State preparation by optical pumping in erbium-doped solids using stimulated emission and spin mixing

Erbium-doped solids are potential candidates for the realization of a quantum memory for photons at telecommunication wavelengths. The implementation of quantum memory proposals in rare-earth-ion-doped solids require spectral tailoring of the inhomogeneous absorption profile by efficient population transfer between ground-state levels (spin polarization) using optical pumping. In this paper we investigate the limiting factors of efficient optical pumping between ground-state Zeeman levels in an erbium-doped ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ crystal. We introduce two methods to overcome these limiting factors: stimulated emission using a second laser and spin mixing using radio frequency excitation. Both methods significantly improve the degree of spin polarization. Population transfer between two Zeeman levels with less than 10% of the total population in the initial ground state is achieved, corresponding to a spin polarization greater than 90%. In addition, we demonstrate spectral tailoring by isolating a narrow absorption peak within a large transparency window.

Figure 1

(a) Spectral hole-burning spectrum of a four-level system. The laser is in resonance with the $-1∕2\to -1∕2$ transition (solid line). The probe transitions (dashed lines) are labeled and the positions of the corresponding holes and antiholes in the transmission spectrum are shown below. The Zeeman splitting of the ground- and the excited-state levels, respectively, is given by ${\Delta }_{e,g}={\mu }_B{g}_{e,g}B∕\hslash$, where $g_g$ and $g_e$ are the $g$ factors for the ground and the excited state, respectively, ${\mu }_B$ is the Bohr magneton, and $B$ is the magnetic field. Note that, in addition to those shown in the figure, further holes and antiholes occur that are due to the inhomogeneous broadening of the absorption line [16, 17, 25]. (b) To enhance the efficiency of the population transfer the excited-state lifetime is artificially lowered by stimulated emission to the short-lived second Kramers doublet of the ground state $\left(Z_2\right)$.

Figure 2

(Color online) (a) Experimental setup. The laser for the hole burning $(\lambda =1536\mathrm{nm})$ and the stimulation laser $(\lambda =1546\mathrm{nm})$ could be intensity modulated independently with acousto-optic modulators (AOMs). They were coupled into the same fiber via a wave division multiplexer. The light of the stimulation laser was filtered out before detection using another WDM. A rf wave could be applied on the crystal using a coil in Helmholtz configuration which could be driven with an arbitrary function generator. (b) Typical pulse sequence. During the readout pulse the frequency of the pump laser was scanned in order to record the absorption profile. For measurement with stimulated emission, the stimulation laser is applied for a time $T_{\text{pump}}+\tau$, where $\tau$ can be varied. (c) Illustration of the angle of the magnetic field with respect to the crystal orientation.

Figure 3

Spectral hole area as a function of the readout delay time for the case of standard optical pumping. The decline is clearly dominated by the excited-state lifetime $T_1$ of $11\mathrm{ms}$. The line is a fit to the data. Only a small fraction of the ions was transferred into the second Zeeman level and provides a slow component $(T_Z\approx 100\mathrm{ms})$ to the decline. The origin of the slowly decaying part is confirmed by the slight enhancement in the optical depth (antiholes) left and right of the wide spectral hole (pit) in the inset. The graph shows a zoom on the absorption line at about $2.8\mathrm{ms}$ after the burning pulse. Here the frequency of the pump laser was swept by $10\mathrm{MHz}$ during the burning pulse in order to widen the hole.

Figure 4

(Color online) Spectral hole area as a function of the frequency of the stimulation laser at $T=4.1\mathrm{K}$. The burning time was $200\mathrm{ms}$. The stimulation pulse was $1\mathrm{ms}$ longer than the burning pulse. The delay for the readout pulse was set to $2.5\mathrm{ms}$. The solid line is a Lorentzian fit giving a full width at half maximum (FWHM) of $14\mathrm{GHz}$.

Figure 5

(Color online) Stimulation rate on the $Y_1\to Z_2$ transition vs applied laser power. The rate at which ions are stimulated down grows linearly with the power of the stimulation laser. It was extracted from the decay curves shown in the inset and as described in the text. Curves for three different values of the power of the stimulation laser are shown. Each data set is normalized to its maximum value $(\tau =0)$. The offset of 0.1 is due to persistent holes, which have already been observed and discussed in [17].

Figure 6

Spectral hole area as a function of the readout delay time with (triangles) and without (open circles) stimulated emission. In the case in which the stimulation laser is applied a clearly enhanced contribution from ions transferred to the second Zeeman level can be observed. The corresponding hole decays with $T_Z\approx 100\mathrm{ms}$ and the overall decay shows a much stronger contribution of this slow component than it can be observed for standard optical pumping. The enhancement in population transfer is confirmed by the strong antiholes shown in the inset. The figure shows the absorption at about $2.8\pm 0.3\mathrm{ms}$ after the burning pulse. For this measurement, a $10\mathrm{MHz}$ sweep was applied on the pump laser, the stimulation pulse was $1\mathrm{ms}$ longer than the pump pulse, and the stimulation power in front of the cryostat was $50\mathrm{mW}$.

Figure 7

(Color online) Efficiency of the spin-mixing method as a function of the applied rf voltage. The central frequency of the rf wave is $135\mathrm{MHz}$, corresponding to the splitting of the excited-state Zeeman levels. The efficiency is estimated by measuring the fraction of the total number of atoms remaining in the initial state after optical pumping. Both stimulated emission $\left(50\mathrm{mW}\right)$ and rf mixing are used. The duration of the pump sequence is $200\mathrm{ms}$. The stimulation pulse is $1\mathrm{ms}$ longer than the pump pulse, in order to empty the excited state. The inset shows an example of a spectral pit created by population transfer with a frequency sweep of $10\mathrm{MHz}$, without and with rf mixing (with the highest rf voltage of $10\mathrm{V}$ peak to peak).

Figure 8

Spectral tailoring in ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ (black curve). A narrow absorption line (FWHM $2\mathrm{MHz}$) could be established inside a spectral pit (FWHM $50\mathrm{MHz}$). An interesting feature is that the structure written into the absorption can as well be observed in the corresponding antiholes, which again confirms the population transfer into the second Zeeman level of the ground state. The gray curve corresponds to the inhomogeneous absorption without the state preparation sequence. For further details, see text.

Figure 9

Level scheme to estimate the population ratio in the case of standard optical pumping.