Figure 1

Spectral hole-burning in the inhomogeneously broadened ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition in 0.2% ${\text{Pr}}^{3+}:{\text{La}}_2{\left({\text{WO}}_4\right)}_3$. At 2.0 K, a 22.5 MHz wide spectral interval (a pit) was completely emptied of absorbing ions. $\alpha L$ is the optical depth where $\alpha$ is the absorption coefficient and $L$ the length of the crystal. The amount of ${\text{Pr}}^{3+}$ ions absorbing at a particular frequency is monitored by recording the absorption.Reuse & Permissions

Figure 2

(a) Hyperfine energy level diagram of the ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition of ${\text{Pr}}^{3+}$ in ${\text{La}}_2{\left({\text{WO}}_4\right)}_3$. ${\delta }_1^g$, ${\delta }_2^g$, ${\delta }_1^e$, and ${\delta }_2^e$ are the hyperfine splittings of the ${{}^3\text{H}}_4\left(0\right)$ ground state and of the ${{}^1\text{D}}_2\left(0\right)$ excited state, respectively. For the eigenstates, $5/2g$ corresponds, for example, to the $|M_I=\pm \frac{5}{2}⟩$ wave function of the ground state. The burn-back frequency (dashed arrow) is on the $5/2g\to 5/2e$ transition for class I. Due to the inhomogeneous distribution of optical resonance frequencies, different absorbers (nine classes in total, I–IX) have different transitions resonant with the burning field. (b) Stick diagram showing all the frequency positions of the different hyperfine transitions for all the different classes I–IX. The lengths reproduce the relative oscillator strengths calculated in this section.Reuse & Permissions

Figure 3

Ions absorbing within a pit in the inhomogeneously broaden ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition in 0.2% ${\text{Pr}}^{3+}:{\text{La}}_2{\left({\text{WO}}_4\right)}_3$. (a) A 22.5 MHz interval was completely emptied of absorbing ions through spectral hole burning. Then different classes of ${\text{Pr}}^{3+}$ ions have been pumped back into the pit by shifting the laser frequency by 51.8 MHz to excite ions from an auxiliary ground-state hyperfine level and let them relax into a new hyperfine level. All the observed transitions are attributed to a particular hyperfine transition belonging to the three different classes I–III. (b) Starting from (a), clean-wrong-class pulses are applied in the 14–21 MHz range [see arrow in (a)] to empty the $1/2g$ level of class II and III. The three transitions of class I starting from level $1/2g$ are isolated. The relative oscillator strengths can be calculated by integration of the line intensities.Reuse & Permissions

Figure 4

Ions absorbing within a pit in the inhomogeneous broadened ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition in 0.2% ${\text{Pr}}^{3+}:{\text{La}}_2{\left({\text{WO}}_4\right)}_3$. (a) Different classes of ${\text{Pr}}^{3+}$ ions were pumped back into the pit, by shifting the laser frequency by 41.8 MHz. All the observed transitions are attributed to a particular hyperfine transition of the three different classes I to III. (b) Starting from (a) clean-wrong-class pulses were applied in the 14–30 MHz range [see arrow in (a)] to empty the level $3/2g$ of the class I and levels $1/2g$ and $3/2g$ of classes II and III. Some population remains on the level $3/2g$ of class III. (c) Starting from (b), clean-wrong-class pulses centered on the transition $3/2g\to 1/2e$ of class III at 27 MHz were applied to empty the starting level [see arrow in (b)]. All the population of level $3/2g$ of class III is transfered to levels $1/2g$ and $5/2g$. (d) Starting from (c), clean-wrong-class pulses centered at 12.3 MHz [see arrow in (c)] are applied to transfer for the class I population from level $1/2g$ to levels $3/2g$ and $5/2g$. The main contribution is now due to the class I. A small contribution of class III indicated by a star can be seen on the wall of the pit.Reuse & Permissions

Figure 5

(a) Hyperfine energy level diagram of the ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition of ${\text{Pr}}^{3+}$ in ${\text{La}}_2{\left({\text{WO}}_4\right)}_3$. The burn-back frequency (dashed arrow) is on the $1/2g\to 1/2e$ transition for class I. (b) Stick diagram of all the different hyperfine transitions which can be obtained for all the different classes.Reuse & Permissions

