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Physical Review Letters

Optical Decoherence in Er 3 + -Doped Silicate Fiber: Evidence for Coupled Spin-Elastic Tunneling Systems

R. M. Macfarlane, Yiwen Sun, Peter B. Sellin, R. L. Cone

Published Jan 27, 2006• 35 citations
Publisher

Abstract

We measured the optical decoherence times T2, or, equivalently, the homogeneous line width, in an Er-doped optical fiber at low temperature as a function of external magnetic field and temperature using two-pulse photon echoes. The decoherence times were up to 230 ns at fields above 3 T. The magnitude of the line narrowing induced by a magnetic field of 3 T is 2.5 MHz, which is anomalously large compared to that typical for oxide crystals with similar Er3+ concentration. This is interpreted as evidence for dephasing by coupled spin-elastic tunneling modes where the normal glass tunneling modes acquire a magnetic character by coupling to the Er3+ spin.

DOI
10.1103/physrevlett.96.033602

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We measured the optical decoherence times T2, or, equivalently, the homogeneous line width, in an Er-doped optical fiber at low temperature as a function of external magnetic field and temperature using two-pulse photon echoes. The decoherence times were up to 230 ns at fields above 3 T. The magnitude of the line narrowing induced by a magnetic field of 3 T is 2.5 MHz, which is anomalously large compared to that typical for oxide crystals with similar Er3+ concentration. This is interpreted as evidence for dephasing by coupled spin-elastic tunneling modes where the normal glass tunneling modes acquire a magnetic character by coupling to the Er3+ spin.
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.
A detailed description is presented of photon echo experiments in Nd3+{\mathrm{Nd}}^{3+}Nd3+-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 T1.3{T}^{1.3}T1.3 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.
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.
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 Er3+{\mathrm{Er}}^{3+}Er3+ 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.
We have measured the optical dephasing time of Er(3+) transitions near 1.5 microm in the two crystallographically inequivalent sites of Y(2)SiO(5), using an external-cavity diode laser amplified by an erbium-doped fiber amplifier. Two-pulse photon echoes were observed at zero field and in magnetic fields up to 55kG, with dephasing times as long as 580 micros (corresponding to a linewidth of 550 Hz). Stimulated echoes were also measured and showed evidence of spectral diffusion during the 13-ms lifetime of the (4)I(13/2) level.
Resonance-fluorescence-line-narrowing studies have been performed on a representative group of Er3+ -doped glasses for excitation in both the 1530 and 980-nm bands at 4.2, 77, 200, and 300 K. Fluorozirconate, fluorophosphate, phosphate, silicate, Ge/P-doped and A1/P-doped silica preforms, and Al/P-doped and Ge-doped fibers were examined. At 77 K the homogeneous linewidths were found to be relatively insensitive to composition. In particular, they vary from 1.4 to 1.8 cm-1 for the different hosts using excitation at 1531 nm. At 300 K weak resonant features were observed in most samples, consistent with a small inhomogeneous contribution to a predominantly homogeneous fluorescence emission.