the antihydrogen atom, the antimatter counterpart of hydrogen. Using narrow-line-width, nanosecond-pulsed laser radiation, the 1S-2P transition was excited in magnetically trapped antihydrogen. The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 ± 0.12 gigahertz (1σ uncertainty) and agrees with the prediction for hydrogen to a precision of 5 × 10 −8 . Comparisons of the properties of antihydrogen with those of its well-studied matter equivalent allow precision tests of fundamental symmetries between matter and antimatter. Alongside the ground-state hyperfine 4,5 and 1S-2S transitions 6,7 recently observed in antihydrogen, the Lyman-α transition will permit laser cooling of antihydrogen 8,9 , thus providing a cold and dense sample of anti-atoms for precision spectroscopy and gravity measurements 10 . In addition to the observation of this fundamental transition, this work represents both a decisive technological step towards laser cooling of antihydrogen, and the extension of antimatter spectroscopy to quantum states possessing orbital angular momentum.
Challenges to antimatter Lyman-α spectroscopy include the difficulty of fabricating optical components and continuous-wave 11 or pulsed laser sources at these extremely short wavelengths, as well as the scarcity of anti-atoms. The current observation was made possible

OPEN
Letter reSeArCH by a number of technical advances, including the development of a solid-state-based, pulsed Lyman-α source 12 , implementation of innovative plasma control techniques 13 , and the ALPHA Collaboration's recent, marked improvement in antihydrogen trapping and accumulation or 'stacking' rate. Stacking provides a sample of several hundred anti-atoms 14 , accumulated over several hours. Taking advantage of a nanosecond-scale laser pulse and our low-background annihilation detection, we have also inferred information on the antihydrogen velocity distribution.
Because matter and antimatter annihilate each other when they meet, antihydrogen must be created and then trapped in strong, inhomogeneous magnetic fields in an ultrahigh-vacuum chamber. The ALPHA-2 apparatus (Fig. 1a) is designed to combine antiprotons from CERN's Antiproton Decelerator 15 with positrons from a positron accumulator 16,17 to produce and to trap atoms of antihydrogen. The techniques that we have developed to produce antihydrogen cold enough (below 0.54 K) to trap can be found elsewhere 13,14,18,19 . A typical trapping trial in ALPHA-2 involves mixing about 90,000 antiprotons and three million positrons to produce 50,000 antihydrogen atoms. Most of the antihydrogen atoms produced are either too energetic or in the wrong quantum state to be captured; typically 10-20 anti-atoms are trapped in one four-minute-long mixing cycle. We have employed the stacking technique referred to above to increase the total number of trapped antihydrogen atoms to several hundred for each measurement sequence.
The trapped anti-atoms are confined by the interaction of their magnetic moments with the inhomogeneous magnetic field, shown in Fig. 1b, c. The cylindrical trapping volume for antihydrogen has a diameter of 44.35 mm and an axial length of 280 mm. The magnetic field minimum of 1.033 T is near the centre of the trap, where the field is oriented axially. The field strength is flat to within one part in 10,000 in a 60 mm (axial) by 4.5 mm (radial) volume around the centre of the trap. The maximum field differential in the trap is 0.82 T along the axial direction and about 0.85 T along the radial direction. Figure 2 shows the energy levels of hydrogen in the 1S and 2P states in a magnetic field. The 2S state is also depicted for reference. Antihydrogen atoms in the states labelled as 1S c and 1S d can be trapped. At zero magnetic field, the excited 2P state splits into two states (2P 3/2 and 2P 1/2 ) owing to the relativistic spin-orbit interaction. In non-zero magnetic fields, due to the Zeeman effect, the 2P 3/2 state splits into four sublevels, while the 2P 1/2 state splits into two. Each of these sublevels in turn splits into two states owing to the nuclear spin of the antiproton, but the splitting is much smaller (less than 0.1 GHz) than that in the ground (1S) state, and is therefore not visible on the scale of Fig. 2.
The 1S-2P c transition studied here is a dipole-allowed transition. When antihydrogen is excited to one of the 2P sublevels, the excited state decays to the ground 1S state within a few nanoseconds by emitting a photon at 121.6 nm. Owing to the mixing of the positron spin states, there is a non-zero probability that the excited atom decays to either the 1S a or 1S b state instead of the original 1S c or 1S d state. Those that decay to the 1S a or 1S b state escape and annihilate at the trap walls and can be detected by the ALPHA-2 silicon vertex detector. The silicon vertex detector affords us single-atom detection capability, which is key to antimatter spectroscopy with few atoms 4,5 . The silicon vertex detector tracks the charged pions from the antiproton annihilation; the pion tracks are reconstructed to determine the location (vertex) of each annihilation. We employ machine-learning techniques, incorporating several parameters from the detector and the track reconstruction in a multi-variate analysis 20 (MVA; see Methods), to distinguish antiproton annihilations from the cosmic ray background.
