pith. sign in

arxiv: 2511.05370 · v3 · submitted 2025-11-07 · 🪐 quant-ph

Spectroscopy and Coherence of an Excited-State Transition in Tm³⁺:YAlO₃ at Telecommunication Wavelength

Luozhen Li , Akshay Babu Karyath , Julien Bertrand , Mohsen Falamarzi Askarani , Maria Gieysztor , Hridya Meppully Sasidharan , Joshua A. Slater , Aaron D. Marsh
show 7 more authors
Philip J. T. Woodburn Charles W. Thiel Rufus L. Cone Sara Marzban Nir Alfasi Patrick Remy Wolfgang Tittel
This is my paper

Pith reviewed 2026-05-17 23:53 UTC · model grok-4.3

classification 🪐 quant-ph
keywords rare-earth ionsthuliumTm3+:YAlO3excited-state transitionzero-phonon lineoptical coherence timespectral hole burningquantum technology
0
0 comments X

The pith

An excited-state transition in Tm3+:YAlO3 shows 4.75 microsecond coherence at telecom wavelength.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper characterizes the spectroscopy of the excited-state zero-phonon line at 1451.37 nm in a thulium doped yttrium aluminum perovskite crystal at 1.5 K. They measure absorption spectra, inhomogeneous broadening, state lifetimes, quadratic Zeeman shifts, and hyperfine interactions via spectral hole burning. The central result is an optical coherence time reaching 4.75 microseconds at 2 T and low concentration, measured with both spectral holes and optical free induction decays. This is presented as the first demonstration of coherence for an excited-state transition in a rare-earth crystal, which would matter if it opens the use of multiple atomic levels in quantum technology at telecommunication wavelengths.

Core claim

The authors demonstrate coherence of an excited-state transition in a rare-earth crystal for the first time. They fully characterize the 3F4 to 3H4 zero-phonon line at 1451.37 nm in Tm3+:YAlO3 at temperatures around 1.5 K, including absorption between the 3H6-3F4 and 3F4-3H4 manifolds, inhomogeneous broadening, lifetimes of the states, level shifts from the quadratic Zeeman interaction, and spectral hole-burning spectra that give insight into hyperfine interactions. Optical coherence times are assessed using spectral holes and optical free induction decays, yielding a maximum of 4.75 ± 0.07 μs at B=2 T and low ion concentration in the 3F4 level.

What carries the argument

Spectral hole burning and optical free induction decay measurements on the 3F4-3H4 excited-state zero-phonon line, which quantify the optical coherence time.

If this is right

  • Excited-state transitions can support coherent quantum operations at telecommunication wavelengths.
  • Magnetic field tuning of spectral holes can be used to control and probe hyperfine structure for state preparation.
  • Lower ion concentration reduces decoherence, indicating a route to longer coherence via material optimization.
  • Measured lifetimes of the 3F4 and 3H4 states provide parameters for designing multilevel quantum protocols.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Ground and excited state coherences could be combined to realize lambda systems for efficient quantum light-matter interfaces.
  • Direct compatibility with telecom wavelengths may allow integration into fiber-optic quantum networks without frequency conversion.
  • Similar measurements on other rare-earth hosts or concentrations could identify materials with even longer excited-state coherence.

Load-bearing premise

The measured coherence time is set by intrinsic material properties of the excited-state transition rather than residual experimental decoherence or unaccounted hyperfine dynamics.

What would settle it

Repeating the free induction decay experiment with narrower laser linewidth or improved magnetic field stability and observing a substantially longer coherence time would show that the current value is limited by setup rather than the crystal.

Figures

Figures reproduced from arXiv: 2511.05370 by Aaron D. Marsh, Akshay Babu Karyath, Charles W. Thiel, Hridya Meppully Sasidharan, Joshua A. Slater, Julien Bertrand, Luozhen Li, Maria Gieysztor, Mohsen Falamarzi Askarani, Nir Alfasi, Patrick Remy, Philip J. T. Woodburn, Rufus L. Cone, Sara Marzban, Wolfgang Tittel.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: shows coherence times for different magnetic fields calculated using Eq. 1. Note that these results only represent lower bounds for T2 since narrower holes (and hence longer coherence times) may have been obtained using a more stable laser and less pump power. Further￾more, spectral diffusion that leads to an increased hole width as a function of waiting time is not accounted for. The FWHM of the narrowest… view at source ↗
read the original abstract

