Towards second-long electron spin coherence of a telecom quantum emitter in naturally abundant CeO$_2$

Abstract: Rare-earth-ion-doped crystals has emerged as a promising platform for quantum technologies, owing to their narrow telecom-band optical emission, long spin memory, and compatibility with silicon integrated photonic architectures. However, the realization of scalable quantum devices requires host materials with intrinsically dilute spin environments to suppress decoherence. In this context, erbium (Er$^{3+}$) doped cerium oxide (CeO$_2$) is an attractive candidate due to the ultra-low concentration of nuclear spins in the host matrix and its compatibility with silicon-based technologies. Here we perform a comprehensive investigation of the coherence properties of Er$^{3+}$ electron spin qubit in CeO$_2$ via semiclassical as well as detailed cluster correlation expansion simulations. By systematically exploring magnetic field strength, pulse sequences, erbium concentration, and spin temperature, we identify regimes where decoherence from the spin bath is strongly suppressed. Our investigations illustrate that at dilute doping concentration (of the order of 10 ppb) and sub-Kelvin temperatures, operation near clock transitions enables Hahn-echo coherence times to approach the second timescale even at natural isotopic abundance. Importantly, from a practical standpoint, coherence times on the order of $\sim 10$ ms are expected even at liquid helium temperature (about 2 K) for similar concentrations. Moreover, we demonstrate that an additional enhancement can be obtained with conventional multi-$π$-pulse dynamical decoupling protocols. Thus, our findings establish Er$^{3+}$ doped CeO$_2$ as a front-runner for realizing spin qubits, quantum memories, and integrated quantum networks.

• The paper establishes near-second electron spin coherence times in Er:CeO2 by utilizing clock transitions at ultra-dilute doping and sub-Kelvin temperatures.
• It employs Cluster Correlation Expansion and magnetic-field-gradient methods to quantitatively analyze decoherence mechanisms affecting spin lifetimes.
• Results reveal scalable prospects for on-chip spin-photon interfaces and quantum repeaters with telecom compatibility in a naturally abundant host.

Second-Scale Spin Coherence in Er:CeO$_2$ for Integrated Quantum Networks

Introduction

The paper "Towards second-long electron spin coherence of a telecom quantum emitter in naturally abundant CeO$_2$" (2605.07332) provides a comprehensive theoretical analysis of coherence properties for electron spins associated with Er$^{3+}$ ions in cerium oxide (CeO$_2$) in the regime pertinent for quantum information science. The context is motivated by the need for solid-state, telecom-compatible, and long-coherent quantum memories and repeaters, especially suited for monolithic integration with silicon photonics.

The work explores electron spin decoherence mechanisms in naturally abundant CeO$_2$, circumventing the necessity for isotopic purification, and identifies the operational regimes that push coherence lifetimes to orders superior to those achieved in previously studied systems.

Material Platform, Spin Hamiltonian, and Decoherence Channels

CeO$_2$ is distinguished by its cubic Fm3m symmetry, providing a high-symmetry, low-spin environment, primarily due to $^{140}$Ce's zero nuclear spin and the extremely dilute population of magnetic $^{17}$O ($\sim0.038\%$ natural abundance, $I=5/2$). Erbium dopants substitute for Ce$_2$0 ions, and charge compensation typically occurs through nearby oxygen vacancies. The rare-earth electronic ground states are represented by effective $_2$1 spins with strong hyperfine interaction for $_2$2Er ($_2$3).

The governing Hamiltonian incorporates Zeeman, hyperfine, and bath interaction terms. Crucially, in CeO$_2$4, the cubic crystal field yields an isotropic $_2$5-tensor and hyperfine coupling, greatly simplifying the energetic landscape relevant for magnetic noise suppression.

Decoherence mechanisms are categorized into:

• Slow, quasi-static Overhauser fields from $_2$6O nuclear spins.
• Temperature- and concentration-dependent spectral diffusion and instantaneous diffusion due to dipolar-coupled Er:CeO$_2$7 electron spins.
• Additional, subdominant contributions from paramagnetic defects associated with charge compensation.

Simulation Methodology

The study leverages a two-pronged computational approach:

1. Cluster Correlation Expansion (CCE): Quantitatively models many-body decoherence induced by nuclear and electron spin baths. Full convergence with respect to cluster size, bath radius, and dipole cut-off is explicitly verified.
2. Rapid Magnetic-Field-Gradient-Based $_2$8 Estimation: Identifies clock transitions by calculating first- and second-order derivatives of central spin transition frequencies w.r.t. field. Coherence is mapped efficiently over a wide parameter space and cross-validated by CCE.

