Hole-burning techniques for isolation and study of individual hyperfine transitions in inhomogeneously broadened solids demonstrated in ${\mathrm{Pr}}^{3+}{:\mathrm{Y}}_2{\mathrm{SiO}}_5$

Due to their narrow homogeneous linewidths, rare-earth ions in inorganic crystals at low temperatures have recently been given considerable attention as test materials for experiments in coherent quantum optics. Because these narrow linewidth transitions have been buried in a wide inhomogeneous line, the scope of experiments that could be carried out in these materials has been limited. However, here we present spectroscopic techniques, based on spectral hole burning and optical pumping, which allow hyperfine transitions that are initially buried within an inhomogeneously broadened absorption line to be studied with no background absorption from other transitions. A sequence of hole-burning pulses is used to isolate selected transitions between hyperfine levels, which makes it possible to directly study properties of the transitions, e.g., transition strengths, and gives access to information that is difficult to obtain in standard hole-burning spectroscopy, such as the ordering of hyperfine levels. The techniques introduced are applicable to absorbers in a solid with long-lived sublevels in the ground state and where the homogeneous linewidth and sublevel separations are smaller than the inhomogeneous broadening of the optical transition. In particular, this includes rare-earth ions doped into inorganic crystals and in the present work the techniques are demonstrated in spectroscopy of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$. Information on the hyperfine structure and relative transition strengths of the ${}^{3}H_4\text{−}{}^{1}D_2$ hyperfine transitions in ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ has been obtained from frequency-resolved absorption measurements, in combination with coherent and incoherent driving of the transitions.

Figure 1

Principles of spectral hole burning through optical pumping and redistribution of absorbers between sublevels in the ground state. The example assumes absorbers with two sublevels in both ground and excited states and that the splitting of the ground state is larger than that of the excited state. (a) Due to inhomogeneous broadening, different subsets of absorbers will have transitions between different sublevels shifted into resonance with the applied light. The figure shows the energy levels of four different subsets, all resonant with the burning laser, but on different transitions. (b) Absorption spectrum after burning at frequency ${\upsilon }_{\mathrm{burn}}$. The position of side holes and antiholes directly give the separations between the sublevels.

Figure 2

Spectral hole burning in the inhomogeneously broadened ${}^{7}F_0\text{−}{}^{5}D_0$ transition in ${\mathrm{Eu}}^{3+}{:\mathrm{YAlO}}_3$. The amount of ${\mathrm{Eu}}^{3+}$ ions absorbing at a particular frequency has been monitored by recording laser induced fluorescence. (a) A $12\mathrm{MHz}$ wide spectral interval has been completely emptied of absorbing ions. At laser frequencies inside the pit, the signal is constant and less than 1% of the fluorescence signal before burning. (b) An ensemble of ions has been moved back into the pit by shifting the laser frequency $69\mathrm{MHz}$ from the center of the pit and thus burning on an auxiliary hyperfine level in the ground state. The resolution of the spectral features in this experiment was limited by laser jitter of the order of $2\mathrm{MHz}$.

Figure 3

Simplified hole-burning sequence, assuming absorbers with three sublevels in the ground state and a single excited state. Energy level diagram is shown for a selected subset of absorbers at a specific position within the inhomogeneous absorption line. (a) Burning at frequencies ${\nu }_0$, $\left({\nu }_0+{\delta }_2^{\mathrm{g}}\right)$, and $\left({\nu }_0+{\delta }_1^{\mathrm{g}}+{\delta }_2^{\mathrm{g}}\right)$ removes absorbers for which these frequencies correspond to other transitions than for the selected subset. (b) Burning at frequencies ${\nu }_0$ and $\left({\nu }_0+{\delta }_2^{\mathrm{g}}\right)$ creates two wide spectral pits and collects the selected subset of absorbers in an auxiliary state. (c) Absorbers within a narrow spectral interval at $\left({\nu }_0+{\delta }_1^{\mathrm{g}}+{\delta }_2^{\mathrm{g}}\right)$ are excited from the auxiliary state, from where they relax to form a narrow peak, absorbing from a selected ground state sublevel.

Figure 4

Energy level diagram and relaxation data for the ${}^{3}H_4\text{−}{}^{1}D_2$ transition of site ${\mathrm{IPr}}^{3+}$ ions in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$. $T_1$, $T_2$, and ${\Gamma }_{\text{hom}}$ are given according to Ref. 27.