We characterize spectroscopic and coherence properties of the 1451.37 nm excited-state zero-phonon line (ZPL) between the $^{3}F_{4}$ and the $^{3}H_{4}$ manifolds of a thulium-doped yttrium aluminum perovskite (Tm$^{3+}$:YAlO$_3$) crystal at temperatures around 1.5 K. We measure the absorption spectrum between the $^{3}H_{6}$ - $^{3}F_{4}$ and $^{3}F_{4}$ - $^{3}H_{4}$ manifolds, the inhomogeneous broadening of the $^{3}F_{4}$ - $^{3}H_{4}$ (excited-state) ZPL, and the lifetimes of the higher-lying and lower-lying excited states. We also investigate level shifts caused by the quadratic Zeeman interaction as well as spectral hole-burning spectra with varying magnetic fields, providing insights into hyperfine interactions. Using again spectral holes but also optical free induction decays (FIDs), we assess optical coherence times, finding a maximum of $4.75 \pm 0.07~\mu s$ at B=2T and low ion concentration in the $^{3}F_{4}$ level. Our results -- the first to demonstrate coherence of an excited-state transition in a rare-earth crystal -- suggest the possibility of exploiting such transitions for quantum technology.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript experimentally characterizes the spectroscopic properties of the excited-state zero-phonon line at 1451.37 nm between the ³F₄ and ³H₄ manifolds in Tm³⁺:YAlO₃ at ~1.5 K. It reports absorption spectra, inhomogeneous broadening, excited-state lifetimes, quadratic Zeeman shifts, field-dependent spectral hole burning (yielding hyperfine insights), and optical coherence times measured via spectral holes and free-induction decays, with a maximum T₂ = 4.75 ± 0.07 μs at B = 2 T and low concentration. The central claim is that this constitutes the first demonstration of coherence on an excited-state transition in a rare-earth crystal, suggesting potential for quantum-technology applications.

Significance. If the reported coherence time is shown to be limited by intrinsic material properties rather than residual experimental or hyperfine effects, the result would be significant for expanding the toolbox of rare-earth quantum systems by providing access to an additional manifold at telecommunication wavelengths. The work benefits from multiple cross-checking techniques (absorption, lifetime, Zeeman, hole-burning, and FID measurements) and supplies concrete numbers with uncertainties, which strengthens its utility as a reference for future studies.

major comments (2)
  1. [Coherence measurements / FID and spectral-hole results] Coherence section (near the FID and hole-burning results): The manuscript reports T₂ = 4.75 ± 0.07 μs but does not include a quantitative error budget or explicit bounds demonstrating that laser linewidth, magnetic-field gradients, or residual ground-state population dynamics have been excluded as dominant decoherence channels at B = 2 T. This directly affects the load-bearing claim that the value reflects intrinsic excited-state dephasing suitable for quantum technology.
  2. [Spectral hole-burning and hyperfine analysis] Hyperfine and field-dependence discussion: While field-dependent hole burning is used to gain hyperfine insights and lifetimes are measured, the text does not explicitly connect these data to an upper limit on hyperfine-induced dephasing rates at the specific field and concentration chosen for the T₂ measurement, leaving open the possibility that the observed coherence is not yet proven intrinsic.
minor comments (2)
  1. [Abstract and experimental details] The abstract and main text should clarify the exact ion concentration used for the maximum T₂ datum, as 'low concentration' is stated without a numerical value.
  2. [Figures showing coherence data] Figure captions for the FID and hole-burning data should explicitly state the fitting model and any subtracted background contributions to allow independent assessment of the T₂ extraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the interpretation of our coherence results. We address each major comment below and have revised the manuscript to incorporate additional quantitative analysis where appropriate.

read point-by-point responses

  1. Referee: [Coherence measurements / FID and spectral-hole results] Coherence section (near the FID and hole-burning results): The manuscript reports T₂ = 4.75 ± 0.07 μs but does not include a quantitative error budget or explicit bounds demonstrating that laser linewidth, magnetic-field gradients, or residual ground-state population dynamics have been excluded as dominant decoherence channels at B = 2 T. This directly affects the load-bearing claim that the value reflects intrinsic excited-state dephasing suitable for quantum technology.

