Physical Review B

Optical decoherence and spectral diffusion at 1.5 μ m in Er 3 + : Y 2 SiO 5 versus magnetic field, temperature, and Er 3 + concentration

Thomas Böttger, Charles W. Thiel, Yiwen Sun, R. L. Cone

Published Feb 1, 2006• 209 citations

Abstract

The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm $^{4}\mathrm{I}_{15∕2}\ensuremath{\rightarrow}^{4}\mathrm{I}_{13∕2}$ transition in ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal ${\mathrm{Er}}^{3+}$ concentrations of 0.0015%, 0.005%, and 0.02%. To understand the effect of spectral diffusion on material decoherence for different environmental conditions and material compositions, data and models were compared to identify spectral diffusion mechanisms and microscopic spin dynamics. Observations were successfully modeled by ${\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Er}}^{3+}$ magnetic dipole interactions and ${\mathrm{Er}}^{3+}$ electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to $^{89}\mathrm{Y}$ nuclear spin flips was also observed. The success in describing our extensive experimental results using simple models provides an important capability for exploring larger parameter spaces, accelerating the design and optimization of materials for spatial-spectral holography, and spectral hole-burning devices. The broad insight into spectral diffusion mechanisms and dynamics is applicable to other paramagnetic materials, such as those containing ${\mathrm{Yb}}^{3+}$ or ${\mathrm{Nd}}^{3+}$.

DOI: 10.1103/physrevb.73.075101

Related papers

Material optimization of Er3+:Y 2 SiO 5 at 1.5 μm for optical processing, memory, and laser frequency stabilization applications

Thomas Boettger, Yongchen Sun, Charles W. Thiel +1 more

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJun 30, 200335 citations

Optical decoherence studies of yttrium oxyorthosilicate Y 2 SiO 5 codoped with Er 3 + and Eu 3 + for optical signal processing and quantum information applications at 1.5 microns

Charles W. Thiel, William Randall Babbitt, R. L. Cone

Physical Review BMay 11, 201238 citations

Controlled compositional disorder in Er 3 + : Y 2 Si O 5 provides a wide-bandwidth spectral hole burning material at 1.5 μ m

Thomas Böttger, Charles W. Thiel, R. L. Cone +1 more

Physical Review BApr 24, 200825 citations

Optical decoherence, spectroscopy, and magnetic g tensors for the 1.5-µm I 15 / 2 4 − I 13 / 2 4 transitions of E r 3 + dopants at the C 2 -symmetry site in Y 2 O 3

Thomas Böttger, Todd L. Harris, G. D. Reinemer +2 more

Physical review. B./Physical review. BJul 17, 20248 citations

Effects of magnetic field orientation on optical decoherence in Er 3 + : Y 2 SiO 5

Thomas Böttger, Charles W. Thiel, R. L. Cone +1 more

Physical Review BMar 10, 2009175 citations

Optical decoherence and spectral diffusion in an erbium-doped silica glass fiber featuring long-lived spin sublevels

Lucile Veissier, Mohsen Falamarzi Askarani, Thomas Lutz +4 more

arXiv:1609.07406Physical review. B./Physical review. BNov 21, 201625 citations

Physical Review B

Optical decoherence and spectral diffusion at 1.5 μ m in Er 3 + : Y 2 SiO 5 versus magnetic field, temperature, and Er 3 + concentration

Thomas Böttger, Charles W. Thiel, Yiwen Sun, R. L. Cone

Published Feb 1, 2006• 209 citations

Publisher

Abstract

The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm

^{4}\mathrm{I}_{15∕2}\ensuremath{\rightarrow}^{4}\mathrm{I}_{13∕2}

transition in

{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from

1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}

to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal

{\mathrm{Er}}^{3+}

concentrations of 0.0015%, 0.005%, and 0.02%. To understand the effect of spectral diffusion on material decoherence for different environmental conditions and material compositions, data and models were compared to identify spectral diffusion mechanisms and microscopic spin dynamics. Observations were successfully modeled by

{\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Er}}^{3+}

magnetic dipole interactions and

{\mathrm{Er}}^{3+}

electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to

^{89}\mathrm{Y}

nuclear spin flips was also observed. The success in describing our extensive experimental results using simple models provides an important capability for exploring larger parameter spaces, accelerating the design and optimization of materials for spatial-spectral holography, and spectral hole-burning devices. The broad insight into spectral diffusion mechanisms and dynamics is applicable to other paramagnetic materials, such as those containing

