Direct Observation of the Hyperfine Transition of Ground-State Positronium

Abstract

We report the first direct measurement of the hyperfine transition of the ground state positronium. The hyperfine structure between ortho-positronium and para-positronium is about 203 GHz. We develop a new optical system to accumulate about 10 kW power using a gyrotron, a mode converter, and a Fabry-Pérot cavity. The hyperfine transition has been observed with a significance of 5.4 standard deviations. The transition probability is measured to be A = 3.1 +1.6 −1.2 × 10 −8 s −1 for the first time, which is in good agreement with the theoretical value of 3.37 × 10 −8 s −1 .Positronium (Ps) [1], a bound state of an electron and a positron, is a purely leptonic system and is a good target to study quantum electrodynamics (QED) in bound state. The triplet (1 3 S 1 ) state of Ps, ortho-positronium (o-Ps), decays into three gamma rays with a lifetime of τ o = 142 ns [2,3]. On the other hand, the singlet (1 1 S 0 ) state of Ps, para-positronium (p-Ps), decays into two gamma rays in τ p = 125 ps [4]. The energy level of the ground state o-Ps is higher than that of the ground state p-Ps due to the spin-spin interaction between the electron and the positron. This difference is called the hyperfine structure of the ground state positronium (Ps-HFS), which is about 203 GHz. Although precise measurements of Ps-HFS have been performed in 1970s and 1980s [5,6], all of them are indirect measurements using Zeeman splitting of about 3 GHz caused by a static magnetic field of about 1 T. There is a discrepancy of 3.9 standard deviations (15 ppm) between the measured and the theoretical value [7]. The largest systematic uncertainty common to all previous measurements is the non-uniformity of the static magnetic field. It is important to directly measure Ps-HFS, in order to avoid the systematic uncertainty of the static magnetic field. Here we present a direct observation of the hyperfine transition between Ps-HFS, which is the first great step toward a direct measurement of Ps-HFS. The hyperfine transition of the ground state Ps, which is M 1 transition, has not yet been observed directly, since the transition probability (Einstein's A coefficient is A = 3.37 × 10 −8 s −1 [8]) is 10 14 times smaller than the decay rate of o-Ps (7.0401(6)×10 6 s −1 [2,3]). In order to cause sufficient amount of stimulated emission from o-Ps to p-Ps, we develop a new optical system which consists of a gyrotron as a sub-THz radiation source, a mode converter to convert the gyrotron output to a Gaussian beam, and a Fabry-Pérot cavity to accumulate high power sub-THz radiation. The gyrotron is a novel FIG. 1: Schematic diagrams of our experimental setup. Top view of the gas chamber is shown in the box. M1 and M2 are parabolic mirrors made of aluminum. We use a gold mesh plane mirror with a transmittance of about 3 % as a beam splitter (BS). Three pyroelectric detectors (PY) are used to monitor the incident, the reflected and the transmitted power.high power radiation source for sub-THz to THz region, which enables us to perform a direct measurement of the...

Experimental progress in positronium laser physics

“…A recent experiment [323] has in fact succeeded in driving a direct singlet-triplet transition using a highpower (300 W) gyrotron and a Fabry-Pérot cavity (with gold mesh mirrors) to produce up to 10 kW of 203 GHz microwave radiation [324,325]. The basic methodology used in this experiment is similar to the earlier Zeemansplit measurements, except of course for the formidable challenges related to producing intense radiation at the required frequencies [326].…”

“…Thus, a large detector array is required to optimize detection. Moreover, to convert triplet atoms to singlets to facilitate two-photon decay, either a several kG spin flipping magnetic field must and applied in a time comparable to the 142 ns Ps lifetime, or a high-power microwave field must be applied [323,594]; neither of these are trivial endeavors [73]. Optical methods may be able to reveal the presence of a BEC and avoid these problems [73,594], although it is by no means obvious that one can unambiguously distinguish between a cold dense Ps ensemble and a Ps BEC when both are present in a material structure.…”

New Precision Measurement of Hyperfine Splitting of Positronium

“…∆ HFS is treated as a constant at each gas density instead of using Eq. (12). This method is similar to the method used in the previous experiments except that our data use timing information, which was not taken in the previous measurement, and 11 resonance lines within 50-440 ns timing window are simultaneously fitted at each gas density.…”

“…One experiment is trying to measure ∆ HFS directly, but it has not obtained the result yet [12,13]. Other independent experiments [14,15] have not yet reached a sufficient level of precision to address the discrepancy.…”

Testing Quantum Electrodynamics with Positronium State

“…Thus the status of the QED prediction for positronium HFS remains ambiguous. Much activity is currently under way to improve the experimental precision [28,29]. On the theoretical side the accuracy is limited by the unknown third-order coefficient D. The corresponding uncertainty may soon become a limiting factor in the study of positronium HFS and the…”