We present a joint experimental and theoretical study of spin coherence properties of 39 K, 85 Rb, 87 Rb, and 133 Cs atoms trapped in a solid parahydrogen matrix. We use optical pumping to prepare the spin states of the implanted atoms and circular dichroism to measure their spin states. Optical pumping signals show order-of-magnitude differences depending on both matrix growth conditions and atomic species. We measure the ensemble transverse relaxation times (T * 2 ) of the spin states of the alkali-metal atoms. Different alkali species exhibit dramatically different T * 2 times, ranging from sub-microsecond coherence times for high mF states of 87 Rb, to ∼ 10 2 microseconds for 39 K. These are the longest ensemble T * 2 times reported for an electron spin system at high densities (n 10 16 cm −3 ). To interpret these observations, we develop a theory of inhomogenous broadening of hyperfine transitions of 2 S atoms in weakly-interacting solid matrices. Our calculated ensemble transverse relaxation times agree well with experiment, and suggest ways to longer coherence times in future work. arXiv:1910.05430v1 [physics.atom-ph]

We measure the transverse relaxation of the spin state of an ensemble of ground-state rubidium atoms trapped in solid parahydrogen at cryogenic temperatures. We find the spin dephasing time of the ensemble (T * 2 ) is limited by inhomogeneous broadening. We determine that this broadening is dominated by electrostatic interactions with the host matrix, and can be reduced by preparing nonclassical spin superposition states. Driving these superposition states gives significantly narrower electron paramagnetic resonance lines and the longest reported electron spin T * 2 in any solid-phase system other than solid helium.PACS numbers: 07.55. Ge, 33.35.+r Measuring the energy splitting between Zeeman levels is at the heart of atomic magnetometry [1], electron paramagntic resonance (EPR) spectroscopy [2], and fundamental physics measurements [3][4][5]. For an ensemble of N atoms, the shot-noise limited precision of a single measurement is σ E ∼ T * 2 √ N [1], where T * 2 is the ensemble's spin dephasing time. In this paper, we show that rubidium atoms in parahydrogen have favorable T * 2 times for a solid state electron spin ensemble. Moreover, their T * 2 can be further extended by using nonclassical superposition states instead of traditional Larmor precession states.Our apparatus is similar to that described in Refs. [6,7]. We grow our crystal by co-depositing hydrogen and rubidium gases onto a cryogenically-cooled sapphire window at 3 Kelvin. We enrich the parahydrogen fraction of hydrogen by flowing the gas over a cryogenicallycooled catalyst. In the data presented in this paper, the orthohydrogen fraction is < 10 −4 . Typical thicknesses of the doped crystals are ∼ 0.3 mm. We use naturalisotopic-abundance rubidium; typical rubidium densities are on the order of 10 17 cm −3 , or a few ppm.We apply a static "bias" magnetic field (B z ) normal to the surface of the crystal. We polarize the spin state of the implanted Rb atoms by optically pumping the atoms with a circularly-polarized laser. We measure the polarization through circular dichroism, measuring the relative transmission of left-hand-and right-hand-circularlypolarized light (LHC and RHC). We drive transitions between Zeeman states with transverse RF magnetic fields generated by a wire a few mm above the surface of the crystal. We take data with bias fields ranging from 40 to 120 Gauss, giving Zeeman shifts that are small compared to the hyperfine splitting, but sufficiently large that transitions between different Zeeman levels can be spectrally resolved. The level structure of ground-state 85 Rb is shown in Fig. 1. * weinstein@physics.unr.edu; http://www.physics.unr.edu/xap/ We measure rubidium's transverse relaxation time by free-induction-decay (FID) decay measurements. After polarizing the spin through optical pumping, an RF pulse is applied to induce Larmor precession. The Larmor precession and its decay are measured optically via circular dichroism [1]. The measured values of T * 2 are shorter than our spin-echo measurements of T 2 by over an order ...