Zeeman-level lifetimes in ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$

We present measurements of Zeeman-level population lifetimes in ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$ at low magnetic fields and low temperatures. Using spectral hole burning spectroscopy, we investigate the dynamics and temperature dependence of the hole structure due to the Zeeman interaction. Evidence for population storage in Zeeman levels with lifetimes of up to 130 ms is found in the form of long-lived spectral holes and antiholes. We also observe that a subset of the erbium ions exhibit very long-lived holes with lifetimes as long as 60 s at 2.8 K.

Figure 1

(a) Four-level hole burning spectrum (Zeeman levels) for the class of ions where the laser is in resonance with the $|g_{-}⟩\to |e_{-}⟩$ transition. The $g_G$ $\left(g_E\right)$ is the $g$ factor for the ground (excited) state, ${\mu }_B$ is the Bohr magneton, and $B$ is the applied magnetic field. The pump transition (solid line) and possible probe transitions (dashed lines) between the four levels are shown in the energy diagram and labeled on the corresponding transmission spectrum of holes and antiholes. (b) Four level hole burning spectrum with inhomogeneous broadening. The four different classes of ions within the inhomogeneous profile that are in resonance with the pump beam are shown, along with the resulting transmission spectrum of holes and antiholes (here the probe transitions are not shown for clarity).

Figure 2

(Color online) Visualization of the angle of the magnetic field $\vec{B}$ with respect to the axes. $\vec{B}$ lies in the plane spanned by $D_1$ and $D_2$. The light propagates in a direction parallel with the $b$ axis.

Figure 3

(Color online) Spectral hole burning spectra recorded 1 ms after the hole burning pulse. Antiholes at first Zeeman splitting become holes for higher temperatures. The magnetic field is 1.2 mT applied at $135°$ to the $D_1$ axis in the $D_1\text{−}{D}_2$ plane.

Figure 4

Ratio of area of antihole to the central hole at 1 ms after burn pulse as a function of temperature for $B$ at $135°$ (circles), as in Fig. 3, and $B$ at $90°$ (squares). The line at zero indicates the crossing between hole and antihole.

Figure 5

(a) Area of the antihole (circles, right axis) and hole (squares, left axis) as a function of delay for $B$ at $135°$. The solid lines are exponential fits with an extracted Zeeman lifetime of $129\pm 4\text{ms}$. The fit for the antihole starts at 50 ms. (b) Ratio of area (absolute value) of antihole to hole as a function of delay for $B$ at $135°$ in the $D_1\text{−}{D}_2$ plane. The temperature for this measurement is 2.1 K.

Figure 6

(Color online) Simulation of hole area as a function of time for optical pumping with different branching ratios $\beta$. We assume a Zeeman lifetime of 129 ms for both excited and ground states and an equal $\beta$ for pumping and relaxation for the various transitions.

Figure 7

Zeeman lifetime as a function of temperature for $B$ at $135°$ (filled circles) and $B$ at $90°$ (open circles).

Figure 8

(Color online) (a) Spectral hole burning spectrum after 500 ms for $B=0.34\text{mT}$ at $135°$ for temperatures from 2.5 to 4.5 K. The spectra are normalized with respect to the maximal transmission for each temperature and shifted vertically for clarity. (b) Lifetimes of the long-lived central hole for $B=0.58\text{mT}$ at $90°$ as a function of temperature.