Effect of a hybrid transition moment on Stark-modulated photon echoes in Er3+:Y2SiO5

The 1538-nm ${}^{4}{\mathrm{I}}_{15/2} \ensuremath{\rightarrow} {}^{4}{\mathrm{I}}_{13/2}$ transition of ${\mathrm{Er}}^{3+}$ has an unusual hybrid electric-magnetic dipole character, and signatures of the hybrid moment can be expected in coherent transient measurements. Here, we investigate the effect of the hybrid moment in both sites of ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ on Stark-modulated photon echo measurements, showing that it results in a reduction of visibility of the modulated signal as well as phase and polarization shifts. We interpret these effects using a simple optical Bloch equation model, showing that site 1 has a strongly mixed moment and site 2 is predominantly magnetic dipole. We discuss the implications of the hybrid moment for quantum information applications of quantum memories. We also use the echo measurements to extract the Stark shift of the optical transition along three orthogonal directions, finding values between 10.50 and $11.93\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 1 and 1.61 and $15.35\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 2, dependent on the direction of the electric field. We observe a modification of the Zeeman shift by the electric field in both sites and discuss how this may be used to electrically control ${\mathrm{Er}}^{3+}$ spin qubits.