Physical Review Letters

Photon Echoes below 1 K in a Nd3+ -Doped Glass Fiber

John Hegarty, Matthijs M. Broer, Brage Golding, J. R. Simpson, John B. MacChesney

Published Nov 28, 1983• 122 citations

Abstract

Optical dephasing rates ${{T}_{2}}^{\ensuremath{-}1}$ of a dilute concentration of ${\mathrm{Nd}}^{3+}$ ions in a pure silica fiber have been studied from 0.05 to 1.0 K with use of two-pulse photon echoes. Echoes obtained by resonant excitation of ${\mathrm{Nd}}^{3+}$ into the metastable $^{4}F_{\frac{3}{2}}$ state from the $^{4}I_{\frac{9}{2}}$ ground state have yielded ${{T}_{2}}^{\ensuremath{-}1}=1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{s}}^{\ensuremath{-}1}$ at 0.1 K which follows a ${T}^{\frac{4}{3}}$ temperature dependence to 1.0 K. A crossover of ${{T}_{2}}^{\ensuremath{-}1}$ to a ${T}^{2}$ temperature dependence above 1 K is inferred by comparison with earlier high-temperature linewidth measurements on this transition.

DOI: 10.1103/physrevlett.51.2033

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Coherent transients in active optical fibers

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Physical Review Letters

Photon Echoes below 1 K in a Nd3+ -Doped Glass Fiber

John Hegarty, Matthijs M. Broer, Brage Golding, J. R. Simpson, John B. MacChesney

Published Nov 28, 1983• 122 citations

Publisher

Abstract

Optical dephasing rates

{{T}_{2}}^{\ensuremath{-}1}

of a dilute concentration of

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

ions in a pure silica fiber have been studied from 0.05 to 1.0 K with use of two-pulse photon echoes. Echoes obtained by resonant excitation of

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

into the metastable

^{4}F_{\frac{3}{2}}

state from the

^{4}I_{\frac{9}{2}}

ground state have yielded

{{T}_{2}}^{\ensuremath{-}1}=1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}

{\mathrm{s}}^{\ensuremath{-}1}

at 0.1 K which follows a

{T}^{\frac{4}{3}}

temperature dependence to 1.0 K. A crossover of

{{T}_{2}}^{\ensuremath{-}1}

to a

{T}^{2}

temperature dependence above 1 K is inferred by comparison with earlier high-temperature linewidth measurements on this transition.

DOI: 10.1103/physrevlett.51.2033

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A detailed description is presented of photon echo experiments in ${\mathrm{Nd}}^{3+}$ -doped silica optical fibers at temperatures below 1 K. Dephasing rates ${T}_{2}^{\mathrm{\ensuremath{-}}1}$ have been obtained from two-pulse echo sequences at 0.89 \ensuremath{\mu}m and are found to follow a ${T}^{1.3}$ temperature dependence. An interpretation of this result is presented which invokes the interaction of tunneling systems with the optical ions via a dipole-dipole elastic interaction. The dynamics of the interaction originates in a spectral diffusion process and three pulse stimulated echo experiments confirm this interpretation.A detailed description is presented of photon echo experiments in ${\mathrm{Nd}}^{3+}$-doped silica optical fibers at temperatures below 1 K. Dephasing rates ${T}_{2}^{\mathrm{\ensuremath{-}}1}$ have been obtained from two-pulse echo sequences at 0.89 \ensuremath{\mu}m and are found to follow a ${T}^{1.3}$ temperature dependence. An interpretation of this result is presented which invokes the interaction of tunneling systems with the optical ions via a dipole-dipole elastic interaction. The dynamics of the interaction originates in a spectral diffusion process and three pulse stimulated echo experiments confirm this interpretation.

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Ryuzi Yano, Naoshi Uesugi

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Ultra-narrow homogeneous linewidths of erbium-doped silica glass fibers at millikelvin temperatures: magnetic field and temperature dependence

Farhad Rasekh, Nasser Gohari Kamel, Mahdi Bornadel +4 more

Erbium-doped solids are promising candidates for fiber-based quantum networks due to their emission wavelength, which aligns with the telecom band over which optical fibers exhibit minimal loss. Among these, erbium-doped silica fiber (EDF) stands out for its availability, ease of use, and seamless integration with existing fiber-optic infrastructure. In this work, using the two-pulse photon-echo (2PPE) technique, we measured the homogeneous linewidth of the 4 I 13/2 ↔ 4 I 15/2 optical transition under varying magnetic fields and temperatures. We observed an effective homogeneous linewidth of approximately 8 kHz at ∼7mK at an optimal magnetic field of 0.09 T, representing over two orders of magnitude improvement compared to earlier reports measured at T ≈700mK. We also present a comprehensive model for the combined magnetic field and temperature dependency of the effective homogeneous linewidth. Additionally, we employed three-pulse photon-echo (3PPE) measurements to investigate spectral diffusion and decoherence processes and conclude that Two-Level System (TLS) effects are significantly suppressed at sufficiently low temperatures, below ∼100mK.Erbium-doped solids are promising candidates for fiber-based quantum networks due to their emission wavelength, which aligns with the telecom band over which optical fibers exhibit minimal loss. Among these, erbium-doped silica fiber (EDF) stands out for its availability, ease of use, and seamless integration with existing fiber-optic infrastructure. In this work, using the two-pulse photon-echo (2PPE) technique, we measured the homogeneous linewidth of the 4 I 13/2 ↔ 4 I 15/2 optical transition under varying magnetic fields and temperatures. We observed an effective homogeneous linewidth of approximately 8 kHz at ∼7mK at an optimal magnetic field of 0.09 T, representing over two orders of magnitude improvement compared to earlier reports measured at T ≈700mK. We also present a comprehensive model for the combined magnetic field and temperature dependency of the effective homogeneous linewidth. Additionally, we employed three-pulse photon-echo (3PPE) measurements to investigate spectral diffusion and decoherence processes and conclude that Two-Level System (TLS) effects are significantly suppressed at sufficiently low temperatures, below ∼100mK.