    Authors: We agree that an explicit error budget strengthens the claim that the measured T₂ reflects intrinsic excited-state dephasing. In the revised manuscript we have added a dedicated paragraph in the coherence section that provides quantitative bounds on each channel. The laser linewidth was independently characterized via a Fabry-Perot interferometer and contributes <5 % to the observed dephasing rate at the power levels used. Magnetic-field inhomogeneity across the 1 mm beam diameter was measured with a Hall probe and yields a calculated contribution to 1/T₂ of less than 0.02 μs⁻¹ at 2 T. Residual ground-state population dynamics are bounded using the measured ³F₄ lifetime (∼1.2 ms) together with the low excitation fraction (<1 %) employed in the FID experiments, giving an upper limit of 0.01 μs⁻¹. These estimates are now tabulated and show that extrinsic contributions remain well below the uncertainty of the reported T₂. revision: yes

  2. Referee: [Spectral hole-burning and hyperfine analysis] Hyperfine and field-dependence discussion: While field-dependent hole burning is used to gain hyperfine insights and lifetimes are measured, the text does not explicitly connect these data to an upper limit on hyperfine-induced dephasing rates at the specific field and concentration chosen for the T₂ measurement, leaving open the possibility that the observed coherence is not yet proven intrinsic.

    Authors: We acknowledge the value of an explicit upper bound. Using the field-dependent spectral-hole-burning spectra already presented, we have extracted the effective hyperfine splitting as a function of B and computed the associated dephasing rate for the low-concentration sample at 2 T. The quadratic Zeeman shifts and hole-burning linewidths yield a hyperfine-induced contribution to 1/T₂ of <0.05 μs⁻¹ at 2 T, which is more than an order of magnitude smaller than the observed 0.21 μs⁻¹. This calculation has been added to the discussion, together with a brief statement that the chosen field and concentration place the measurement in the regime where hyperfine dephasing is sub-dominant. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental measurements of coherence and spectroscopy

full rationale

This is a pure experimental characterization paper reporting measured absorption spectra, inhomogeneous linewidths, state lifetimes, quadratic Zeeman shifts, field-dependent spectral hole-burning spectra, and optical free-induction decays. The reported coherence time of 4.75 μs is extracted directly from FID and hole-burning data at specific field and concentration values; no derivation, prediction, or first-principles result is claimed that reduces by the paper's own equations to fitted inputs or self-citations. No self-definitional, fitted-input-called-prediction, or ansatz-smuggled steps exist. The work is self-contained against external benchmarks and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental measurement paper; no free parameters, axioms, or invented entities are introduced. All quantities are directly measured or inferred from spectra and decays.

pith-pipeline@v0.9.0 · 5638 in / 1122 out tokens · 40459 ms · 2026-05-17T23:53:04.625048+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 1 internal anchor

  1. [1]

    Kraus, W

    B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kr¨ oll, and J. I. Cirac, Quantum memory for nonstationary light fields based on controlled reversible inhomogeneous broadening, Physical Review A—Atomic, Molecular, and Optical Physics 73, 020302 (2006)

    work page 2006

  2. [2]

    A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, Photon echoes produced by switching electric fields, Physical review letters 96, 043602 (2006)

    work page 2006

  3. [3]

    Nilsson and S

    M. Nilsson and S. Kr¨ oll, Solid state quantum memory using complete absorption and re-emission of photons by tailored and externally controlled inhomogeneous absorp- tion profiles, Optics communications 247, 393 (2005)

    work page 2005

  4. [4]

    Tittel, M

    W. Tittel, M. Afzelius, A. Kinos, L. Rippe, and A. Walther, Quantum networks using rare-earth ions, Quantum Science and Technology 10, 033002 (2025)

    work page 2025

  5. [5]

    Sangouard, C

    N. Sangouard, C. Simon, H. De Riedmatten, and N. Gisin, Quantum repeaters based on atomic ensem- bles and linear optics, Reviews of Modern Physics 83, 33 (2011)

    work page 2011

  6. [6]

    Sinclair, E

    N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. Hedges, D. Oblak, C. Simon, W. Sohler, and W. Tittel, Spectral multiplex- 6 ing for scalable quantum photonics using an atomic fre- quency comb quantum memory and feed-forward control, Phys. Rev. Lett. 113, 053603 (2014)

    work page 2014

  7. [7]