{\mathrm{Yb}}^{3+}

{\mathrm{Nd}}^{3+}

DOI: 10.1103/physrevb.73.075101

Related papers

Material optimization of Er3+:Y 2 SiO 5 at 1.5 μm for optical processing, memory, and laser frequency stabilization applications

Thomas Boettger, Yongchen Sun, Charles W. Thiel +1 more

Spatial-spectral holography using spectral hole burning materials is a powerful technique for performing real-time, wide-bandwidth information storage and signal processing. For operation in the important 1.5 μm communication band, the material Er3+:Y2SiO5 enables applications such as laser frequency stabilization, all-optical correlators, analog signal processing, and data storage. Site-selective absorption and emission spectroscopy identified spectral hole burning transitions and excited state T1 lifetimes in the 1.5 μm spectral region. The effects of crystal temperature, Er3+-dopant concentration, magnetic field strength, and crystal orientation on spectral diffusion were explored using stimulated photon echo spectroscopy, which is the "prototype" interaction mechanism for device applications. The performance of Er3+:Y2SiO5 and related Er3+ materials has been dramatically enhanced by reducing the effect of spectral diffusion on the coherence lifetime T2 through fundamental material design coupled with the application of an external magnetic field oriented along specific directions. A preferred magnetic field orientation that maximized T2 by minimizing the effects of spectral diffusion was determined using the results of angle-dependent Zeeman spectroscopy. The observed linewidth broadening due to spectral diffusion was successfully modeled by considering the effect of one-phonon (direct) processes on Er3+ - Er3+ interactions. The reported studies improved our understanding of Er3+ materials, explored the range of conditions and material parameters required to optimize performance for specific applications, and enabled measurement of the narrowest optical resonance ever observed in a solid-with a homogeneous linewidth of 73 Hz. With the optimized materials and operating conditions, photon echoes were observed up to temperatures of 5 K, enabling 0.5 GHz bandwidth optical signal processing at 4.2 K and providing the possibility for operation with a closed-cycle cryocooler.Spatial-spectral holography using spectral hole burning materials is a powerful technique for performing real-time, wide-bandwidth information storage and signal processing. For operation in the important 1.5 μm communication band, the material Er3+:Y2SiO5 enables applications such as laser frequency stabilization, all-optical correlators, analog signal processing, and data storage. Site-selective absorption and emission spectroscopy identified spectral hole burning transitions and excited state T1 lifetimes in the 1.5 μm spectral region. The effects of crystal temperature, Er3+-dopant concentration, magnetic field strength, and crystal orientation on spectral diffusion were explored using stimulated photon echo spectroscopy, which is the "prototype" interaction mechanism for device applications. The performance of Er3+:Y2SiO5 and related Er3+ materials has been dramatically enhanced by reducing the effect of spectral diffusion on the coherence lifetime T2 through fundamental material design coupled with the application of an external magnetic field oriented along specific directions. A preferred magnetic field orientation that maximized T2 by minimizing the effects of spectral diffusion was determined using the results of angle-dependent Zeeman spectroscopy. The observed linewidth broadening due to spectral diffusion was successfully modeled by considering the effect of one-phonon (direct) processes on Er3+ - Er3+ interactions. The reported studies improved our understanding of Er3+ materials, explored the range of conditions and material parameters required to optimize performance for specific applications, and enabled measurement of the narrowest optical resonance ever observed in a solid-with a homogeneous linewidth of 73 Hz. With the optimized materials and operating conditions, photon echoes were observed up to temperatures of 5 K, enabling 0.5 GHz bandwidth optical signal processing at 4.2 K and providing the possibility for operation with a closed-cycle cryocooler.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJun 30, 200335 citations

Optical decoherence studies of yttrium oxyorthosilicate Y 2 SiO 5 codoped with Er 3 + and Eu 3 + for optical signal processing and quantum information applications at 1.5 microns