In this experiment, the antihydrogen atoms were excited to the 2P c state (Fig. 2) by light that was linearly polarized, the polarization vector being nearly perpendicular to the direction of the axial magnetic field. Narrow-line-width (about 65 MHz), pulsed (about 12-ns duration) laser radiation at 121.6 nm was used for the excitation. The system is described in detail in Methods, and the schematic diagram of the laser system is shown in Extended Data Fig. 1.
For each experimental sequence, about 500 antihydrogen atoms were accumulated in the trapping region by multiple stacking (typically 30 stacks) over an approximately two-hour period. Experience from past microwave manipulation experiments 5,6 indicates that the 1S c and 1S d states are equally populated in the initially trapped sample. The trapped atoms were irradiated for about two hours by laser pulses using a 10-Hz repetition rate. During each two-hour sequence, the trapped atoms were exposed to radiation at twelve different frequencies around the calculated hydrogen resonance frequency of 2,466,051.625 GHz (using the average of the two 1S hyperfine levels). The magnetic field magnitude was determined by electron cyclotron resonance 21 . The frequency detunings ranged from −2.47 GHz to +0.85 GHz. The laser frequency was switched every 20 s in a pattern designed to minimize saturation and depletion effects (due to the finite population size) at each frequency. After each two-hour exposure, the remaining antihydrogen atoms were released and counted by ramping down the trap magnets in 15.6 s. We repeated the described sequence four times. The number of detected events is summarized in Table 1. With average laser pulse energies between 0.53 nJ and 0.65 nJ, about 60% of the trapped antihydrogen atoms were expelled and detected during the exposure time of two hours.
Because the laser is pulsed, and the excitation light is present for about 12 ns for each pulse, the annihilation events due to the excitation  Letter reSeArCH are only expected to occur in the approximately 1-ms time window in which the untrapped atoms are forced to the trap wall. This greatly helps us to distinguish between signals due to laser-driven annihilations and those due to cosmic background. Figure 3 illustrates the power of the pulsed excitation method by comparing (1)  With the MVA (red line) the background almost disappears. In Fig. 3c, d we present two-dimensional plots for the axial position versus the TOF of the annihilation events. These plots also illustrate the selection criteria or 'cuts' (0 ms < t < 1 ms and −100 mm < z < 100 mm) used to accept events for the spectral shape determination described below. These cuts were predetermined on the basis of simulation information. Figure 4a shows the spectral line shape of the transition, obtained using events with the above cuts applied. In this plot, the probability is normalized to the pulse energy; we have thus assumed that the excitation probability is linearly proportional to the laser pulse energy. The plotted data show that the transition from the 1S c and 1S d states to the 2P c state has a line width of about 1.5 GHz (full-width at half-maximum, FWHM). If the hyperfine coupling constants of antihydrogen between the 1S and 2P states are the same as those for normal hydrogen, the spectrum in the magnetic field of 1.033 T would comprise two lines with a separation of 0.74 GHz. The two distinct lines are caused by the possible orientations of the antiproton nuclear spin in the 1S ground state. However, this hyperfine splitting is not resolved under the present experimental conditions owing to the Doppler broadening of the transitions caused by the motion of trapped antihydrogen atoms parallel with the laser beam. We note that the Doppler shift of the Lyman-α transition of hydrogen with a velocity of 75 m s −1 (characteristic for our magnetic trap depth) is 0.6 GHz. A fit to the measured data yields a resonant frequency of 2,466,051.7(0.12) GHz, in good agreement with the calculated hydrogen frequency quoted above. The contributions to the quoted uncertainty of 0.12 GHz are the wavemeter accuracy (0.06 GHz), the 730-nm laser (Methods) cavity lock stability (0.06 GHz), modelling uncertainties (0.07 GHz), and the statistical uncertainty in the curve fit (0.04 GHz). Many of these uncertainties may be reduced in the future, but the large natural line width of 2π × 99.6 MHz is an obstacle to using the Lyman-α transition for very high-precision measurements as tests of charge-parity-time-reversal (CPT) invariance.
