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:1408.2944 · Physical Review B

Strong coupling between whispering gallery modes and chromium ions in ruby

Warrick G. Farr, Maxim Goryachev, Daniel Lloyd Creedon, Michael Edmund Tobar

Published Aug 13, 2014• 19 citations
arXivHTMLPDF

Abstract

We report the study of interactions between cavity photons and paramagnetic ${\mathrm{Cr}}^{3+}$ spins in a ruby ${(\mathrm{Cr}}^{3+}:{\mathrm{Al}}_{2}{\mathrm{O}}_{3})$ whispering gallery mode (WGM) resonator. Examining the system at microwave frequencies and millikelvin temperatures, spin-photon couplings up to 610 MHz or about 5% of photon energy are observed between the impurity spins and high quality factor $(Q>{10}^{5})$ WGM. Large tunability and spin-spin interaction allows operation in the strong coupling regime. The system exhibits behavior not predicted by the usual Tavis-Cummings model because of interactions within the two-level spin bath, and the existence of numerous photonic modes.

DOI
10.1103/physrevb.90.054409

Related papers

Collective behavior of Cr3+ ions in ruby revealed by whispering gallery modes

Jeremy Bourhill, Maxim Goryachev, Warrick G. Farr +1 more

We present evidence for the collective action of ${\mathrm{Cr}}^{3+}$ ion impurities in a highly concentrated ruby crystal coupled to microwave whispering gallery modes (WGMs). The cylindrical geometry of the crystal allows the creation of superradiant or ``spin-mode'' doublets, with spatial structures similar to that of WGMs. The formation of these spin patterns allows us to observe directly different selection rules, namely, wave number and azimuthal phase matching. The demonstration is made via an avoided level crossing between spin and photon mode doublets as well as absence of coupling between spin modes of different wave numbers. The effect is observable due to strong spin-photon coupling (67 MHz) exceeding both spin ensemble and cavity losses as well as the photon doublet splitting. We demonstrate that a four harmonic oscillator model not only with coupling between photon resonances (0.43 MHz) but also with a spin doublet (73 MHz) is necessary to accurately describe these results.

arXiv:1504.07733•Physical Review A•Aug 4, 2015•4 citations

Ultrasensitive microwave spectroscopy of spin ensembles in solids for hybrid quantum systems

Warrick G. Farr

Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. In this thesis, a novel spectroscopic technique using electron spin resonance (ESR) is presented. Microwave whispering gallery modes (WGM) in cylindrical dielectric resonators are used to probe paramagnetic impurities at millikelvin temperatures under the influence of an applied dc magnetic field. This technique couples the naturally high quality factor and the relatively high magnetic filling factor of WGMs in crystalline hosts. Precision spectroscopy has been performed on a number of dielectric samples including, sapphire, ruby, quartz, yttrium orthosilicate (YSO) and yttrium aluminium garnet (YAG). Spectroscopic characterisation of sapphire reveals trace ion impurities at parts per billion, which have been used to control strong coupling between the WGM doublets. Moreover, time-reversal symmetry breaking has been observed when a WGM interacts with an ESR, a result of selection rules being created as a consequence of conservation of angular momentum. Following this, interactions between WGM microwave photons and spin resonances are shown in a range of systems. Results achieved include coupling between WGM photons and Cr3+ ions in ruby with normal mode splitting on the order of 600 MHz at 13.9 GHz, the coupling of iron group ion impurities to WGM photons in YSO, which also revealed a strong coupling regime with very low magnetic field, and coupling of Er3+ to WGMs in YAG with evidence of dilute ferromagnetism - the first observation of such an effect outside of iron group doped semiconductors. In addition a novel double-post re-entrant cavity is presented, which is able to focus the rf magnetic field into a small sample, in this case a sub-millimetre sized Yttrium Iron Garnet (YIG) ferrite microsphere that supports magnon resonances. Ultra-high cooperatively of 105 between photon and magnon modes is demonstrated at millikelvin temperatures and microwave frequencies. A coupling strength (normal mode splitting) of 2 GHz at 20 GHz, equivalent to 76 cavity linewidths, is achieved for the bright cavity mode. This constitutes about 10% of the photon energy and shows that ultra-strong coupling is possible in spin systems at microwave frequencies.

