🔬 atomic physics

Optical characterization of excited-state spin Hamiltonians and clock transitions at telecommunication wavelength in Tm3+:YAlO3

This paper characterizes the magnetic properties and establishes the spin Hamiltonians for the lowest Stark levels of the 3F4 and 3H4 manifolds in Tm3+:YAlO3 to predict optical clock transitions at telecommunication wavelengths, aiming to enhance optical coherence times for quantum applications.

Original authors: Akshay Babu Karyath, Luozhen Li, Julien Bertrand, Alexandre Kings, Tianyang Shen, Gabriel Aeppli, Simon Gerber, Guy Matmon, Wolfgang Tittel

Published 2026-09-28

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CC BY 4.0

Original authors: Akshay Babu Karyath, Luozhen Li, Julien Bertrand, Alexandre Kings, Tianyang Shen, Gabriel Aeppli, Simon Gerber, Guy Matmon, Wolfgang Tittel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet, ultra-cold world of quantum physics, scientists are constantly searching for ways to make information last longer. Imagine trying to hold a delicate thought in your mind while a noisy crowd shouts around you; the thought fades quickly. In the quantum realm, this "crowd" is often made of tiny, fluctuating magnetic fields that scramble the information stored in atoms. To build the future of secure communication and powerful computers, researchers need atoms that can hold onto their quantum state for a long time, even when the environment is not perfectly still. One promising way to protect these atoms is to find a special setting, a kind of magnetic sweet spot, where the atom becomes temporarily deaf to the surrounding noise. This concept relies on understanding exactly how the internal parts of an atom react to magnetic forces, a task that requires mapping out the atom's energy landscape with extreme precision.

A team of researchers at the University of Geneva and the Paul Scherrer Institute has taken a significant step toward this goal by studying a specific type of atom: the thulium ion, which is embedded inside a crystal made of yttrium aluminum perovskite. These ions are special because they can interact with light at a wavelength of about 1451 nanometers, a color that travels very efficiently through the fiber-optic cables used for global internet and telecommunications. While scientists already knew that these ions could store light-based information, the memory was short-lived, lasting only a few microseconds before the magnetic noise of the crystal caused the information to fade. The researchers wanted to understand exactly why this happened and, more importantly, how to stop it. They focused on the two excited energy levels of the thulium ion that are connected by this telecommunication light, aiming to map out the invisible magnetic rules that govern how these levels shift and split when exposed to a magnetic field.

To do this, the team placed a tiny crystal containing the thulium ions inside a machine that cooled it down to nearly absolute zero, a temperature just above the point where all molecular motion stops. They then applied a strong, uniform magnetic field to the crystal, carefully changing both the strength of the field and the direction in which it pointed. Using a precise laser, they created tiny "holes" in the crystal's ability to absorb light at specific frequencies. By watching how the positions of these holes moved and how they split apart as the magnetic field changed, the researchers could deduce the hidden magnetic properties of the atoms inside. It was like listening to the pitch of a bell change as you tapped it with different forces and from different angles to figure out exactly what the bell was made of.

The measurements revealed a detailed map of how the thulium ions behave. The team found that the magnetic field causes the energy levels of the ions to shift in a predictable way, but the size of this shift depends heavily on the direction of the field relative to the crystal's internal structure. They calculated the specific values that describe how the electron and nuclear spins of the thulium ion interact with the magnetic field, creating a complete mathematical description known as a spin Hamiltonian. This description acts as a blueprint, allowing scientists to predict exactly how the atom will react to any magnetic field they might apply in the future. Crucially, they discovered that the interaction between the electron and the nucleus is much stronger than some previous calculations had suggested, a finding that highlights how the unique shape of the crystal environment alters the atom's behavior.

With this new blueprint in hand, the researchers used their findings to predict the existence of "optical clock transitions." These are very specific combinations of magnetic field strength and direction where the frequency of the light absorbed by the atom becomes almost completely immune to small fluctuations in the magnetic field. In these special spots, the atom is effectively shielded from the noise that usually destroys its quantum information. The team identified several such points, including one where the magnetic field strength is about 30.88 millitesla and points in a specific direction. At this precise setting, the sensitivity of the atom to magnetic noise drops dramatically, suggesting that the memory time could be extended by more than a factor of thirteen compared to other settings.

This work does not yet prove that these long-lived memories can be built, but it provides the essential roadmap for doing so. By identifying the exact conditions under which the thulium ions become stable, the study opens a clear path toward creating quantum memories and single-photon sources that operate at telecommunication wavelengths. If engineers can build devices that operate at these predicted "clock points," they could finally unlock the potential for quantum networks that span long distances, using the existing fiber-optic infrastructure to transmit information that is both secure and indistinguishable from the light we use every day.