The kinetic energy distribution of the trapped anti-atoms is also of interest. We expect, from previous measurements and simulations of the antihydrogen production and trapping processes 22 , that the trapped antihydrogen atoms are not in thermal equilibrium. Our standard model for antihydrogen formation is that the atoms are formed from antiprotons in equilibrium with the positron cloud, which has a temperature of about 20 K. The expected distribution of trapped atoms thus comprises the low-temperature tail of a Maxwellian distribution, truncated at the maximum trap depth of about 0.5 K. The measured line shape of the transition should thus be different from a Gaussian shape for a Doppler-broadened line. Therefore, we carried out detailed simulations (Methods), based on the known physics of hydrogen, to determine the expected line shape and intensity of the transition in our experimental environment. The simulated line shape is model dependent. Two examples of simulated results are shown in Fig. 4a in red and in blue. The calculated transition probability and line width match the data reasonably well over the region measured. The general agreement between the simulation and the observed spectral feature indicates that the observed line shape is indeed dominated by Doppler broadening, corresponding to an average energy of a few hundred millikelvin. The total number of antihydrogen atoms detected during the laser irradiation and during the release of remaining atoms is tabulated for each sequence. The MVA identifies annihilations with an efficiency of 0.807 for the laser irradiation and 0.851 for the release of the remaining atoms. a, Temporal distribution of detected signals between −2 ms and 10 ms with respect to the laser pulse. The laser frequency was at the resonance of the 1S-2P transition (detuning 0 GHz). The black trace shows the raw detector triggers. The red trace shows events after background suppression due to an MVA-based machine-learning algorithm. The y axis is the total number of counts (bin size, 50 μs) for 24,000 pulses at the resonant frequency. b, Same as a, but the laser frequency was off-resonance; the detuning was −2.47 GHz. c, The axial position of the annihilation events is plotted versus the TOF. The detuning was 0 GHz. d, Same as c, but the detuning was −2.47 GHz. Events within the dashed box for each laser frequency were selected for the spectral shape determination (Fig. 4a). Figure 4b compares the time distribution of the detected signals following the laser pulse (black) to a simulated distribution (red) obtained using the standard formation model. The agreement between the simulation and the detected signal for these TOF distributions confirms that the radial velocity distribution of trapped antihydrogen is consistent with the model. For comparison, we have also simulated the TOF distribution of ejected atoms originating from hypothetical thermal distributions of 100 mK and 10 mK (Fig. 4b), which indicates that the detected time distribution should be sensitive to the radial temperature of trapped antihydrogen. In Fig. 4c we plot the measured axial distribution of laser-induced annihilation events, and we compare it to simulated results at various temperatures. These distributions also exhibit some dependence on antihydrogen temperature and may facilitate diagnosis of future laser cooling attempts.

Letter reSeArCH
In conclusion, we have reported here the observation of the 1S-2P, Lyman-α transition in antihydrogen, based on 966 detected events and an estimated background of 14 events. The frequency of this fundamental anti-atomic transition is determined to a precision of about 5 × 10 −8 , via narrow-line-width, nanosecond-pulsed, vacuum-ultraviolet laser spectroscopy. We also report a method of directly characterizing the kinetic energy of anti-atoms from their TOF to annihilation, following the laser-induced transition. These observations represent very important steps in the field of low-energy antimatter studies [23][24][25][26][27] . The techniques of optical manipulations and laser cooling, which have revolutionized the field of atomic physics over the past few decades, are about to be applied to anti-atoms. With its natural line width of about 100 MHz (comparable to our laser width), the Lyman-α transition can in principle be employed to cool antihydrogen to the 2.4-mK Doppler limit. Our simulations predict that cooling to about 20 mK is possible with the current ALPHA-2 set-up 9 . This, combined with other planned improvements, would reduce the 1S-2S transition line width by more than an order of magnitude and should eventually allow various other spectroscopic measurements with precisions approaching those achieved in hydrogen [28][29][30] . At such levels of precision, antihydrogen spectroscopy will have an impact on the determination of fundamental constants 31 , in addition to providing elegant tests of CPT symmetry. Furthermore, laser cooling will be crucial for a precision test of the weak equivalence principle via antihydrogen free fall 10 or antiatom interferometry 32 at the 10 −2 level and beyond. Access to the 2P state in antihydrogen greatly expands the future experimental horizon; for example, we will now be able to study fine-structure effects in an anti-atom.

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Any Methods, including any statements of data availability and Nature Research reporting summaries, along with any additional references and Source Data files, are available in the online version of the paper at https://doi.org/10.1038/s41586-018-0435-1.