•May 1, 2015•0 citations

Spin-photon interaction in a cavity with time-reversal symmetry breaking

Maxim Goryachev, Warrick G. Farr, Daniel Lloyd Creedon +1 more

Employing a sapphire whispering gallery mode resonator, we demonstrate features of the spin-photon interaction in cavities with broken time-reflection symmetry. The broken symmetry leads to a lifting of the degeneracy between left-handed and right-handed polarized cavity photons, which results in an observable gyrotropic effect. In the high-$Q$ cavity limit, such a situation requires a modification of the Tavis-Cummings Hamiltonian to take into account conservation of spin angular momentum and the corresponding selection rules. As a result, the system is represented by a system of two linearly coupled bosonic modes, with each one coupled to its own subensemble of two-level systems with different energy splittings. In the experimental example, these subensembles originate from ${\text{Fe}}^{3+}$ impurity ions effectively seen as a two-level system at the interaction frequency. The temperature dependence of the population of each subensemble (in terms of effective susceptibility of the medium) is determined experimentally in accordance with the theoretical predictions revealing various paramagnetic impurity types in the solid. The regimes of backscatterer and spin ensemble domination are discussed and compared.

arXiv:1405.7458•Physical Review B•Jun 11, 2014•30 citations

Ultrasensitive microwave spectroscopy of paramagnetic impurities of sapphire crystals at millikelvin temperatures

Warrick G. Farr, Daniel Lloyd Creedon, Maxim Goryachev +2 more

Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realisation of such devices by doping solid state cavities with paramagnetic ions imposes a trade-off between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultra-pure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid Whispering Gallery/Electron Spin Resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of a high purity sapphire cooled close to 100 mK reveal the presence of Fe$^{3+}$, Cr$^{3+}$, and V$^{2+}$ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition ($Δm_s =2$) for Fe$^{3+}$, as well as hyperfine transitions of V$^{2+}$.

arXiv:1311.1049•Nov 5, 2013•0 citations

Ultrasensitive microwave spectroscopy of paramagnetic impurities in sapphire crystals at millikelvin temperatures

Warrick G. Farr, Daniel Lloyd Creedon, Maxim Goryachev +2 more

Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realization of such devices by doping solid-state cavities with paramagnetic ions imposes a tradeoff between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultrapure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid whispering gallery/electron spin resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of high-purity sapphire cooled close to 100 mK reveal the presence of Fe${}^{3+}$, Cr${}^{3+}$, and V${}^{2+}$ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition ($\ensuremath{\Delta}{m}_{s}=2$) for Fe${}^{3+}$, as well as hyperfine transitions of V${}^{2+}$.

Physical Review B•Dec 31, 2013•59 citations

High Q-factor sapphire whispering gallery mode microwave resonator at single photon energies and millikelvin temperatures

Daniel Lloyd Creedon, Yarema Reshitnyk, Warrick G. Farr +3 more

The microwave properties of a crystalline sapphire dielectric whispering gallery mode resonator have been measured at very low excitation strength (E/ℏω≈1) and low temperatures (T≈30 mK). The measurements were sensitive enough to observe saturation due to a highly detuned electron spin resonance, which limited the loss tangent of the material to about 2×10−8 measured at 13.868 and 13.259 GHz. Small power dependent frequency shifts were also measured which correspond to an added magnetic susceptibility of order 10−9. This work shows that quantum limited microwave resonators with Q-factors >108 are possible with the implementation of a sapphire whispering gallery mode system.