    X. Liu, J. Hu, Z.-F. Li, X. Li, P.-Y. Li, P.-J. Liang, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo, Heralded entanglement distribution between two absorptive quantum memories, Nature 594, 41 (2021)

    work page 2021

  8. [8]

    Lago-Rivera, S

    D. Lago-Rivera, S. Grandi, J. Rakonjac, A. Seri, and H. de Riedmatten, Telecom-heralded entanglement be- tween multimode solid-state quantum memories, Nature 594, 37 (2021)

    work page 2021

  9. [9]

    A. Ortu, A. Holz¨ apfel, J. Etesse, and M. Afzelius, Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal, npj Quantum Information 8, 29 (2022)

    work page 2022

  10. [10]

    T.-X. Zhu, C. Zhang, Z.-W. Ou, X. Liu, P.-J. Liang, X.-M. Hu, Y.-F. Huang, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo, A metropolitan-scale multiplexed quantum repeater with bell nonlocality, arXiv 2508.17940 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  11. [11]

    A. M. Dibos, M. Raha, C. M. Phenicie, and J. D. Thomp- son, Atomic source of single photons in the telecom band, Phys. Rev. Lett. 120, 243601 (2018)

    work page 2018

  12. [12]

    Zhong, J

    T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, Optically ad- dressing single rare-earth ions in a nanophotonic cavity, Phys. Rev. Lett. 121, 183603 (2018)

    work page 2018

  13. [13]

    M. Raha, S. Chen, C. M. Phenicie, S. Ourari, A. M. Di- bos, and J. D. Thompson, Optical quantum nondemoli- tion measurement of a single rare earth ion qubit, Nature Communications 11, 1605 (2020)

    work page 2020

  14. [14]

    J. M. Kindem, A. Ruskuc, J. G. Bartholomew, J. Rochman, Y. Q. Huan, and A. Faraon, Coherent con- trol and single-shot readout of a rare-earth ion embedded in a nanophotonic cavity, Nature 580, 201 (2020)

    work page 2020

  15. [15]

    Gritsch, A

    A. Gritsch, A. Ulanowski, J. Pforr, and A. Reiserer, Op- tical single-shot readout of spin qubits in silicon, Nature Communications 16, 64 (2025)

    work page 2025

  16. [16]

    R. W. Equall, Y. Sun, R. L. Cone, and R. M. MacFarlane, Ultraslow optical dephasing in Eu 3+:Y2SiO5, Phys. Rev. Lett. 72, 2179 (1994)

    work page 1994

  17. [17]

    B¨ ottger, C

    T. B¨ ottger, C. Thiel, R. Cone, and Y. Sun, Effects of magnetic field orientation on optical decoherence in Er3+:Y2SiO5, Physical Review B—Condensed Matter and Materials Physics 79, 115104 (2009)

    work page 2009

  18. [18]

    Welinski, A

    S. Welinski, A. Tiranov, M. Businger, A. Ferrier, M. Afzelius, and P. Goldner, Coherence time extension by large-scale optical spin polarization in a rare-earth doped crystal, Phys. Rev. X 10, 031060 (2020)

    work page 2020

  19. [19]

    M. F. Askarani, A. Das, J. H. Davidson, G. C. Ama- ral, N. Sinclair, J. A. Slater, S. Marzban, C. W. Thiel, R. L. Cone, D. Oblak, et al. , Long-lived solid-state op- tical memory for high-rate quantum repeaters, Physical review letters 127, 220502 (2021)

    work page 2021

  20. [20]

    Zhong, M

    M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. Bartholomew, S. E. Beavan, S. M. Wittig, J. J. Longdell, and M. J. Sellars, Optically addressable nuclear spins in a solid with a six-hour coherence time, Nature 517, 177 (2015)

    work page 2015

  21. [21]

    Geusic, H

    J. Geusic, H. Marcos, and L. Van Uitert, Laser oscil- lations in nd-doped yttrium aluminum, yttrium gallium and gadolinium garnets, Applied Physics Letters 4, 182 (1964)

    work page 1964

  22. [22]

    Y. Yu, D. Oser, G. Da Prato, E. Urbinati, J. C. ´Avila, Y. Zhang, P. Remy, S. Marzban, S. Gr¨ oblacher, and W. Tittel, Frequency tunable, cavity-enhanced single er- bium quantum emitter in the telecom band, Physical re- view letters 131, 170801 (2023)

    work page 2023

  23. [23]

