Precision laser spectroscopy experiments on antiprotonic helium

At CERN’s Antiproton Decelerator (AD) facility, the Atomic Spectroscopy and Collisions Using Slow Antiprotons (ASACUSA) collaboration is carrying out precise laser spectroscopy experiments on antiprotonic helium (pHe ⌘ p + He + e−) atoms. By employing bu↵er-gas cooling techniques in a cryogenic gas target, samples of atoms were cooled to temperature T = 1.5–1.7 K, thereby reducing the Doppler width in the single-photon resonance lines. By comparing the results with three-body quantum electrodynamics calculations, the antiproton-to-electron mass ratio was determined as Mp/me = 1836.1526734(15). This agreed with the known proton-to-electron mass ratio with a precision of 8 ⇥ 10−10. Further improvements in the experimental precision are currently being attempted. The high-quality antiproton beam provided by the future Extra Low Energy Antiproton Ring (ELENA) facility should further increase the experimental precision.


Introduction
The metastable antiprotonic helium (pHe + ⌘ p + He 2+ + e − ) atom is an exotic long-lived system made of a helium nucleus, an electron in the ground state, and an antiproton occupying a Rydberg state of principal and orbital angular momentum quantum numbers n ⇠`− 1 ⇠ 38 [1][2][3]. The unusual longevity of the atom allows us to measure its transition frequencies by laser spectroscopy. By comparing the values with the results of three-body quantum electrodynamics (QED) calculations, the antiproton-to-electron mass ratio M p /m e can in principle be determined with a relative precision of ⇠ 10 −11 [4][5][6]. This corresponds to the best determinations of the proton-to-electron mass ratio M p /m e obtained from Penning trap experiments [7][8][9][10][11], or laser spectroscopy of HD + molecular ions [12][13][14]. The pHe + experiments also provide a consistency test of CPT symmetry [15], which may be complementary to the spectroscopy experiments on antihydrogen atoms [16][17][18]. It provides experimental constraints on any exotic fifth force that may exist at the ⇠ 1 Å length scale [19][20][21][22].
The atoms can be readily synthesized via the reaction, p + He ! pHe + + e − , by allowing an antiproton beam [23] to come to rest in a helium gas target [24][25][26]. The transition frequencies of pHe + spanning the infrared to ultraviolet range have been calculated [4][5][6] to a relative precision of ⇠ 10 −10 by evaluating the quantum electrodynamics (QED) corrections up to order m e ↵ 7 in atomic units. Here m e and ↵ respectively denote the electron mass and the fine structure constant. These calculations used the International Council for  [3] used to synthesize pHe + and cool them to temperature T = 1.5-1.7 K (top). Laser system used for single-photon spectroscopy (bottom).
Science Committee on Data for Science and Technology (CODATA) 2010 recommended values of the fundamental constants [27], including the fine structure constant ↵, the 3 He-and 4 He-to-electron mass ratios, the Bohr radius, and the Rydberg constant. The corrections to the transition frequencies that arise from the finite charge radii of the helium nucleus (4 to 7 MHz) and of the antiproton [28] (< 1 MHz) are small because the spatial overlap between the Rydberg antiproton orbital and the nucleus is relatively small, and because the antiproton is polarized away from the 1s electron in the atom.

