Ramsey Spectroscopy of the $2{\mathrm{S}}_{1/2}$ Hyperfine Interval in Atomic Hydrogen

The $2{\mathrm{S}}_{1/2}$ hyperfine interval in atomic hydrogen was measured using Ramsey spectroscopy with a thermal beam cooled to cryogenic temperatures. The measured value is 177 556 838.87(85) Hz, which represents the most precise determination of this interval to date. The $1{\mathrm{S}}_{1/2}$ hyperfine interval $f(1{\mathrm{S}}_{1/2})$ and the $2{\mathrm{S}}_{1/2}$ hyperfine interval $f(2{\mathrm{S}}_{1/2})$ can be combined to give the quantity $D_{21}=8f(2{\mathrm{S}}_{1/2})-f(1{\mathrm{S}}_{1/2})$, which mostly eliminates uncertainty due to nuclear structure effects and is well described by bound-state quantum electrodynamics. Using the value of $f(2{\mathrm{S}}_{1/2})$ from this work gives a value of $D_{21}^{\mathrm{expt}}=48959.2(6.8)\mathrm{Hz}$, which is in agreement with the theoretical value of $D_{21}^{\text{Theory}}=48954.1(2.3)\mathrm{Hz}$.

Figure 1

Schematic of the experimental apparatus. Atoms initially prepared in the ${2\mathrm{S}}_{1/2}^{F=0}$ state enter a magnetically shielded region where Ramsey spectroscopy is performed. A solenoid allows for a bias magnetic field to be applied. Any remaining population in the ${2\mathrm{S}}_{1/2}^{F=0}$ state is selectively quenched to the ${2\mathrm{P}}_{1/2}^{F=1}$ state using an electric-dipole transition. The excited-state population is detected using a CEM.

Figure 2

Example line shape from an average of six scans of the ${2\mathrm{S}}_{1/2}^{F=0}(m_F=0)–{2\mathrm{S}}_{1/2}^{F=1}(m_F=0)$ resonance obtained using Ramsey spectroscopy with room temperature hydrogen beam with a numerical simulation overlaid. The FWHM of the central peak is approximately 4 kHz.

Figure 3

(a) Example phase shift extrapolation between temperatures of 6 and 30 K as a function of the extracted linewidth. The shaded gray region corresponds to the 1 standard deviation confidence interval. (b) Extrapolated zero-phase line centers after bias magnetic field correction. Squares, triangles, and circles represent data taken at 8, 16, and 24 mG applied magnetic field, respectively. The shaded gray region represents 1 standard deviation from the statistical mean. The reduced ${\chi }^2$ for the 17 datasets is 1.05.

Figure 4

Relative shift of the resonance as a function of applied magnetic field from solenoid. In the main figure, error bars are not included because they are too small to be visible.

Figure 5

Experimental (rf 1956 [19], rf 2000 [20], optical 2003 [21], and optical 2009 [22]) and theoretical [15] values of $D_{21}$. The dashed line represents the theoretical value.