Enhanced spin coherence of rubidium atoms in solid parahydrogen

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 electrostaticlike 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.

Figure 1

Schematic of the Zeeman levels of gas-phase ${}^{85}\mathrm{Rb}$, showing some of the relevant transitions of Fig. 2. The energy eigenstates (black) are labeled by their low-field quantum numbers $F$ and $m_F$, and we refer to them throughout the paper by that terminology. The slender arrows denote the single-photon transitions. The wide arrows denote the two-photon transitions between states which are approximate time reversals of each other; each two-photon transition is shown as a single arrow. To better illustrate the nondegenerate frequencies of the transitions, the Zeeman levels are plotted over a larger range of magnetic fields than used in this experiment; likewise, the transition arrows are horizontally offset for ease of viewing.

Figure 2

Depolarization spectroscopy signals, as discussed in the text, taken with $B_z=82$ G. The vertical axis measures the ratio of the transmission of LHC and RHC probe beams; under conditions of no spin polarization the ratio is 1. The signal is plotted as a function of the rf frequency; in these data the rf is swept from high to low frequency. The dashed vertical lines mark the calculated single-photon and two-photon transition frequencies for gas-phase ${}^{85}\mathrm{Rb}$ [13]; the yellow labels denote $m_F\leftrightarrow m_F^{\prime }$.

Figure 3

Measured linewidths of ${}^{85}\mathrm{Rb}$ in the $F=3$ hyperfine state and ${}^{87}\mathrm{Rb}$ in the $F=2$ hyperfine state. For the single-photon linewidth, we plot the average of the $|m_F=\pm 1\rangle \leftrightarrow |m_F=0\rangle$ transitions. For the two-photon linewidth we plot the linewidth of the $+1\leftrightarrow -1$ transition.

Figure 4

(a) Ab initio PES for Rb-${\mathrm{H}}_2$ plotted as a function of the Jacobi coordinates $R$ and $\theta$. (b) Tensor matrix shifts of ${}^{85}\mathrm{Rb}$ (solid line) and ${}^{87}\mathrm{Rb}$ (dashed line) interacting with six $p\text{−}{\mathrm{H}}_2$ molecules as a function of the $\mathrm{Rb}\text{−}{\mathrm{H}}_2$ distance $R$.