Characterization of the hyperfine interaction in europium-doped yttrium orthosilicate and europium chloride hexahydrate

We present characterization of the hyperfine interaction for the europium in hydrated europium chloride and as a dopant in yttrium orthosilicate. The Zeeman and pseudoquadrupole tensors were determined by measuring the hyperfine splittings while rotating the direction of a weak $(\sim 300\mathrm{G})$ magnetic field. The hyperfine spectra were recorded using Raman-heterodyne spectroscopy, an radio-frequency optical double resonance technique. For both materials magnetic field values were identified where there is no first order Zeeman shift in a europium hyperfine transition. These field insensitive transitions will have application in achieving very long hyperfine coherence times.

Figure 1

The hyperfine level structure in zero magnetic field for ${}^{151}\mathrm{Eu}$, for the ground electronic state of the two systems investigated in this work. These splittings were first measured by Yano et al. for $\mathrm{Eu}:{\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ (Ref. 16) and Martin et al. for $\mathrm{Eu}{\mathrm{Cl}}_3\bullet 6{\mathrm{H}}_2\mathrm{O}$ (Ref. 11).

Figure 2

Optical repumping scheme for $\mathrm{Eu}:{\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. When measuring the $\pm 1∕2\leftrightarrow \pm 3∕2$ transitions field. A takes on the role of probe beam and field $B$ repump. When investigating the $\pm 3∕2\leftrightarrow \pm 5∕2$ transitions the roles are reversed.

Figure 3

Image showing the experimentally obtained spectra for the $\pm 1∕2\leftrightarrow \pm 3∕2$ transition in $\mathrm{Eu}{\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. Each vertical slice is a spectra for a particular magnetic field value with the darkness denoting the strength of the Raman heterodyne signal.

Figure 4

The 200 magnetic field values that were used to gather each of the hyperfine spectra rotation patterns.

Figure 5

(Color online) The peak positions from the measured spectra for $\mathrm{Eu}:{\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ are shown with the crosses for each of the 200 spectra taken. The lines are the transition frequencies calculated from the extracted spin Hamiltonian parameters.

Figure 6

(Color online) The peak positions from the measured spectra for $\mathrm{Eu}{\mathrm{Cl}}_3\bullet 6{\mathrm{H}}_2\mathrm{O}$ are shown with the crosses for each of the 200 spectra taken. The lines are the transition frequencies calculated from the extracted spin Hamiltonian parameters.

Figure 7

An example of a ZEFOZ transition. The graph shows the calculated energy levels for one orientation of $\mathrm{Eu}:{\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ as a magnetic field is increased from zero in a particular direction. At $1.82\mathrm{T}$, for the transition marked, the slope of the two energy levels with magnetic field are equal. This means that, to first order, a change in the radial magnetic field component will have no effect on the transition frequency and cause no dephasing. Not shown in this figure is that the the transition frequency is also insensitive to field changes in the other two dimensions.

Figure 8

(Color online) A scatter plot showing the different ZEFOZ transitions that have been identified for three systems. The magnetic field required is plotted vs the second order Zeeman dependence. The second order Zeeman coefficient is a tensor valued quantity, it is reduced to a single number by taking the largest of the absolute values of the eigenvalues. According to the spin Hamiltonians determined here and in Ref. 10 the ZEFOZ transitions marked A, B, and C occur at magnetic fields of ($-732\mathrm{G}$, $-173\mathrm{G}$, $219\mathrm{G}$), ($-104\mathrm{G}$, $-378\mathrm{G}$, $-143\mathrm{G}$) and ($1.77\mathrm{T}$, $-0.63\mathrm{T}$, $-0.45\mathrm{T}$) and have transition frequencies of $8.65\mathrm{MHz}$, $7.27\mathrm{MHz}$, and $29.18\mathrm{MHz}$.