Charles W. Thiel, William Randall Babbitt, R. L. Cone

We report detailed studies of the optical decoherence and spectroscopic properties of the 1536-nm optical transition of the bandwidth-engineered material 0.02 $%$ Er:1 $%$ Eu:Y ${}_{2}$ SiO ${}_{5}$ . This work is motivated by the need for comprehensive understanding of new resonant optical materials for spatial-spectral holography and quantum information applications. The dependence of optical decoherence on excitation frequency, applied magnetic field strength and orientation, crystal temperature, measurement time scale, and optical excitation density was studied using stimulated photon echo spectroscopy and time-resolved spectral hole-burning techniques. The effects of weak disorder generated by the introduction of Eu ${}^{3+}$ ions into the lattice was probed by comparing measurements across the static disorder-induced distribution of transition frequencies as well as by comparing with measurements on 0.02 $%$ Er:Y ${}_{2}$ SiO ${}_{5}$ . The results reveal that the coherence properties of Er:Y ${}_{2}$ SiO ${}_{5}$ are preserved in the disordered system; moreover, the increased inhomogeneity produced by the disorder acts to suppress optical decoherence by inhibiting the electronic spin diffusion process, improving material properties for low magnetic field strengths and at increased temperatures desirable for practical applications.We report detailed studies of the optical decoherence and spectroscopic properties of the 1536-nm optical transition of the bandwidth-engineered material 0.02$%$Er:1$%$Eu:Y${}_{2}$SiO${}_{5}$. This work is motivated by the need for comprehensive understanding of new resonant optical materials for spatial-spectral holography and quantum information applications. The dependence of optical decoherence on excitation frequency, applied magnetic field strength and orientation, crystal temperature, measurement time scale, and optical excitation density was studied using stimulated photon echo spectroscopy and time-resolved spectral hole-burning techniques. The effects of weak disorder generated by the introduction of Eu${}^{3+}$ ions into the lattice was probed by comparing measurements across the static disorder-induced distribution of transition frequencies as well as by comparing with measurements on 0.02$%$Er:Y${}_{2}$SiO${}_{5}$. The results reveal that the coherence properties of Er:Y${}_{2}$SiO${}_{5}$ are preserved in the disordered system; moreover, the increased inhomogeneity produced by the disorder acts to suppress optical decoherence by inhibiting the electronic spin diffusion process, improving material properties for low magnetic field strengths and at increased temperatures desirable for practical applications.

Physical Review BMay 11, 201238 citations

Controlled compositional disorder in Er 3 + : Y 2 Si O 5 provides a wide-bandwidth spectral hole burning material at 1.5 μ m

Thomas Böttger, Charles W. Thiel, R. L. Cone +1 more

The subgigahertz spectral bandwidth of the lowest energy $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ ${\mathrm{Er}}^{3+}$ $^{4}I_{15∕2}\ensuremath{\rightarrow}^{4}I_{13∕2}$ optical transition in ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ has been increased to $\ensuremath{\sim}22\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ by intentionally introducing compositional disorder through codoping with ${\mathrm{Eu}}^{3+}$ impurity ions. This illustrates a general bandwidth control technique for spectral hole burning device applications including spatial-spectral holography and quantum computing. Coherence measurements by stimulated photon echoes demonstrated that the increased disorder does not perturb the dynamical properties of the ${\mathrm{Er}}^{3+}$ transition and, thus, gives the desired bandwidth enhancement without penalty in other properties. The echo measurements and model analysis also show that phonon-driven spin flips of ${\mathrm{Er}}^{3+}$ ions in the ground state are responsible for the spectral diffusion that was observed for the optical transition. These results collectively give a better understanding of both the nature of disorder and of the ion-ion interactions in doped materials, and they also enable the high bandwidths required for signal processing and memory applications at $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ based on spectral hole burning.The subgigahertz spectral bandwidth of the lowest energy $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ ${\mathrm{Er}}^{3+}$ $^{4}I_{15∕2}\ensuremath{\rightarrow}^{4}I_{13∕2}$ optical transition in ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ has been increased to $\ensuremath{\sim}22\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ by intentionally introducing compositional disorder through codoping with ${\mathrm{Eu}}^{3+}$ impurity ions. This illustrates a general bandwidth control technique for spectral hole burning device applications including spatial-spectral holography and quantum computing. Coherence measurements by stimulated photon echoes demonstrated that the increased disorder does not perturb the dynamical properties of the ${\mathrm{Er}}^{3+}$ transition and, thus, gives the desired bandwidth enhancement without penalty in other properties. The echo measurements and model analysis also show that phonon-driven spin flips of ${\mathrm{Er}}^{3+}$ ions in the ground state are responsible for the spectral diffusion that was observed for the optical transition. These results collectively give a better understanding of both the nature of disorder and of the ion-ion interactions in doped materials, and they also enable the high bandwidths required for signal processing and memory applications at $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ based on spectral hole burning.

