Microwave spectroscopy of the $1snp {}^{3}P_J$ fine structure of high Rydberg states in ${}^4\mathrm{He}$

The $1snp{}^{3}P_J$ fine structure of high Rydberg states in helium has been measured by microwave spectroscopy of single-photon transitions from $1sns{}^{3}S_1$ levels in pulsed supersonic beams. For states with principal quantum numbers in the range from $n=34$ to 36, the $J=0\to 2$ and $J=1\to 2$ fine structure intervals were both observed. For values of $n$ between 45 and 51 only the larger $J=0\to 2$ interval was resolved. The experimental results are in good agreement with theoretical predictions. Detailed characterization of residual uncanceled electric and magnetic fields in the experimental apparatus and calculations of the Stark and Zeeman structures of the Rydberg states in weak fields were used to quantify systematic contributions to the uncertainties in the measurements.

Figure 1

Zeeman structure of the $1s45p{}^{3}P$ term in helium. The vertical axis is displayed with respect to the energy of the $J=2$ level in zero magnetic field.

Figure 2

(a) Calculated Stark structure of the $1s36p{}^{3}P$ term in helium. The vertical axis is displayed with respect to the energy of the $J=2$ level in zero electric field. The calculated interval, ${\nu }_{0,2}$, between the $1s36p{}^3{P}_0$ and $1s36p{}^3{P}_2$ levels is shown in panel (b), while the smaller interval, ${\nu }_{1,2}$, between the $1s36p{}^3{P}_1$ and $1s36p{}^3{P}_2$ levels is shown in panel (c). The three curves in panel (b) represent the intervals between the $1s36p{}^3{P}_0$ sublevel with $M_J=0$ and the $1s36p{}^3{P}_2$ sublevels with $|M_J|=0$, 1, and 2. In panel (c) the three continuous (dashed) curves represent the intervals between the $1s36p{}^3{P}_1$ sublevel with $M_J=0$ ($|M_J|=1$) and the $1s36p{}^3{P}_2$ sublevels with $|M_J|=0$, 1, and 2.

Figure 3

Schematic diagram of the metastable helium beam source and Rydberg-state photoexcitation and detection regions. Three pairs of parallel plate electrodes are used for (I) ion deflection, (II) to define the electric fields in the laser photoexcitation and microwave spectroscopy regions, and (III) to apply time-dependent electric fields to ionize the Rydberg atoms and accelerate the resulting electrons to an MCP detector.

Figure 4

Microwave spectra of the $1s45s{}^{3}S_1\to 1s45p{}^3{P}_J$ transitions measured in two different magnetic fields. The vertical bars represent the set of allowed electric dipole transitions between the Zeeman-split sublevels and their relative intensities. The dashed curves are calculated spectra, shifted by $-170$ kHz (see text for details).

Figure 5

The $1s55s{}^{3}S_1\to 1s56s{}^3{S}_1$ two-photon transition frequency measured for a range of electric potentials applied to the upper electrode in the excitation region. The continuous curve represents a quadratic function fit to the data.

Figure 6

(a) Microwave spectra of the single-photon $1s55s{}^{3}S_1\to 1s56s{}^3{S}_1$ transition in a range of electric fields. The experimental data (thin curves) have been fit with Gaussian functions (thick curves). (b) Interdependence of the integrated spectral intensities and the transition frequencies in panel (a). The continuous line in panel (b) represents a least-squares fit to the data.

Figure 7

Microwave spectra of the $1sns{}^{3}S_1\to 1snp{}^{3}P_J$ transitions for $n=34$, 35, and 36. The frequency offset on the horizontal axis corresponds to the calculated $1sns{}^{3}S_1\to 1snp{}^3{P}_2$ transition frequency, ${\nu }_2$. The calculated frequencies and relative intensities of the transitions to the $J=0$, 1, and 2 levels are indicated by the vertical gray bars. The partial spectrum, slightly offset from the background for $n=34$, was recorded with a microwave intensity 2.5 times higher than that used in recording the full spectrum.

Figure 8

(a) Measured values of the fine-structure interval ${\nu }_{0,\overline{12}}$ for values of $n$ between 34 and 51 (points). The continuous blue curve represents the function $\nu =a{n}^{-3}$ fit to the experimental data such that $a=2.076\left(9\right)\times {10}^8$ kHz. The dashed black curve, which is indistinguishable from the fit, indicates the calculated values for the same interval. (b) The differences, $\mathrm{\Delta }\nu$, between the measured and calculated data in panel (a).