Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.08525

Coupling between CaWO$_4$ phonons and Er$^{3+}$ dopants

Mikhael T. Sayat, Federico Pisani, Hin Lok Chang, Yaroslav Zhumagulov, Kirrily C. Rule, Tom Fennell, Jakob Nunnendorf, Chee Kwan Gan, Oleg V. Yazyev, Ping Koy Lam, Jian-Rui Soh

cond-mat.mtrl-sciquant-phSubmitted Feb 9, 2026• Announced Feb 10, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the lattice dynamics of CaWO$_4$, a promising host crystal for erbium-based quantum memories, using inelastic neutron scattering together with density-functional perturbation theory. The measured phonon dispersion along the (100), (001), and (101) reciprocal space direction reveals phonon bands extending up to 130 meV, with a gap between 60 and 80 meV, in good agreement with our calculations. From a symmetry analysis of the phonon eigenmodes, we identify eight Raman-active modes that can couple directly to the Er$^{3+}$ crystal-field operators, including a low-energy $B_g$ mode at 9.1 meV that is expected to play a dominant role in phonon-assisted spin-lattice relaxation. These results provide a microscopic description of the phonon bath in CaWO$_4$ and establish a basis for engineering phononic environments to mitigate the loss of stored quantum states and optimize Er-doped CaWO$_4$ for quantum-memory applications.

Comments
8 pages, 6 figures

Related papers

Phonon-bottlenecked spin relaxation of Er$^{3+}$:CaWO$_4$ at milliKelvin temperatures

S. Rajendran, B. Mistri, P. K. Sharma +5 more

We study spin-lattice relaxation times of electron spins in Er$^{3+}$:CaWO$_4$ at millikelvin temperature, detected via their coupling to a low-mode volume superconducting resonator. At large magnetic field supporting strong phonon-emission rates, we observe a noticeable increase in relaxation times with increasing spin-excitations, which exhibit a unique $[\tanh (\hbar ω_0/k_\text{B} T)]^2$ temperature dependence. These observations are typical of a phonon-bottlenecked spin relaxation, and have implications for quantum technologies that exploit rare-earth spin ensembles as coherent resources.

quant-pharXiv:2605.18208•May 19, 2026•0 citations

Nuclear quadrupole interaction and zero first-order Zeeman transitions of Er 167 3 + in CaWO 4

Lewin Marsh, Yang Yikai, Cesare Mattiroli +5 more

We report microwave spectroscopy of $^{167}$Er$^{3+}$ doped in CaWO$_4$ which reveals the hyperfine splitting of the erbium electronic ground state ($Z_1$, $J_\mathrm{eff.}$=15/2) induced by the $I$=7/2 nuclear spin. From spectra measured below$\sim$50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron $\textbf{g}$, hyperfine $\textbf{A}$, and nuclear electric quadrupolar $\textbf{Q}$ tensors. Crucially, our analysis demonstrate unambiguously, that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the $c$ axis or within the $a$-$b$ plane. These results establish CaWO$_4$ as a promising host for long lifetime quantum memories.

arXiv:2601.16362•Physical review. B./Physical review. B•Jan 6, 2026•0 citations

Polarisation and temperature dependence of Er 3+ :CaWO 4 —towards a solid-state rare-earth ion-doped quantum memory

Mikhael Sayat, Trevor Rei Lee, Suchit Negi +6 more

Abstract In the development of high-performance optical quantum memories, Er 3+ :CaWO 4 has emerged as a compelling rare-earth ion-doped solid-state platform owing to its long optical coherence times and compatibility with the 1550nm telecommunications band. In this work, we systematically investigate how optical polarisation and temperature influence the absorption strength, central wavelength, and linewidth of the Z 1 → Y 1 and Z 1 → Y 2 transitions, with light incident along the crystal a and c axes. We identify the Z 1 → Y 1 transition at 1532.6 nm with the incident laser propagating along the c -axis at cryogenic temperatures (∼3 K) as particularly advantageous for memory operation. Under these conditions, the transition exhibits a stable central wavelength, narrower linewidth, polarisation-independent absorption, and an enhanced absorption cross-section, while residing within the telecommunication C-band. These combined attributes position the Z 1 → Y 1 line as a robust and suitable point for Er 3+ :CaWO 4 based quantum memories.

