Spectral hole lifetimes and spin population relaxation dynamics in neodymium-doped yttrium orthosilicate

We present a detailed study of the lifetime of optical spectral holes due to population storage in Zeeman sublevels of ${\mathrm{Nd}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. The lifetime is measured as a function of magnetic field strength and orientation, temperature, and ${\mathrm{Nd}}^{3+}$ doping concentration. At the lowest temperature of 3 K we find a general trend where the lifetime is short at low field strengths, then increases to a maximum lifetime at a few hundred mT, and then finally decays rapidly for high field strengths. This behavior can be modeled with a relaxation rate dominated by ${\mathrm{Nd}}^{3+}-{\mathrm{Nd}}^{3+}$ cross relaxation at low fields and spin lattice relaxation at high magnetic fields. The maximum lifetime depends strongly on both the field strength and orientation, due to the competition between these processes and their different angular dependencies. The cross relaxation limits the maximum lifetime for concentrations as low as 30 ppm of ${\mathrm{Nd}}^{3+}$ ions. By decreasing the concentration to less than 1 ppm we could completely eliminate the cross relaxation, reaching a lifetime of 3.8 s at 3 K. At higher temperatures the spectral hole lifetime is limited by the magnetic-field-independent Raman and Orbach processes. In addition we show that the cross relaxation rate can be strongly reduced by creating spectrally large holes of the order of the optical inhomogeneous broadening. Our results are important for the development and design of new rare-earth-ion doped crystals for quantum information processing and narrow-band spectral filtering for biological tissue imaging.

Figure 1

Kramers doublet splitting under an external magnetic field $B$ for the case of ${\mathrm{Nd}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$. Each crystal-field level within the electronic states ${}^{4}I_{9/2}$ and ${}^{4}F_{3/2}$ consists of two magnetic sublevels $m_s=\pm 1/2$. Note that only the lowest crystal-field level of each electronic state is shown here. The magnetic sublevels become nondegenerate under the presence of a magnetic field. The splitting in energy depends linearly on the magnetic field $B$ and on the effective $g$ factor $g\left(\theta \right)$, which characterizes the angular dependence of the splitting. On the right, the convention used for the magnetic field angle $\theta$ is shown. The magnetic field is static and is applied in the ${\mathbf{D}}_1-{\mathbf{D}}_2$ plane, where ${\mathbf{D}}_1$ and ${\mathbf{D}}_2$ are the so-called polarization extinction axes of the ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. Absorption is maximal when the polarization of light is linear and aligned with ${\mathbf{D}}_1$.

Figure 2

Illustration of the creation of two spin populations by spectral hole burning on an optical transition within a four-level system as shown in Fig. 1. For simplicity we assume that only two transitions are spectrally distinguishable, originating from each ${}^{4}I_{9/2}$ spin level. These optical transitions are inhomogeneously broadened with average frequencies ${\omega }_1$ and ${\omega }_2$. A narrow hole is burned into the ${\omega }_2$ absorption line by optically pumping the spins into the upper ${}^{4}I_{9/2}$ spin level. This creates a highly polarized spin ensemble in that narrow spectral region, denoted as ensemble A (in red), while the remaining ions have a thermal distribution, denoted as ensemble B (in cyan). A spin of ensemble A can flip-flop with a spin of ensemble B, as depicted by dashed arrows. This causes a decrease in the spin polarization of ensemble A and a time-dependent decay of the spectral hole. The associated increase in absorption on the ${\omega }_1$ line is not measurable since it is distributed over the large spectral region made up of ensemble B spins. Note that spectral hole burning would in principle lead to several side holes and antiholes [34], of which only one antihole at ${\omega }_1$ is shown here for simplicity.

Figure 3

Lifetime of the spectral hole versus magnetic field strength, for a ${\text{Nd}}^{3+}$ concentration of $30\mathrm{ppm}$ and at three different angles $\theta =0^{\circ }$ (blue circles), $\theta ={90}^{\circ }$ (red filled squares), and $\theta ={120}^{\circ }$ (black diamonds). Data for $\theta ={90}^{\circ }$ and the crystal with $75\mathrm{ppm}{\text{Nd}}^{3+}$ concentration is also shown (red open squares). The figure shows both experimental data and fits from the model based on SLR and FF (see Sec. 4a for details). The temperature was 3 K for all data sets.

Figure 4

Maximum spectral hole lifetime for each of the measured angles in the crystal with 30 ppm ${\mathrm{Nd}}^{3+}$ concentration at a temperature of 3 K. We can distinguish a global maximum at $\theta ={120}^{\circ }$ and a local maximum at $\theta =0^{\circ }$. As discussed in Sec. 4a, the global maximum is at $\theta ={120}^{\circ }$ because the FF rate is minimal at this angle.

Figure 5

Angular dependence of the coupling parameters presented in the main text and the relaxation rate. In (a) we show the angular variation of ${\alpha }_{\mathrm{D}}\left(\theta \right)g{\left(\theta \right)}^2$ (in units of Hz/${\mathrm{T}}^5$) and ${\gamma }_{\mathrm{FF}}\left(\theta \right)$ (in units of $\mathrm{Hz}\mathrm{T}$). The direct SLR process varies somewhat like a sine function, with a minimum around ${\mathbf{D}}_1$, while the FF appears to have two minima, at ${\mathbf{D}}_1$ and $\theta ={120}^{\circ }$, respectively. In (b) we show the angular dependence of the total relaxation rate $R_{\mathrm{SLR}}+R_{\mathrm{FF}}$ for $B=0.1$, 0.4, 0.7, and 1 T. The minimum rate at about $\theta ={120}^{\circ }$, for a field of 0.4 T, explains the maximum lifetime of 156 ms observed for this field strength (cf. Fig. 4).

Figure 6

Spectral hole lifetime as a function of temperature for the ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystals doped with $30\mathrm{ppm}$ (blue diamonds) and $75\mathrm{ppm}$ (black squares) of ${\mathrm{Nd}}^{3+}$ ions. The magnetic field strength was $B=0.3\mathrm{T}$, oriented with an angle of $\theta ={120}^{\circ }$ with respect to the ${\mathbf{D}}_1$ axis. Both full and dashed lines represent different models used to interpret the data, and are discussed in detail in Sec. 4b.

Figure 7

Spectral hole lifetimes for the crystals with $30\mathrm{ppm}$ (red circles), $75\mathrm{ppm}$ (blue squares), and $\le 1$ ppm (black stars) ${\mathrm{Nd}}^{3+}$ doping concentrations. The temperature was 3 K and the field was oriented along the ${\mathbf{D}}_2$ axis ($\theta ={90}^{\circ }$). We also provide an extrapolation of the model for the spectral hole lifetime (solid line) for a crystal where there is no flip-flop mechanism (see Sec. 4c for details). The green star shows the lifetime achieved by burning a very large spectral hole in the $30\mathrm{ppm}$ crystal, as discussed in Sec. 4d.

Figure 8

Spectral hole decay measurements for a narrow spectral hole (blue squares) and a large spectral hole (red diamonds). The narrow hole has a linewidth of a few MHz, while the large hole represents optical pumping of about 50% of the ions within the optical inhomogeneous linewidth of about 6 GHz. The solid lines show the fitted single-exponential curves, which give lifetimes of 50 ms (blue line) and 320 ms (red line), respectively. Inset: Shown are a narrow (blue line) and large (red line) spectral hole burned into the inhomogeneous broadening. The structure of the large hole is a result of the pattern of holes and antiholes convoluted with the rectangular burn spectrum.