We show that Stark-pulse-modulated photon echoes in an impurity-ion-doped crystal are generally characterized by a complex oscillatory behavior with two or more frequency components which results from the interference of the static dipole moment differences of ions located at inequivalent sites. We analyze this phenomenon using group theory and present experimental evidence for a ${\mathrm{Pr}}^{3+}$ - and ${\mathrm{Eu}}^{3+}$ -codoped ${\mathrm{YAlO}}_{3}$ and a ${\mathrm{Pr}}^{3+}$ -doped ${\mathrm{Y}}_{2}$ ${\mathrm{SiO}}_{5}$ crystal. It is demonstrated that the orientations of the dipole moments and of the crystal axes can be determined with subdegree accuracy.We show that Stark-pulse-modulated photon echoes in an impurity-ion-doped crystal are generally characterized by a complex oscillatory behavior with two or more frequency components which results from the interference of the static dipole moment differences of ions located at inequivalent sites. We analyze this phenomenon using group theory and present experimental evidence for a ${\mathrm{Pr}}^{3+}$- and ${\mathrm{Eu}}^{3+}$-codoped ${\mathrm{YAlO}}_{3}$ and a ${\mathrm{Pr}}^{3+}$-doped ${\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5}$ crystal. It is demonstrated that the orientations of the dipole moments and of the crystal axes can be determined with subdegree accuracy.

Physical review. B, Condensed matterMay 1, 199727 citations

Modulation of photon echoes in a three-level system

A.I. Alekseyev, Ashat M. Basharov, Igor V. Yevseyev

Physics Letters ADec 1, 19780 citations

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

Rose L. Ahlefeldt, Alexey Lyasota, Jodie Smith +2 more

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.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.

Physical review. B./Physical review. BNov 13, 20231 citation

Effect of a hybrid transition moment on Stark-modulated photon echoes in Er $^{3+}$ :Y $_2$ SiO $_5$ Effect of a hybrid transition moment on Stark-modulated photon echoes in Er$^{3+}$:Y$_2$SiO$_5$

Rose L. Ahlefeldt, Alexey Lyasota, Smith, Jodie +2 more

The 1538 nm ${}^4$ I $_{15/2}$ - ${}^4$ I $_{13/2}$ transition of 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 Er $^{3+}$ :Y $_2$ 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 kHz/(V/cm) for site 1 and 1.61 and 15.35 kHz/(V/cm) for site 2. 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 Er $^{3+}$ spin qubits.The 1538 nm ${}^4$I$_{15/2}$ - ${}^4$I$_{13/2}$ transition of 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 Er$^{3+}$:Y$_2$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 kHz/(V/cm) for site 1 and 1.61 and 15.35 kHz/(V/cm) for site 2. 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 Er$^{3+}$ spin qubits.

arXiv:2306.12007Jun 21, 20230 citations

{\mathrm{Pr}}^{3+}

- and

{\mathrm{Eu}}^{3+}

-codoped

{\mathrm{YAlO}}_{3}

and a

{\mathrm{Pr}}^{3+}

-doped

{\mathrm{Y}}_{2}

{\mathrm{SiO}}_{5}

crystal. It is demonstrated that the orientations of the dipole moments and of the crystal axes can be determined with subdegree accuracy.

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.

Effect of a hybrid transition moment on Stark-modulated photon echoes in Er

^{3+}

_2

SiO

_5

The 1538 nm

{}^4

_{15/2}

{}^4

_{13/2}

transition of Er

^{3+}

^{3+}

_2

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 kHz/(V/cm) for site 1 and 1.61 and 15.35 kHz/(V/cm) for site 2. 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 Er

^{3+}

spin qubits.