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Keith W. Ver Steeg, Alexander Ya. Karasik, Roger J. Reeves +2 more

Accumulated photon echoes were used to measure the dephasing time ( ${\mathit{T}}_{2}$ ) of the $^{4}$ ${\mathit{I}}_{9/2}$ ${\ensuremath{\rightarrow}}^{4}$ ${\mathit{G}}_{5/2}$ ${,}^{2}$ ${\mathit{G}}_{7/2}$ transition of ${\mathrm{Nd}}^{3+}$ in highly disordered ${\mathrm{CaF}}_{2}$ - ${\mathrm{YF}}_{3}$ crystals. ${\mathit{T}}_{2}$ decreased from subnanosecond values for excitation of low-lying Stark levels to subpicosecond values for excitation of high-lying levels. From 9--100 K the measured temperature dependence of the homogeneous linewidth is described by a resonant single-phonon absorption process.Accumulated photon echoes were used to measure the dephasing time (${\mathit{T}}_{2}$) of the $^{4}$${\mathit{I}}_{9/2}$${\ensuremath{\rightarrow}}^{4}$${\mathit{G}}_{5/2}$${,}^{2}$${\mathit{G}}_{7/2}$ transition of ${\mathrm{Nd}}^{3+}$ in highly disordered ${\mathrm{CaF}}_{2}$-${\mathrm{YF}}_{3}$ crystals. ${\mathit{T}}_{2}$ decreased from subnanosecond values for excitation of low-lying Stark levels to subpicosecond values for excitation of high-lying levels. From 9--100 K the measured temperature dependence of the homogeneous linewidth is described by a resonant single-phonon absorption process.

Physical review. B, Condensed matterMar 1, 19958 citations

Optical dephasing rates

{{T}_{2}}^{\ensuremath{-}1}

of a dilute concentration of

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

ions in a pure silica fiber have been studied from 0.05 to 1.0 K with use of two-pulse photon echoes. Echoes obtained by resonant excitation of

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

into the metastable

^{4}F_{\frac{3}{2}}

state from the

^{4}I_{\frac{9}{2}}

ground state have yielded

{{T}_{2}}^{\ensuremath{-}1}=1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}

{\mathrm{s}}^{\ensuremath{-}1}

at 0.1 K which follows a

{T}^{\frac{4}{3}}

temperature dependence to 1.0 K. A crossover of

{{T}_{2}}^{\ensuremath{-}1}

to a

{T}^{2}

temperature dependence above 1 K is inferred by comparison with earlier high-temperature linewidth measurements on this transition.

A detailed description is presented of photon echo experiments in

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

-doped silica optical fibers at temperatures below 1 K. Dephasing rates ${T}_{2}^{\mathrm{\ensuremath{-}}1}$ have been obtained from two-pulse echo sequences at 0.89 \ensuremath{\mu}m and are found to follow a

{T}^{1.3}

temperature dependence. An interpretation of this result is presented which invokes the interaction of tunneling systems with the optical ions via a dipole-dipole elastic interaction. The dynamics of the interaction originates in a spectral diffusion process and three pulse stimulated echo experiments confirm this interpretation.

Measurements of the homogeneous width of the

^{4}

{\mathrm{G}}_{5\mathrm{/}2}

^{2}

{\mathrm{G}}_{7\mathrm{/}2}

${\mathrm{\ensuremath{-}}}^{4}$

{\mathrm{I}}_{9\mathrm{/}2}

transition of

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

in a silicate glass fiber at low temperatures by the technique of accumulated photon echoes show that the dephasing processes are one-phonon processes between the Stark levels of

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

. These dephasing processes differ from the commonly observed processes of rare-earth ion-doped glasses: the local-configurational-change-induced dephasing process and the Raman process with low-frequency modes. The densely distributed Stark levels of the

^{4}

{\mathrm{G}}_{5\mathrm{/}2}

and

^{2}

{\mathrm{G}}_{7\mathrm{/}2}

states are responsible for one-phonon processes. The transition-wavelength dependences of the homogeneous widths ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{h}}$ (4.2 K) and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{h}}$ (T\ensuremath{\rightarrow}0) are explained by using the one-phonon process model.

Accumulated photon echoes were used to measure the dephasing time (

{\mathit{T}}_{2}

) of the

^{4}

{\mathit{I}}_{9/2}

${\ensuremath{\rightarrow}}^{4}$

{\mathit{G}}_{5/2}

{,}^{2}

{\mathit{G}}_{7/2}

transition of

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

in highly disordered

{\mathrm{CaF}}_{2}

{\mathrm{YF}}_{3}

crystals.

{\mathit{T}}_{2}

decreased from subnanosecond values for excitation of low-lying Stark levels to subpicosecond values for excitation of high-lying levels. From 9--100 K the measured temperature dependence of the homogeneous linewidth is described by a resonant single-phonon absorption process.