Physical Review BApr 24, 200825 citations

Optical decoherence, spectroscopy, and magnetic g tensors for the 1.5-µm I 15 / 2 4 − I 13 / 2 4 transitions of E r 3 + dopants at the C 2 -symmetry site in Y 2 O 3

Thomas Böttger, Todd L. Harris, G. D. Reinemer +2 more

Erbium-doped solids are a promising platform for quantum technology due to the $\mathrm{E}{\mathrm{r}}^{3+}$ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic ${\mathrm{C}}_{2}$ site of $\mathrm{E}{\mathrm{r}}^{3+}$ in ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}$ $\ensuremath{\leftrightarrow}$ $^{4}I_{13/2}$ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state $g$ tensors. The ${\mathrm{C}}_{2}$ -site $g$ tensor components for the ground state are ${g}_{x}=1.60$ , ${g}_{y}=4.71$ , and ${g}_{z}=11.93$ with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are ${g}_{x}=1.08$ , ${g}_{y}=4.36$ , and ${g}_{z}=10.07$ with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all ${\mathrm{C}}_{2}$ sites become nearly magnetically equivalent with large $g$ values so that spin flips of neighboring $\mathrm{E}{\mathrm{r}}^{3+}$ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With $\mathrm{E}{\mathrm{r}}^{3+}$ : ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.Erbium-doped solids are a promising platform for quantum technology due to the $\mathrm{E}{\mathrm{r}}^{3+}$ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic ${\mathrm{C}}_{2}$ site of $\mathrm{E}{\mathrm{r}}^{3+}$ in ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}$$\ensuremath{\leftrightarrow}$$^{4}I_{13/2}$ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state $g$ tensors. The ${\mathrm{C}}_{2}$-site $g$ tensor components for the ground state are ${g}_{x}=1.60$, ${g}_{y}=4.71$, and ${g}_{z}=11.93$ with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are ${g}_{x}=1.08$, ${g}_{y}=4.36$, and ${g}_{z}=10.07$ with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all ${\mathrm{C}}_{2}$ sites become nearly magnetically equivalent with large $g$ values so that spin flips of neighboring $\mathrm{E}{\mathrm{r}}^{3+}$ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With $\mathrm{E}{\mathrm{r}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.

Physical review. B./Physical review. BJul 17, 20248 citations

Effects of magnetic field orientation on optical decoherence in Er 3 + : Y 2 SiO 5

Thomas Böttger, Charles W. Thiel, R. L. Cone +1 more

The influence of the anisotropic Zeeman effect on optical decoherence was studied for the 1.54 μm telecom transition in Er3+:Y2SiO5 using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state g factor variations for all inequivalent Er3+ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz.The influence of the anisotropic Zeeman effect on optical decoherence was studied for the 1.54 μm telecom transition in Er3+:Y2SiO5 using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state g factor variations for all inequivalent Er3+ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz.

Physical Review BMar 10, 2009175 citations

Optical decoherence and spectral diffusion in an erbium-doped silica glass fiber featuring long-lived spin sublevels

Lucile Veissier, Mohsen Falamarzi Askarani, Thomas Lutz +4 more

Understanding decoherence in cryogenically cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly doped erbium silica glass fiber motivated by our recent observation of efficient and long-lived Zeeman sublevel storage in this material and by its potential for applications at telecommunication wavelengths. We analyze photon echo decays as well as the potential mechanisms of spectral diffusion that can be caused by coupling with dynamic disorder modes that are characteristic for glassy hosts, and by the magnetic dipole-dipole interactions between ${\mathrm{Er}}^{3+}$ ions. We also investigate the effective linewidth as a function of magnetic field, temperature, and time, and then present a model that describes these experimental observations. We highlight that the operating conditions (0.6 K and 0.05 T) at which we previously observed efficient spectral hole burning coincide with those for narrow linewidths (1 MHz)---an important property for applications that has not been reported before for a rare-earth-ion doped glass.Understanding decoherence in cryogenically cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly doped erbium silica glass fiber motivated by our recent observation of efficient and long-lived Zeeman sublevel storage in this material and by its potential for applications at telecommunication wavelengths. We analyze photon echo decays as well as the potential mechanisms of spectral diffusion that can be caused by coupling with dynamic disorder modes that are characteristic for glassy hosts, and by the magnetic dipole-dipole interactions between ${\mathrm{Er}}^{3+}$ ions. We also investigate the effective linewidth as a function of magnetic field, temperature, and time, and then present a model that describes these experimental observations. We highlight that the operating conditions (0.6 K and 0.05 T) at which we previously observed efficient spectral hole burning coincide with those for narrow linewidths (1 MHz)---an important property for applications that has not been reported before for a rare-earth-ion doped glass.

arXiv:1609.07406Physical review. B./Physical review. BNov 21, 201625 citations

The mechanisms and effects of spectral diffusion for optical transitions of paramagnetic ions have been explored using the inhomogeneously broadened 1536 nm