Figure 5

(a) The experimental result of applying the hole-burning sequence detailed in Sec. 3 to ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. A group of ions is prepared in state $\pm 1∕2$, such that they absorb to each of the excited state hyperfine levels on frequencies inside a previously emptied spectral pit. In this experiment, the spectral resolution was limited by a fast readout chirp rate $\left(r\approx 1\mathrm{MHz}∕\mu \mathrm{s}\right)$ and the peak corresponding to the transition $\pm 1∕2\text{−}\pm 5∕2$ was not resolved. See Fig. 7a for a closeup of the central region. (b)–(d) Relative number of ions absorbing at each optical frequency from the three ground state hyperfine levels, after applying the sequence of burning pulses in Sec. 3. (b) Ions in state $\pm 1∕2$, (c) ions in state $\pm 3∕2$, and (d) ions in state $\pm 5∕2$. Each ion can absorb at three different frequencies. (Solid lines) Absorption to the $\pm 1∕2$ hyperfine level in the excited state. (Dashed lines) Absorption to excited state $\pm 3∕2$. (Dotted lines) Absorption to excited state $\pm 5∕2$. The total absorption, corresponding to (a) can be obtained by summing the absorption on the nine possible transitions in (b)–(d), weighted according to transition strengths.

Figure 6

Setup used in the experiments. See Sec. 4 for details.

Figure 7

Ions absorbing on specific hyperfine transitions, inside the inhomogeneously broadened ${}^{3}H_4\text{−}{}^{1}D_2$ transition in ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. The three curves correspond to three separate experiments. The three peaks of varying size, in each curve, are due to the same ensemble of ions absorbing on different transitions. The intensity was attenuated by a factor ${10}^3$ during readout, in order not to cause significant excitation when probing the transitions. The scan rate during readout was of the order of $r\approx 0.1\mathrm{MHz}∕\mu \mathrm{s}$. Single-shot measurements.

Figure 8

Incoherent burning on transitions going from state $\pm 3∕2$. (a) A group of ions have been prepared in state $\pm 3∕2$, inside a wide region emptied of other absorbing ions. Absorption on transition $\pm 3∕2\text{−}\pm 5∕2$ is barely detectable. (b)–(d) In three separate experiments, a large number of burning pulses are applied at the frequencies indicated in (a). When the ions are pumped away via (b) the $\pm 1∕2$ or (c) the $\pm 3∕2$ hyperfine levels in the excited state, a large fraction of the ions relax to $\pm 1∕2$ in the ground state and are detected after the burning. (d) When the ions are pumped away via the $\pm 5∕2$ excited state, they disappear from the monitored region, indicating that they have relaxed to $\pm 5∕2$ in the ground state, since all transitions from this state are resonant with higher frequencies. Moderate burning at other frequencies inside the pit, i.e., not resonant with any of the peaks, does not change the absorption spectrum. Single-shot measurements.

Figure 9

(Solid line) Experimental hole-burning spectrum in the ${}^{3}H_4\text{−}{}^{1}D_2$ transition in site I ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$. The hole was created by applying a burn pulse during $1\mathrm{s}$. The data are an average of 30 readout scans. The spectral resolution is limited by laser jitter during burning and readout. Dashed line: Simulated hole-burning spectrum using hyperfine parameters from Table .

Figure 10

Coherent driving of the $\pm 1∕2\text{−}\pm 3∕2$ transition. Pulses with a variable pulse area $\left(\theta =\Omega t\right)$ was applied to the transition using $3\mu \mathrm{s}$ long pulses with varying intensity. The population difference between the ground [$\pm 1∕2$(g)] and optically excited [$\pm 3∕2$(e)] states, after the pulse, was monitored by recording the transmission at the resonance frequency. (b)–(e) An ensemble of ions absorbing/emitting on the transition after the application of a pulse with (b) $\theta =0$, (c) $\theta \approx \pi ∕3$, (d) $\theta \approx \pi$, and (e) $\theta \approx 2\pi$.

Figure 11

Coherent driving of the $\pm 5∕2\text{−}\pm 1∕2$ transition. Pulses with a variable pulse area $\left(\theta =\Omega t\right)$ was applied to the transition using $3\mu \mathrm{s}$ long pulses with varying intensity. The number of ions left in the ground state, $\pm 5∕2$(g), after the pulse, was monitored by recording the absorption on the $\pm 5∕2\text{−}\pm 5∕2$ transition. (b)–(d) An ensemble of ions absorbing on $\pm 5∕2\text{−}\pm 5∕2$ after the application of a pulse with (b) $\theta =0$, (c) $\theta \approx \pi$, and (d) $\theta \approx 2\pi$, resonant with $\pm 5∕2\text{−}\pm 1∕2$.