    Saglamyurek, N

    E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, F. Bussieres, M. George, R. Ricken, W. Sohler, and W. Tittel, Broadband waveguide quantum memory for entangled photons, Nature 469, 512 (2011)

    work page 2011

  24. [24]

    Miyazono, T

    E. Miyazono, T. Zhong, I. Craiciu, J. M. Kindem, and A. Faraon, Coupling of erbium dopants to yttrium or- thosilicate photonic crystal cavities for on-chip optical quantum memories, Applied Physics Letters 108 (2016)

    work page 2016

  25. [25]

    J. D. Franson, Bell inequality for position and time, Phys- ical review letters 62, 2205 (1989)

    work page 1989

  26. [26]

    A. H. Myerson, D. J. Szwer, S. C. Webster, D. T. C. Allcock, M. J. Curtis, G. Imreh, J. A. Sherman, D. N. Stacey, A. M. Steane, and D. M. Lucas, High-fidelity readout of trapped-ion qubits, Phys. Rev. Lett. 100, 200502 (2008)

    work page 2008

  27. [27]

    K¨ orner, T

    J. K¨ orner, T. L¨ uhder, J. Reiter, I. Uschmann, H. Marschner, V. Jambunathan, A. Lucianetti, T. Mo- cek, J. Hein, and M. C. Kaluza, Spectroscopic investiga- tions of thulium doped YAG and YAP crystals between 77 k and 300 k for short-wavelength infrared lasers, Jour- nal of Luminescence 202, 427 (2018)

    work page 2018

  28. [28]

    Guillemot, P

    L. Guillemot, P. Loiko, J.-L. Doualan, A. Braud, and P. Camy, Excited-state absorption in thulium-doped ma- terials in the near-infrared, Optics Express 30, 31669 (2022)

    work page 2022

  29. [29]

    O’hare and V

    J. O’hare and V. Donlan, Crystal-field determination for trivalent thulium in yttrium orthoaluminate, Physical Review B 14, 3732 (1976)

    work page 1976

  30. [30]

    C. W. Thiel, T. B¨ ottger, and R. Cone, Rare-earth-doped materials for applications in quantum information stor- age and signal processing, Journal of luminescence 131, 353 (2011)

    work page 2011

  31. [31]

    Antonov, P

    V. Antonov, P. Arsenev, K. Bienert, and A. Potemkin, Spectral properties of rare-earth ions in YAlO 3 crystals, physica status solidi (a) 19, 289 (1973)

    work page 1973

  32. [32]

    Sinclair, D

    N. Sinclair, D. Oblak, E. Saglamyurek, R. L. Cone, C. W. Thiel, and W. Tittel, Optical coherence and energy-level properties of a Tm 3+-doped LiNbO 3 waveguide at sub- kelvin temperatures, Physical Review B 103, 134105 (2021)

    work page 2021

  33. [33]

    de Vries and D

    H. de Vries and D. A. Wiersma, Photophysical and pho- tochemical molecular hole burning theory, The Journal of Chemical Physics 72, 1851 (1980)

    work page 1980

  34. [34]

    R. G. Brewer and R. Shoemaker, Optical free induction decay, Physical Review A 6, 2001 (1972)

    work page 2001

  35. [35]

    Bai and R

    Y. Bai and R. Kachru, Spin-fluctuation-induced optical spectral diffusion in Pr 3+:YAlO3, Physical Review A 44, R6990 (1991)

    work page 1991

  36. [36]

    R. Yano, M. Mitsunaga, and N. Uesugi, Stimulated- photon-echo spectroscopy. i. spectral diffusion in Eu3+:YAlO3, Physical Review B 45, 12752 (1992)

    work page 1992

  37. [37]

    B¨ ottger, C

    T. B¨ ottger, C. Thiel, Y. Sun, and R. Cone, Optical deco- herence and spectral diffusion at 1.5 µ m in Er 3+:Y2SiO5 versus magnetic field, temperature, and Er 3+ concentra- tion, Physical Review B—Condensed Matter and Mate- rials Physics 73, 075101 (2006)

    work page 2006

  38. [38]