This combined strategy enables identification and verification of field-insensitive transitions conducive to maximal coherence enhancement without brute-force bath enumeration.

Results: Identification and Exploitation of Clock Transitions

The energy spectrum analysis as a function of field reveals multiple clock transitions resulting from electron-nuclear level anti-crossings, with transition frequencies showing suppressed linear and quadratic magnetic-field gradients. Specifically, three clock transitions—identified near $_2$9 mT$^{3+}$0 GHz$^{3+}$1, $^{3+}$2 mT$^{3+}$3 GHz$^{3+}$4, and $^{3+}$5 mT$^{3+}$6 GHz$^{3+}$7—support maximal magnetic noise protection.

Statistical CCE simulations across 150 bath realizations show that the ensemble-averaged Hahn-echo (as well as Ramsey) coherence times peak sharply at these fields, confirming that coherence lifetimes are maximized where field sensitivities vanish. At ultra-dilute conditions (10 ppb Er) and sub-Kelvin temperatures, $^{3+}$8 exceeding $^{3+}$9 ms is theoretically attainable—approaching the second timescale for electron spins in a naturally abundant host without isotopic purification.

The cubic symmetry in CeO$_2$0 ensures that the field directionality dependence of coherence near clock transitions is negligible, dramatically reducing experimental complexity for accessing optimal $_2$1.

Temperature and Concentration Dependence

A systematic study over $_2$2 mK–$_2$3 K and $_2$4 ppb–$_2$5 ppm Er$_2$6 content demonstrates that:

• At sub-$_2$7 mK and $_2$8 ppb Er concentration, the system resides in the nuclear-bath-limited regime.
• Increasing Er content introduces significant electron-spin bath-induced decoherence, sharply reducing $_2$9 unless temperature is kept well below $_2$0 mK, where thermal polarization suppresses electron spin flip-flops.
• Even at $_2$1 K, for $_2$2–$_2$3 ppb doping, order-of-10 ms coherence times are feasible at the clock transitions, ensuring compatibility with liquid helium cooling instead of dilution refrigeration.

Dynamical Decoupling Efficacy

Applying multi-pulse CPMG sequences near clock transitions provides further $_2$4 enhancement, well described by a stretched exponential with a concentration-, temperature-, and pulse-number-dependent scaling exponent. The power-law scaling $_2$5 shows $_2$6 in the nuclear-dominated regime, indicating efficient noise filtration, while decreased exponents at elevated temperatures reflect faster electron-mediated decoherence and reduced decoupling efficacy.

Nonetheless, at $_2$7 K and $_2$8 ppb Er, $_2$9 can still approach $_2$0 ms with $_2$1 CPMG pulses, consolidating the potential for robust, long-lived quantum storage under practical conditions.

Implications and Outlook

The convergence of long-lived electron spin coherence ($_2$2 s at the fundamental limit), lack of necessity for isotopic purification, telecom-wavelength optical compatibility, and negligible field misalignment sensitivity positions Er:CeO$_2$3 as a high-priority platform for:

• On-chip, long-coherence spin-photon interfaces
• Microwave/telecom quantum transduction
• Scalable quantum repeater nodes

The analytical framework and simulation code accompanying this work enable efficient exploration of clock-transition-enhanced qubits in similar cubic, low-nuclear-spin hosts, and can inform both material design (dopant species, host selection) and device engineering (field alignment constraints, dilution required).

Possible immediate extensions include experimental confirmation of predicted regimes, application to other rare-earth ions (e.g., Yb$_2$4, Tm$_2$5), and integration with silicon-based nanophotonic structures.

Conclusion

This work establishes, via rigorous many-body simulation and analytical field-sensitivity analysis, the feasibility of achieving near-second electron spin coherence times in Er:CeO$_2$6 under practical, naturally abundant conditions. The identified operational regime—ultra-dilute doping, sub-Kelvin to helium temperatures, and operation at cubic-symmetry clock transitions—addresses key bottlenecks in solid-state quantum memory design. The demonstrated compatibility with telecom-band transitions and silicon integration paves the way for implementing robust, scalable quantum interconnects and long-lived quantum memories in this platform.