Figure 6

Ions absorbing within a pit in the inhomogeneous broadened ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition in 0.2% ${\text{Pr}}^{3+}:{\text{La}}_2{\left({\text{WO}}_4\right)}_3$. (a) After cleaning a 22.5 MHz interval, different classes of ${\text{Pr}}^{3+}$ ions were pumped back into the pit, by shifting the laser frequency by $-32.2\text{MHz}$. All the observed transitions are attributed to particular hyperfine transitions belonging to three different classes I to III. (b) Starting from (a) clean-wrong-class pulses are applied in the 33–36 MHz range [see arrow in (a)] to empty the $5/2g$ level of class II. The three transitions of class I starting from level $5/2g$ are isolated with a small contribution of the transition $5/2g\to 5/2e$ of class III at 39.4 MHz.Reuse & Permissions

Figure 7

(a) Transmission of the $1/2g\to 5/2e$ transition for different values of the pulse area. For the sake of clarity, the spectra are vertically shifted. (b) Coherent driving of the $1/2g\to 5/2e$ transition. Super-Gaussian pulses with $t_{\text{FWHM}}=0.5\mu \text{s}$, $t_{\text{cutoff}}=1.5\mu \text{s}$ and with variable pulse area $\left(\theta =\Omega t\right)$ were applied to the transition. ${\theta }_{\text{max}}$ is $1.3\pi$ in our experiment. The population difference between the ground and the excited state is obtained by recording the transmission across the transition $8\mu \text{s}$ after the coherent pulse.Reuse & Permissions

Figure 8

a) Energy level diagram of ${\text{Pr}}^{3+}$ for the ${{}^3\text{H}}_4\left(0\right)\to {{}^1\text{D}}_2\left(0\right)$ transition in ${\text{La}}_2{\left({\text{WO}}_4\right)}_3$. The hyperfine coherences are excited by a bichromatic pulse at the two frequencies ${\omega }_1$ and ${\omega }_2$ tuned on the $1/2g\to 5/2e$ and $3/2g\to 5/2e$ transitions. The read-out depicted by dashed arrows is performed by applying a super-Gaussion pulse at the frequency ${\omega }_3$ on the $1/2g\to 3/2e$ transition which transfers the hyperfine coherence on the transition $3/2g\to 3/2e$ at ${\omega }_4$. [(b) and (c)] FID and Raman echo sequences, respectively. The probing is performed on the $1/2g\to 5/2e$ optical transition which has not been excited by the first bichromatic pulse. $T$ is the delay between the first pulse and the probing for the FID experiment and between the first and the second bichromatic pulse for the Raman echo. The FID and the Raman echo are observed by measuring the amplitude of the beatnote between ${\omega }_3$ and ${\omega }_4$ by means of Fourier transform. (d) Preparation step before the FID and echo sequences. Only class I appears with a small contribution of class III. The different frequencies are indicated on the graph as well as the hyperfine splitting ${\delta }_2^g$.Reuse & Permissions

Figure 9

(a) FID decay as function of the delay $T$ between the first pulse and the read-out pulse. The inset gathers the FT signal linked to the beatnote amplitude for different values of the delay. An exponential fit (solid line) of the decay gives $T_{2,\text{Raman}}^{\ast }=5.6\pm 0.2\mu \text{s}$. (b) Raman echo decay as a function of the delay $T$ between the first pulse and the second bichromatic pulse, with an inset that gathers the FT peak at ${\delta }_2^g$ for different values of $T$. Two decays can be seen on Fig. 9b, a fast one in the $0–30\mu \text{s}$ time range which corresponds to the contribution of the FID of the second bichromatic pulse, and a long one in the $40–240\mu \text{s}$ time range due to the Raman echo decay. An exponential fit of this last decay in the $40–240\mu \text{s}$ range gives a value of $T_{2,\text{Raman}}=250\pm 15\mu \text{s}$.Reuse & Permissions