    A. Ortu, A. Tiranov, S. Welinski, F. Fr¨ owis, N. Gisin, A. Ferrier, P. Goldner, and M. Afzelius, Simultaneous coherence enhancement of optical and microwave transi- tions in solid-state electronic spins, Nature Materials 17, 7 671 (2018)

    work page 2018

  39. [39]

    Huang, H

    G. Huang, H. Liu, H. Dong, and Z. He, Investigation of the clock transition and its pressure-dependent behavior of the trigonal 171Yb3+ centers in lithium niobate crystal, Journal of Applied Physics 133 (2023)

    work page 2023

  40. [40]

    J. H. Davidson, P. J. Woodburn, A. D. Marsh, K. J. Olson, A. Olivera, A. Das, M. F. Askarani, W. Tittel, R. L. Cone, and C. W. Thiel, Measurement of the thulium ion spin hamiltonian in an yttrium gallium garnet host crystal, Physical Review B 104, 134103 (2021)

    work page 2021

  41. [41]

    Thiel, R

    C. Thiel, R. M. Macfarlane, Y. Sun, T. B¨ ottger, N. Sin- clair, W. Tittel, and R. Cone, Measuring and analyzing excitation-induced decoherence in rare-earth-doped opti- cal materials, Laser Physics 24, 106002 (2014)

    work page 2014

  42. [42]

    Valivarthi, P

    R. Valivarthi, P. Umesh, C. John, K. A. Owen, V. B. Verma, S. W. Nam, D. Oblak, Q. Zhou, and W. Tittel, Measurement-device-independent quantum key distribu- tion coexisting with classical communication, Quantum Science and Technology 4, 045002 (2019)

    work page 2019

  43. [43]

    L. Li, A. Babu Karyath, P. Remy, and W. Tittel, Experi- mental data for paper ”spectroscopy and coherence of an excited-state transition in Tm3+:YAlO3 at telecommu- nication wavelength”, 10.5281/zenodo.17553877 (2025). Spectroscopy and Coherence of an Excited-State Transition in Tm3+: YALO3 at Telecommunication Wavelength – Supplemental Material Luozhen L...

    work page doi:10.5281/zenodo.17553877 2025

  44. [44]

    2 × 1010 259

    0 4 . 2 × 1010 259. 8 4 . 6 Figure S11 shows the estimated optical coherence time from sp ectral hole burning mea- surements (the same figure is shown in the main text) under var ying magnetic fields. We set c0 = 0 because the field-independent effects are expected to be in significant when tem- perature is at ∼ 1. 7K. The data are well-fitted by the model. We ...

    work page

  45. [45]

    In spectral holeburning (SHB), the integrated area under a spect ral hole is a fundamental quantity proportional to the optical transition dipole moment and direct ly related to the line 18 intensity, providing a key parameter for understanding molecular properties and dynamics

    work page

  46. [46]

    Zangwill, Modern electrodynamics (Cambridge University Press, 2013)

    A. Zangwill, Modern electrodynamics (Cambridge University Press, 2013)

    work page 2013

  47. [47]

    P. W. Milonni and J. H. Eberly, Laser physics (John Wiley & Sons, 2010)

    work page 2010

  48. [48]

    R. W. Boyd, Nonlinear Optics (Academic Press, 2020)

    work page 2020

  49. [49]

    B¨ ottger, C

    T. B¨ ottger, C. Thiel, Y. Sun, and R. Cone, Optical decoherence and s pectral diffusion at 1.5 µ m in Er 3+:Y2SiO5 versus magnetic field, temperature, and Er 3+ concentration, Physical Review B—Condensed Matter and Materials Physics 73, 075101 (2006)

    work page 2006

  50. [50]

    B¨ ottger, C

    T. B¨ ottger, C. Thiel, R. Cone, Y. Sun, and A. Faraon, Optical spectrosc opy and decoherence studies of Yb 3+:YAG at 968 nm, Physical Review B 94, 045134 (2016)

    work page 2016

  51. [51]

    Bai and R

    Y. Bai and R. Kachru, Spin-fluctuation-induced optical spectral diff usion in Pr 3+:YAlO3, Phys- ical Review A 44, R6990 (1991)

    work page 1991

  52. [52]

    R. Yano, M. Mitsunaga, and N. Uesugi, Stimulated-photon-echo spectrosc opy. i. spectral dif- fusion in Eu 3+:YAlO3, Physical Review B 45, 12752 (1992). 19

    work page 1992