^{4}\mathrm{I}_{15∕2}\ensuremath{\rightarrow}^{4}\mathrm{I}_{13∕2}

transition in

{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

. Using photon echo spectroscopy, spectral diffusion was measured by observing the evolution of the effective coherence lifetimes over time scales from

1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}

to 20 ms for magnetic-field strengths from 0.3 to 6.0 T, temperatures from 1.6 to 6.5 K, and nominal

{\mathrm{Er}}^{3+}

{\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Er}}^{3+}

magnetic dipole interactions and

{\mathrm{Er}}^{3+}

electron spin flips driven by the one-phonon direct process. At temperatures of 4.2 K and higher, spectral diffusion due to

^{89}\mathrm{Y}

{\mathrm{Yb}}^{3+}

{\mathrm{Nd}}^{3+}

We report detailed studies of the optical decoherence and spectroscopic properties of the 1536-nm optical transition of the bandwidth-engineered material 0.02

%

Er:1

%

Eu:Y

{}_{2}

SiO

{}_{5}

. This work is motivated by the need for comprehensive understanding of new resonant optical materials for spatial-spectral holography and quantum information applications. The dependence of optical decoherence on excitation frequency, applied magnetic field strength and orientation, crystal temperature, measurement time scale, and optical excitation density was studied using stimulated photon echo spectroscopy and time-resolved spectral hole-burning techniques. The effects of weak disorder generated by the introduction of Eu

{}^{3+}

ions into the lattice was probed by comparing measurements across the static disorder-induced distribution of transition frequencies as well as by comparing with measurements on 0.02

%

Er:Y

{}_{2}

SiO

{}_{5}

. The results reveal that the coherence properties of Er:Y

{}_{2}

SiO

{}_{5}

are preserved in the disordered system; moreover, the increased inhomogeneity produced by the disorder acts to suppress optical decoherence by inhibiting the electronic spin diffusion process, improving material properties for low magnetic field strengths and at increased temperatures desirable for practical applications.

The subgigahertz spectral bandwidth of the lowest energy $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$

{\mathrm{Er}}^{3+}

$^{4}I_{15∕2}\ensuremath{\rightarrow}^{4}I_{13∕2}$ optical transition in

{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}

has been increased to $\ensuremath{\sim}22\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ by intentionally introducing compositional disorder through codoping with

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

impurity ions. This illustrates a general bandwidth control technique for spectral hole burning device applications including spatial-spectral holography and quantum computing. Coherence measurements by stimulated photon echoes demonstrated that the increased disorder does not perturb the dynamical properties of the

{\mathrm{Er}}^{3+}

transition and, thus, gives the desired bandwidth enhancement without penalty in other properties. The echo measurements and model analysis also show that phonon-driven spin flips of

{\mathrm{Er}}^{3+}

ions in the ground state are responsible for the spectral diffusion that was observed for the optical transition. These results collectively give a better understanding of both the nature of disorder and of the ion-ion interactions in doped materials, and they also enable the high bandwidths required for signal processing and memory applications at $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ based on spectral hole burning.

Erbium-doped solids are a promising platform for quantum technology due to the

\mathrm{E}{\mathrm{r}}^{3+}

1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic

{\mathrm{C}}_{2}

site of

\mathrm{E}{\mathrm{r}}^{3+}

{\mathrm{Y}}_{2}{\mathrm{O}}_{3}

for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the

\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}

$\ensuremath{\leftrightarrow}$

^{4}I_{13/2}

transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state

g

tensors. The

{\mathrm{C}}_{2}

-site

g

tensor components for the ground state are

{g}_{x}=1.60

{g}_{y}=4.71

, and

{g}_{z}=11.93

with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are

{g}_{x}=1.08

{g}_{y}=4.36

, and

{g}_{z}=10.07

with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all

{\mathrm{C}}_{2}

sites become nearly magnetically equivalent with large

g

values so that spin flips of neighboring

\mathrm{E}{\mathrm{r}}^{3+}

ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With

\mathrm{E}{\mathrm{r}}^{3+}

{\mathrm{Y}}_{2}{\mathrm{O}}_{3}

absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.

{\mathrm{Er}}^{3+}

ions. We also investigate the effective linewidth as a function of magnetic field, temperature, and time, and then present a model that describes these experimental observations. We highlight that the operating conditions (0.6 K and 0.05 T) at which we previously observed efficient spectral hole burning coincide with those for narrow linewidths (1 MHz)---an important property for applications that has not been reported before for a rare-earth-ion doped glass.