Physica Scripta•Jan 27, 2026•1 citation

Experimental Quantification of Spin-Phonon Coupling in Molecular Qubits using Inelastic Neutron Scattering

Stefan H. Lohaus, Kay T. Xia, Yongqiang Cheng +1 more

Electronic spin superposition states enable nanoscale sensing through their sensitivity to the local environment, yet their sensitivity to vibrational motion also limits their coherence times. In molecular spin systems, chemical tunability and atomic-scale resolution are accompanied by a dense, thermally accessible phonon spectrum that introduces efficient spin relaxation pathways. Despite extensive theoretical work, there is little experimental consensus on which vibrational energies dominate spin relaxation or how molecular structure controls spin-phonon coupling (SPC). We present a fully experimental method to quantify SPC coefficients by combining temperature-dependent vibrational spectra from inelastic neutron scattering with spin relaxation rates measured by electron paramagnetic resonance. We apply this framework to two model S = 1/2 systems, copper(II) phthalocyanine (CuPc) and copper(II) octaethylporphyrin (CuOEP). Two distinct relaxation regimes emerge: below 40 K, weakly coupled lattice modes below $50~\mathrm{cm}^{-1}$ dominate, whereas above 40 K, optical phonons above ~$185~\mathrm{cm}^{-1}$ become thermally populated and drive relaxation with SPC coefficients nearly three orders of magnitude larger. Structural distortions in CuOEP that break planar symmetry soften the crystal lattice and enhance anharmonic scattering, but also raise the energy of stretching modes at the molecular core where the spins reside. This redistributes vibrational energy toward the molecular periphery and out of plane, ultimately reducing SPC relative to CuPc and enabling room-temperature spin coherence in CuOEP. Although our method does not provide mode-specific SPC coefficients, it quantifies contributions from distinct spectral regions and establishes a broadly applicable, fully experimental link between crystal structure, lattice dynamics, and spin relaxation.

quant-pharXiv:2602.02792•Feb 4, 2026

Polarisation and Temperature Dependence of Er$^{3+}$:CaWO$_4$ -- Towards a Solid-State Rare-Earth Ion-Doped Quantum Memory

Mikhael Sayat, Lee, Trevor R., Suchit Negi +6 more

In the endeavour of developing quantum memories, Er$^{3+}$:CaWO$_4$ has emerged as a promising rare-earth ion-doped (REID) crystal platform due to its long optical coherence times and compatibility with the 1550 nm telecommunications band. This work investigates the effects of polarisation and temperature on the absorption strength, central wavelength, and linewidth of the $Z_1\to Y_1$ and $Z_1\to Y_2$ optical transitions, with light incident along the crystal $a$ and $c$ axes. It is found that the $Z_1\to Y_1$ transition at 1532.6 nm with the incident laser along the $c$-axis at cryogenic temperatures ($\sim$3 K) is particularly favourable. The transition exhibits a stable central wavelength, narrower linewidth, polarisation independence, larger absorption cross-section, and lies within the C-band -- attributes that make it highly suitable for quantum memory applications.

arXiv:2507.15051•Jul 20, 2025•0 citations

Clock-transition-enabled long electron spin coherence of telecom emitters in CeO$_2$

Basanta Mistri, Vishal Ranjan, Siddharth Dhomkar

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.

