Hyperfine structure of laser-cooling transitions in fermionic erbium-167

We have measured and analyzed the hyperfine structure of two lines, one at 583 nm and one at 401 nm, of the only stable fermionic isotope of atomic erbium as well as determined its isotope shift relative to the four most-abundant bosonic isotopes. Our work focuses on the $J\to J+1$ laser cooling transitions from the $\left[\text{Xe}\right]4f^{12}6s^2{(}^3{H}_6)$ ground state to two levels of the excited $\left[\text{Xe}\right]4f^{12}6s6p$ configuration, which are of major interest for experiments on quantum degenerate dipolar Fermi gases. From a fit to the observed spectra of the strong optical transition at 401 nm we find that the magnetic dipole and electric quadrupole hyperfine constants for the excited state are $A_e/h=-100.1\left(3\right)\mathrm{MHz}$ and $B_e/h=-3079\left(30\right)\mathrm{MHz}$, respectively. The hyperfine spectrum of the narrow transition at 583 nm, was previously observed and accurate $A_e$ and $B_e$ coefficients are available. A simulated spectrum based on these coefficients agrees well with our measurements. We have also determined the hyperfine constants using relativistic configuration-interaction ab initio calculations. The agreement between the ab initio and fitted data for the ground state is better than 0.1%, while for the two excited states the agreement is 1% and 11% for the $A_e$ and $B_e$ constants, respectively.

Figure 1

Energy levels of atomic Er up to $E/\left(hc\right)=25000{\mathrm{cm}}^{-1}$ for different electronic angular momentum quantum numbers $J$ [27, 30]. States with odd (even) parity are indicated by black (red) horizontal lines. The two relevant laser-cooling transitions at $401\mathrm{nm}$ and $583\mathrm{nm}$ are indicated by arrows.

Figure 2

Modulation transfer spectroscopy of Er for the 401 nm and 583 nm transitions. (a) Laser setup for spectroscopy on a hollow cathode discharge lamp (HCL); see text. The pump (probe) light has a power of $3.3\mathrm{mW}$ ($0.6\mathrm{mW}$) for the 401 nm transition and $20\mathrm{mW}$ ($1\mathrm{mW}$) for the 583 nm transition. (b), (c) Obtained spectroscopy signals for the 401 nm and the 583 nm transitions of different isotopes. Signals related to the hyperfine structure of ${}^{167}$Er are indicated by arrows. The relative amplitudes of the observed signals reflect the natural isotope abundances.

Figure 3

Spectroscopy signal and hyperfine assignment of the 401 nm transition of the fermionic ${}^{167}$Er. The black solid line is the recorded line. The red line is a simulated line shape obtained using a nonlinear fit to the line positions and a linewidth of $\gamma /\left(2\pi \right)=90$ MHz. The simulated line shape is a sum of the first derivative of several Lorentzians, one for each hyperfine transition, whose relative strength is given by a theoretical estimate of the line strength. We scaled the overall size of the simulated line shape to fit to the experiment. The assignment of the $P$-branch transitions ($F_g\to F_e=F_g+1$) is shown by vertical lines and pairs $(F_g,F_e)$. The hyperfine coefficients of the excited state are $A_e/h=-100.1$ MHz and $B_e/h=-3079$ MHz.

Figure 4

Spectroscopy signal and hyperfine assignment of the 583 nm transition of the fermionic ${}^{167}$Er. The solid black line is the experimental spectrum, while the red line is a simulated line shape using a linewidth of $\gamma /\left(2\pi \right)=20$ MHz. The $P$-branch transitions ($F_g\to F_e=F_g+1$) are assigned by pairs $(F_g,F_e)$. Three $P$-branch resonances and several $Q$-branch ($F_g\to F_e=F_g$) resonances are predicted to lie outside of the measurement range. The simulated line shape is a sum of the first derivative of several Lorentzians, one for each hyperfine transition, whose relative strength is given by a theoretical estimate of the line strength. We scaled the overall size of the simulated line shape to fit to the experiment. The hyperfine coefficients of the excited state are $A_e/h=-172.7$ MHz and $B_e/h=-4457.2$ MHz.

Figure 5

Isotope shifts for the 583 nm and 401 nm lines of the isotopes ${}^{164}$Er up to ${}^{170}$Er as a function of mass number where the transition energy for the bosonic isotope ${}^{166}$Er is taken as energy reference. The isotope shift of the bosonic isotopes falls on a single straight line, with the isotope shift of the center of gravity of the fermionic ${}^{167}$Er isotope, green cross and green square, is slightly displaced from this linear dependence.

Figure 6

Hyperfine levels of the ground (g.s.) and two excited states of ${}^{167}$Er with particular interest for laser cooling. The level splitting was calculated using $A$ and $B$ constants given in Table for the respective transitions. The arrows depict two laser-cooling transitions. The transition at 401 nm used for Zeeman slowing is shown in blue and the transition used for magneto-optical trapping at 583 nm is shown in yellow.