[Paper Review] Strong Coupling Between Whispering Gallery Photons and Spin States of Iron Group Impurity Ions

Maxim Goryachev, Warrick G. Farr+6 more|arXiv (Cornell University)|Oct 24, 2014

Advanced Fiber Laser Technologies3 references8 citations

TL;DR

This study discovers strong coupling between whispering gallery mode (WGM) microwave photons and spin states of iron group impurity ions (Cr³⁺, Cr⁴⁺, Ni²⁺) in Er³⁺:Y₂SiO₅ and Eu³⁺:Y₂SiO₅ single crystals, with coupling strengths reaching 3.3 MHz at near-zero magnetic fields. The coupling arises from unintentional co-doping during crystal growth, enabling high-fidelity spin-photon interactions at 100 ppb impurity levels.

ABSTRACT

Interaction of Whispering Gallery Modes (WGM) with dilute spin ensembles in solids is an interesting paradigm of Hybrid Quantum Systems potentially beneficial for Quantum Signal Processing applications. In the present work, WGM spectroscopy of Rare-Earth doped YSO crystal reveals the existence of Iron Group Ion (IGI) co-dopings with concentration levels of order 100 ppb. The IGI spin ensembles demonstrate large Zero Field Splittings at 14.7GHz, 18.4GHz and 25.4GHz, considerable anisotropy of the extrm{g}-tensors, as well as two inequivalent lattice sites. Strong coupling regimes between an ensemble of IGI spins and WGM photons have been demonstrated at $18.4$ GHz and near zero field. This approach together with useful optical properties of these ions opens a new avenue for 'spins-in-solids' Quantum Electrodynamics.

Motivation & Objective

• To identify and characterize unexpected spin impurities in rare-earth-doped Y₂SiO₅ crystals used for quantum applications.
• To investigate the interaction strength between whispering gallery mode (WGM) microwave photons and dilute spin ensembles of iron group ions (IGIs).
• To determine whether these IGI spin states can achieve strong coupling with WGMs under experimentally accessible conditions, particularly near zero magnetic field.
• To assess the potential of these systems for hybrid quantum systems (HQS) and quantum information processing by evaluating coherence and coupling parameters.
• To clarify the origin and electronic structure of observed zero-field splittings (ZFS) and g-tensor anisotropies in terms of specific IGI species (e.g., Cr³⁺, Cr⁴⁺, Ni²⁺).

Proposed method

• WGM spectroscopy was performed on 7 cylindrical Y₂SiO₅ crystals doped with Er³⁺ or Eu³⁺, cooled to 20 mK in a superconducting magnet.
• Microwave frequency sweeps were applied to probe electron spin resonance (ESR) transitions, with detection via WGM frequency shifts in high-Q dielectric cavities (Q ~ 10⁸).
• Spectra were acquired with magnetic field applied along the crystal axis to collapse magnetically inequivalent sites, enabling identification of ZFS and g-tensor anisotropy.
• Comparison of undoped and doped crystals revealed that iron group impurities (Cr, Ni) are introduced during co-doping at concentrations ~100 ppb.
• Anisotropy in g-factors was quantified by rotating the crystal axis by 45°, showing a factor-of-two change in effective g-factor for certain transitions.
• Temperature-dependent measurements confirmed the paramagnetic nature of the spin ensemble, with coupling strength scaling as expected for spin systems.

Experimental results

Research questions

• RQ1 What causes the unexpected electron spin resonance transitions observed in Er³⁺:Y₂SiO₅ and Eu³⁺:Y₂SiO₅ crystals at 14.7 GHz, 18.4 GHz, and 25.4 GHz?
• RQ2 Can iron group impurity ions (IGIs) such as Cr³⁺, Cr⁴⁺, or Ni²⁺ be responsible for the observed zero-field splittings and g-tensor anisotropy?
• RQ3 Is the coupling strength between WGM photons and IGI spin ensembles sufficient to reach the strong coupling regime in the near-zero magnetic field regime?
• RQ4 What is the origin of the two-peak splitting in the g₂₊ line, and how does it relate to site inequivalence?
• RQ5 How do the observed coupling strengths and linewidths compare to those required for integration with superconducting qubits?

Key findings

• Three distinct zero-field splittings were observed at 14.7 GHz, 18.4 GHz, and 25.4 GHz, corresponding to spin systems with S = 3/2 and S = 1.
• The 25.4 GHz ZFS is attributed to Cr⁴⁺ (S = 1), the 18.4 GHz ZFS to Ni²⁺ (S = 1), and the 14.7 GHz ZFS to Cr³⁺ (S = 3/2).
• The coupling strength between the WGM photons and the IGI spin ensemble reached 3.3 MHz, exceeding typical spin linewidths of 1–2 MHz and decay rates of superconducting circuits.
• A strong dependence of the effective g-factor on crystal orientation was observed, with a factor-of-two change upon 45° rotation, indicating significant magnetic anisotropy.
• The two-peak splitting in the g₂₊ line, with Δg = 0.03, is attributed to two inequivalent lattice sites for the same IGI species, likely due to slight misalignment or local distortion.
• IGI impurities are estimated at ~100 ppb, introduced unintentionally during co-doping of Er³⁺ or Eu³⁺, and are responsible for the observed strong spin-photon coupling.