Technical Summary: Optical Characterization of Excited-State Spin Hamiltonians and Clock Transitions in Tm³⁺:YAlO₃

Problem Statement
Trivalent thulium ions (Tm³⁺) doped in inorganic crystals are promising candidates for quantum communication technologies, offering long optical and spin coherence times at cryogenic temperatures. While the ground-state transition (³H₆ ↔ ³H₄) at 795 nm has been extensively studied, the excited-state transition between the ³F₄ and ³H₄ manifolds in Tm³⁺:YAlO₃ offers a distinct advantage: its zero-phonon line (ZPL) lies at approximately 1451 nm, within the telecommunication E-band where fiber transmission loss is minimal. Previous work established an optical coherence time of 4.75 µs for this transition. However, to realize applications such as long-lived optical quantum memory and indistinguishable single-photon sources, this coherence time must be extended. The primary limitation is magnetic noise from spin flip-flops in the host crystal and thulium-thulium interactions. A well-established strategy to mitigate this noise is to operate at "clock transitions" (or zero-first-order-Zeeman, ZEFOZ, points), where the transition frequency is first-order insensitive to magnetic field fluctuations. Locating these points requires a complete characterization of the spin Hamiltonians for the relevant energy levels, specifically the lowest Stark levels of the ³F₄ (Y₁) and ³H₄ (X₁) manifolds.

Methodology
The authors employed spectral hole burning (SHB) and optical spectroscopy to characterize the spin Hamiltonians of the Y₁ and X₁ levels in a 0.1% Tm³⁺:YAlO₃ crystal at approximately 800 mK. The experimental setup utilized two continuous-wave lasers: one at 1685 nm to pump population from the ground state (Z₁) to the ³F₄ manifold, and a tunable probe laser at 1451 nm to interrogate the Y₁ ↔ X₁ transition.

The characterization relied on two complementary measurements under varying external magnetic field amplitudes (up to 2 T) and orientations:

Enhanced Nuclear Zeeman Splitting: By creating side holes via spectral hole burning, the authors measured the frequency detuning of these holes relative to the central absorption line. This splitting arises from the linear splitting of Stark levels into nuclear-spin sublevels due to the enhanced nuclear Zeeman effect.
Quadratic Zeeman Shift: The authors measured the shift of the center of the inhomogeneously broadened Y₁ ↔ X₁ absorption line as a function of magnetic field magnitude. This shift results from the second-order (quadratic) Zeeman interaction.

Theoretical modeling was based on the effective spin Hamiltonian for a non-Kramers ion in a low-symmetry crystal field. The Hamiltonian includes terms for the hyperfine interaction, electronic Zeeman interaction, and nuclear Zeeman interaction. For non-Kramers ions like Tm³⁺ (I = 1/2), the first-order electronic Zeeman and hyperfine terms vanish, leaving the nuclear Zeeman term as the first-order contribution and the second-order terms (involving the mixing of Stark levels via the Λ tensor) as the dominant corrections.

Key Contributions and Results

Spin Hamiltonian Characterization: The authors successfully determined the full spin Hamiltonians for the lowest Stark levels of the ³F₄ (Y₁) and ³H₄ (X₁) manifolds. This involved extracting the principal values of the enhanced nuclear Zeeman tensor (Γ) and the magnetic hyperfine constants (A) for both manifolds.
- The hyperfine constants were determined to be $A_{3H4}/h = -465.54 \pm 4.43$ MHz and $A_{3F4}/h = -430.05 \pm 2.33$ MHz. The authors note that the value for the ³H₄ level differs from previous theoretical calculations, likely due to the low Cs point symmetry of the Tm³⁺ site in YAlO₃, which challenges the assumption of a radial 4f wavefunction used in those calculations.
- The Λ tensors, which describe the mixing of Stark levels, were also fully characterized for both sites in the crystal.
Prediction of Optical Clock Transitions: Using the characterized Hamiltonians, the authors numerically calculated the first-order magnetic sensitivity ( $S_1$ $S_{1}$ ) for various transitions (Z₁ ↔ Y₁, Z₁ ↔ X₁, and Y₁ ↔ X₁) across a grid of magnetic field orientations and magnitudes.
- They identified specific magnetic field configurations (amplitude and orientation) where $S_1 \approx 0$ , defining these as optical clock points.
- Table III in the paper lists these points. The authors note that all optical clock transitions involving the Z₁ level of the ³H₆ ground-state manifold exhibit significantly larger second-order sensitivity ( $S_2$ ) compared to the excited-state Y₁ ↔ X₁ transition, making the latter more suitable for coherence applications. For instance, the $Y_1^\uparrow \leftrightarrow X_1^\uparrow$ transition at $|B| \approx 30.88$ mT has an $S_2$ value of 8.9 Hz/G², whereas specific ground-state clock points exhibit values ranging from $\sim 10^3$ to $\sim 10^6$ Hz/G².

Significance
The paper claims that the characterization of these spin Hamiltonians enables the prediction of optical clock transitions for the 1451 nm telecommunication wavelength transition. The authors posit that operating at these specific clock points will suppress the decoherence caused by magnetic field fluctuations (specifically spin flip-flops), thereby extending the optical coherence time of the Y₁ ↔ X₁ transition. This extension is presented as a necessary step toward developing long-lived quantum memories and indistinguishable single-photon sources operating at telecommunication wavelengths. The work demonstrates that optical techniques alone can fully characterize the spin properties of excited states in rare-earth ions, a capability that can be generalized to other crystal systems.

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