Buffer gas cooling of pHe + atoms
The thermal motions of pHe + in the experimental target at temperature T broadens the width of the measured single-photon laser resonances by a factor, ⌫ p 8k B T log 2/Mc 2 . Here ⌫ denotes the transition frequency, k B the Boltzmann constant, M the atom's mass, and c the speed of light. This loss in the spectral resolution limited [29,30] the precision of determining the resonance centroid to around 10 −7 -10 −8 . One way to reach a precision beyond this Doppler limit was provided by two-photon spectroscopy [2,31], in which the pHe + was irradiated by two counterpropagating ultraviolet laser beams.
An alternative method involved cooling some 2 ⇥ 10 9 pHe + atoms to a temperature T = 1.5-1.7 K, by allowing the pHe + to undergo elastic collisions with cryogenic helium gas [3]. This cooling behavior is in contrast to some other kinds of hadronic exotic atoms, such as pionic hydrogen [32], which was found to be heated by collisions with H 2 molecules that deexcite the atom. The density of the bu↵er gas (T ⇠ 1.5 K and P = 40-170 Pa) used in the experiment was carefully adjusted so that the pHe + atoms, once formed, rapidly underwent a few hundred or more cooling collisions. It was then interrogated by the resonant laser beam. The 1s electron protected a significant fraction of the pHe + from annihilation during this cooling.
The experiment (Fig. 1) was carried out by utilizing the pulsed beam of AD that contained between 2 ⇥ 10 7 and 3 ⇥ 10 7 antiprotons with a kinetic energy E = 5.3 MeV and repetition rate f = 0.01 Hz. Some of the antiprotons were slowed down to E = 75 keV by allowing them to traverse a 3 m long radiofrequency quadrupole decelerator [29,33]. This setup was also recently used to attempt to measure the annihilation cross sections of antiprotons that traversed some thin target foils [34][35][36][37][38]. The emerging 75-keV antiprotons were transported by a beamline and allowed to enter the cryogenic helium gas target. The target was in thermal contact with an open-cycle Joule-Thomson cryocooler at temperature T = 1.3 K. The pHe + were irradiated by ∆t = 40 to 100 ns long laser pulses [39] with peak powers P = 0.5 to 10 kW and wavelengths λ = 264 to 841 nm, which were generated by Ti:Sapphire and dye laser systems.
The spectra in Figs  Eight transition frequencies of p 4 He + atoms and five frequencies of p 3 He + were measured with relative uncertainties between 2.5 ⇥ 10 −9 and 15 ⇥ 10 −9 . The frequencies ⌫ exp (Fig.  3A, open circles with error bars) agree with theoretical ⌫ th values (filled squares). Due to the cooling techniques described here, this agreement is a factor of 1.4 to 10 times better than previous single-photon experiments [30] of pHe + . The uncertainties for most of the theoretical frequencies ⌫ th arise from QED contributions of orders higher than m e ↵ 7 which have not been calculated yet. When the antiproton-to-electron mass ratio M p /m e used in the calculations was changed by 1 ⇥ 10 −9 , the theoretical pHe + frequencies ⌫ th changed by 2.6 ⇥ 10 −9 to 2.7 ⇥ 10 −9 . The mass ratio was determined as, M p /m e = 1836.1526734 (15), by minimizing the di↵erence between the frequencies ⌫ exp and ⌫ th . The one-standard deviation uncertainty in the parenthesis includes the three contributions 9 ⇥ 10 −7 , 11 ⇥ 10 −7 , and 3 ⇥ 10 −7 of the experimental statistical and systematic uncertainties, and the theoretical uncertainty, respectively.
The atomic mass of the electron was recently determined [10] with a relative precision of 3 ⇥ 10 −11 by confining a 12 C 5+ ion in a Penning trap. The cyclotron frequency of its motion in a magnetic field and the precession frequency of the electron spin was then measured, and the results compared with the latest QED calculations of its g-factor [40]. From this and the proton mass which was recently measured in a separate measurement involving a Penning trap [11] from the same collaboration, the proton-to-electron mass ratio was determined as, M p /m e = 1836.152673346(81). In Fig. 3(B), the latest M p /m e mass ratios are shown together with the previous experimental values that were determined by comparing the cyclotron frequencies of protons and electrons in a Penning trap [7], laser spectroscopy of cold HD + molecular ions [12], and the CODATA 2010 recommended value [27]. These recent high-precision values are in good agreement with the M p /m e ratio determined from pHe + . The TRAP and BASE experiments of CERN have compared the cyclotron frequencies of antiprotons and H − ion pairs confined in a Penning trap [41][42][43]; a limit of 5 ⇥ 10 −10 was set [3,44] on any deviation between the antiproton and proton masses and charges by combining the results with the pHe + spectroscopic data.
The p 4 He + transition (n,`) = (40, 36)! (41,35) was also studied by laser spectroscopy [45]. A stimulated first-order Raman scattering process in a H 2 gas cell was utilized to generate the 7 ns long laser pulses of wavelength λ = 1154.9 nm needed to excite this transition. The measurements revealed that most of the metastable populations are concentrated into states of principal quantum number n ≥ 40, whereas the states n > 41 contain very few antiprotons. A laser-microwave-laser triple resonance method was used to study the hyperfine structure of the (n,`) = (36, 34) state of p 3 He + [46].

Future perspectives
Currently the precision on the calculations of pHe + energies are more than an order of magnitude higher than the experimental uncertainties. Further improvements in the theoretical precision are expected in the next 5 years. The Extra Low Energy Antiproton Ring (ELENA) facility due to begin operation in 2021 will provide a high-quality, cooled antiproton beam of energy E = 100 keV. Samples of pHe + would then be formed in a smaller volume, so that lasers of lower power and higher spectral resolution could be used in the experiments. The high stability of the antiproton beam should ensure an improved signal-to-noise ratio on the pHe + spectral lines. This may allow us to resolve weak atomic transitions between metastable states of smaller natural width, which can be measured with a higher precision. Intensive e↵orts are currently underway to achieve this goal. Metastable pionic helium (⇡He + ) is a three-body atom [47][48][49] consisting of a helium nucleus, an electron in the 1s ground state, and a negative-charged pion in a Rydberg state of quantum numbers n ⇠`− 1 ⇠ 16. The spectral lines of these atoms have never been directly observed, and so the existence of ⇡He + is so far hypothetical. Laser spectroscopy of ⇡He + is currently being attempted at the 590 MeV ring cyclotron facility of the Paul Scherrer Institute. By comparing the experimental frequencies with those derived from QED calculations, the ⇡ − mass can in principle be determined with a fractional precision of 10 −8 to 10 −6 .