Cold Collision Frequency Shift in Two-Dimensional Atomic Hydrogen

We report a measurement of the cold collision frequency shift in atomic hydrogen gas adsorbed on the surface of superfluid ${}^4\mathrm{He}$ at $T\lesssim 90\mathrm{mK}$. Using two-photon electron and nuclear magnetic resonance in 4.6 T field we separate the resonance line shifts due to the dipolar and exchange interactions, both proportional to surface density $\sigma$. We find the clock shift $\Delta {\nu }_c=-1.0(1)\times {10}^{-7}\mathrm{Hz}{\mathrm{cm}}^{-2}\times \sigma$, which is about 100 times smaller than the value predicted by the mean field theory and known scattering lengths in the three-dimensional case.

Figure 1

(a) Schematic drawing of the sample cell: FPR, Fabry-Perot ESR resonator; HR, helical NMR resonator; MF, Mylar foil; B, bolometer; CS, cold spot. (b) Hyperfine level diagram for a hydrogen atom in a strong magnetic field. Arrows denote electron and nuclear spin projections.

Figure 2

Observed ESR and two-photon spectra. Upper traces, absorption; lower traces, dispersion. (a) Bulk gas (left peak) and surface (right peak) ESR lines; (b) two-photon resonances observed at lowest surface temperature of $\approx 70\mathrm{mK}$.

Figure 3

Frequency shift of the $a\mathrm{\text{−}}b$ transition as a function of the ESR line shift obtained by the two-photon method: (○) pure ${}^4\mathrm{He}$ film, (▲) ${}^3\mathrm{He}\mathrm{\text{−}}{}^4\mathrm{He}$ mixture, (▪) difference of the ESR and NMR resonance line positions measured at fixed frequencies ${\nu }_{bc}$ and ${\nu }_{ab}$. Solid lines are linear fits to the data.