quant-pharXiv:2605.07332•Physical review. B./Physical review. B•May 11, 2026•0 citations
Coupling between CaWO4_44​ phonons and Er3+^{3+}3+ dopants
We investigate the lattice dynamics of CaWO4_44​, a promising host crystal for erbium-based quantum memories, using inelastic neutron scattering together with density-functional perturbation theory. The measured phonon dispersion along the (100), (001), and (101) reciprocal space direction reveals phonon bands extending up to 130 meV, with a gap between 60 and 80 meV, in good agreement with our calculations. From a symmetry analysis of the phonon eigenmodes, we identify eight Raman-active modes that can couple directly to the Er3+^{3+}3+ crystal-field operators, including a low-energy BgB_gBg​ mode at 9.1 meV that is expected to play a dominant role in phonon-assisted spin-lattice relaxation. These results provide a microscopic description of the phonon bath in CaWO4_44​ and establish a basis for engineering phononic environments to mitigate the loss of stored quantum states and optimize Er-doped CaWO4_44​ for quantum-memory applications.
Phonon-bottlenecked spin relaxation of Er3+^{3+}3+:CaWO4_44​ at milliKelvin temperatures
We study spin-lattice relaxation times of electron spins in Er3+^{3+}3+:CaWO4_44​ at millikelvin temperature, detected via their coupling to a low-mode volume superconducting resonator. At large magnetic field supporting strong phonon-emission rates, we observe a noticeable increase in relaxation times with increasing spin-excitations, which exhibit a unique [tanh⁡(ℏω0/kBT)]2[\tanh (\hbar ω_0/k_\text{B} T)]^2[tanh(ℏω0​/kB​T)]2 temperature dependence. These observations are typical of a phonon-bottlenecked spin relaxation, and have implications for quantum technologies that exploit rare-earth spin ensembles as coherent resources.
We report microwave spectroscopy of 167^{167}167Er3+^{3+}3+ doped in CaWO4_44​ which reveals the hyperfine splitting of the erbium electronic ground state (Z1Z_1Z1​, Jeff.J_\mathrm{eff.}Jeff.​=15/2) induced by the III=7/2 nuclear spin. From spectra measured below$\sim$50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron g\textbf{g}g, hyperfine A\textbf{A}A, and nuclear electric quadrupolar Q\textbf{Q}Q tensors. Crucially, our analysis demonstrate unambiguously, that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the ccc axis or within the aaa-bbb plane. These results establish CaWO4_44​ as a promising host for long lifetime quantum memories.
Abstract In the development of high-performance optical quantum memories, Er 3+ :CaWO 4 has emerged as a compelling rare-earth ion-doped solid-state platform owing to its long optical coherence times and compatibility with the 1550nm telecommunications band. In this work, we systematically investigate how optical polarisation and temperature influence the absorption strength, central wavelength, and linewidth of the Z 1 → Y 1 and Z 1 → Y 2 transitions, with light incident along the crystal a and c axes. We identify the Z 1 → Y 1 transition at 1532.6 nm with the incident laser propagating along the c -axis at cryogenic temperatures (∼3 K) as particularly advantageous for memory operation. Under these conditions, the transition exhibits a stable central wavelength, narrower linewidth, polarisation-independent absorption, and an enhanced absorption cross-section, while residing within the telecommunication C-band. These combined attributes position the Z 1 → Y 1 line as a robust and suitable point for Er 3+ :CaWO 4 based quantum memories.
Electronic spin superposition states enable nanoscale sensing through their sensitivity to the local environment, yet their sensitivity to vibrational motion also limits their coherence times. In molecular spin systems, chemical tunability and atomic-scale resolution are accompanied by a dense, thermally accessible phonon spectrum that introduces efficient spin relaxation pathways. Despite extensive theoretical work, there is little experimental consensus on which vibrational energies dominate spin relaxation or how molecular structure controls spin-phonon coupling (SPC). We present a fully experimental method to quantify SPC coefficients by combining temperature-dependent vibrational spectra from inelastic neutron scattering with spin relaxation rates measured by electron paramagnetic resonance. We apply this framework to two model S = 1/2 systems, copper(II) phthalocyanine (CuPc) and copper(II) octaethylporphyrin (CuOEP). Two distinct relaxation regimes emerge: below 40 K, weakly coupled lattice modes below 50 cm−150~\mathrm{cm}^{-1}50 cm−1 dominate, whereas above 40 K, optical phonons above ~185 cm−1185~\mathrm{cm}^{-1}185 cm−1 become thermally populated and drive relaxation with SPC coefficients nearly three orders of magnitude larger. Structural distortions in CuOEP that break planar symmetry soften the crystal lattice and enhance anharmonic scattering, but also raise the energy of stretching modes at the molecular core where the spins reside. This redistributes vibrational energy toward the molecular periphery and out of plane, ultimately reducing SPC relative to CuPc and enabling room-temperature spin coherence in CuOEP. Although our method does not provide mode-specific SPC coefficients, it quantifies contributions from distinct spectral regions and establishes a broadly applicable, fully experimental link between crystal structure, lattice dynamics, and spin relaxation.
Polarisation and Temperature Dependence of Er3+^{3+}3+:CaWO4_44​ -- Towards a Solid-State Rare-Earth Ion-Doped Quantum Memory
In the endeavour of developing quantum memories, Er3+^{3+}3+:CaWO4_44​ has emerged as a promising rare-earth ion-doped (REID) crystal platform due to its long optical coherence times and compatibility with the 1550 nm telecommunications band. This work investigates the effects of polarisation and temperature on the absorption strength, central wavelength, and linewidth of the Z1→Y1Z_1\to Y_1Z1​→Y1​ and Z1→Y2Z_1\to Y_2Z1​→Y2​ optical transitions, with light incident along the crystal aaa and ccc axes. It is found that the Z1→Y1Z_1\to Y_1Z1​→Y1​ transition at 1532.6 nm with the incident laser along the ccc-axis at cryogenic temperatures ($\sim$3 K) is particularly favourable. The transition exhibits a stable central wavelength, narrower linewidth, polarisation independence, larger absorption cross-section, and lies within the C-band -- attributes that make it highly suitable for quantum memory applications.
Clock-transition-enabled long electron spin coherence of telecom emitters in CeO2_22​
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 (Er3+^{3+}3+) doped cerium oxide (CeO2_22​) 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 Er3+^{3+}3+ electron spin qubit in CeO2_22​ 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 ∼10\sim 10∼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-πππ-pulse dynamical decoupling protocols. Thus, our findings establish Er3+^{3+}3+ doped CeO2_22​ as a front-runner for realizing spin qubits, quantum memories, and integrated quantum networks.