arXiv:1103.6094•Applied Physics Letters•May 30, 2011•62 citations
We report the study of interactions between cavity photons and paramagnetic Cr3+{\mathrm{Cr}}^{3+}Cr3+ spins in a ruby (Cr3+:Al2O3){(\mathrm{Cr}}^{3+}:{\mathrm{Al}}_{2}{\mathrm{O}}_{3})(Cr3+:Al2​O3​) whispering gallery mode (WGM) resonator. Examining the system at microwave frequencies and millikelvin temperatures, spin-photon couplings up to 610 MHz or about 5% of photon energy are observed between the impurity spins and high quality factor (Q>105)(Q>{10}^{5})(Q>105) WGM. Large tunability and spin-spin interaction allows operation in the strong coupling regime. The system exhibits behavior not predicted by the usual Tavis-Cummings model because of interactions within the two-level spin bath, and the existence of numerous photonic modes.
We present evidence for the collective action of Cr3+{\mathrm{Cr}}^{3+}Cr3+ ion impurities in a highly concentrated ruby crystal coupled to microwave whispering gallery modes (WGMs). The cylindrical geometry of the crystal allows the creation of superradiant or ``spin-mode'' doublets, with spatial structures similar to that of WGMs. The formation of these spin patterns allows us to observe directly different selection rules, namely, wave number and azimuthal phase matching. The demonstration is made via an avoided level crossing between spin and photon mode doublets as well as absence of coupling between spin modes of different wave numbers. The effect is observable due to strong spin-photon coupling (67 MHz) exceeding both spin ensemble and cavity losses as well as the photon doublet splitting. We demonstrate that a four harmonic oscillator model not only with coupling between photon resonances (0.43 MHz) but also with a spin doublet (73 MHz) is necessary to accurately describe these results.
Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. In this thesis, a novel spectroscopic technique using electron spin resonance (ESR) is presented. Microwave whispering gallery modes (WGM) in cylindrical dielectric resonators are used to probe paramagnetic impurities at millikelvin temperatures under the influence of an applied dc magnetic field. This technique couples the naturally high quality factor and the relatively high magnetic filling factor of WGMs in crystalline hosts. Precision spectroscopy has been performed on a number of dielectric samples including, sapphire, ruby, quartz, yttrium orthosilicate (YSO) and yttrium aluminium garnet (YAG). Spectroscopic characterisation of sapphire reveals trace ion impurities at parts per billion, which have been used to control strong coupling between the WGM doublets. Moreover, time-reversal symmetry breaking has been observed when a WGM interacts with an ESR, a result of selection rules being created as a consequence of conservation of angular momentum. Following this, interactions between WGM microwave photons and spin resonances are shown in a range of systems. Results achieved include coupling between WGM photons and Cr3+ ions in ruby with normal mode splitting on the order of 600 MHz at 13.9 GHz, the coupling of iron group ion impurities to WGM photons in YSO, which also revealed a strong coupling regime with very low magnetic field, and coupling of Er3+ to WGMs in YAG with evidence of dilute ferromagnetism - the first observation of such an effect outside of iron group doped semiconductors. In addition a novel double-post re-entrant cavity is presented, which is able to focus the rf magnetic field into a small sample, in this case a sub-millimetre sized Yttrium Iron Garnet (YIG) ferrite microsphere that supports magnon resonances. Ultra-high cooperatively of 105 between photon and magnon modes is demonstrated at millikelvin temperatures and microwave frequencies. A coupling strength (normal mode splitting) of 2 GHz at 20 GHz, equivalent to 76 cavity linewidths, is achieved for the bright cavity mode. This constitutes about 10% of the photon energy and shows that ultra-strong coupling is possible in spin systems at microwave frequencies.
Employing a sapphire whispering gallery mode resonator, we demonstrate features of the spin-photon interaction in cavities with broken time-reflection symmetry. The broken symmetry leads to a lifting of the degeneracy between left-handed and right-handed polarized cavity photons, which results in an observable gyrotropic effect. In the high-QQQ cavity limit, such a situation requires a modification of the Tavis-Cummings Hamiltonian to take into account conservation of spin angular momentum and the corresponding selection rules. As a result, the system is represented by a system of two linearly coupled bosonic modes, with each one coupled to its own subensemble of two-level systems with different energy splittings. In the experimental example, these subensembles originate from Fe3+{\text{Fe}}^{3+}Fe3+ impurity ions effectively seen as a two-level system at the interaction frequency. The temperature dependence of the population of each subensemble (in terms of effective susceptibility of the medium) is determined experimentally in accordance with the theoretical predictions revealing various paramagnetic impurity types in the solid. The regimes of backscatterer and spin ensemble domination are discussed and compared.
Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realisation of such devices by doping solid state cavities with paramagnetic ions imposes a trade-off between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultra-pure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid Whispering Gallery/Electron Spin Resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of a high purity sapphire cooled close to 100 mK reveal the presence of Fe3+^{3+}3+, Cr3+^{3+}3+, and V2+^{2+}2+ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition (Δms=2Δm_s =2Δms​=2) for Fe3+^{3+}3+, as well as hyperfine transitions of V2+^{2+}2+.
Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realization of such devices by doping solid-state cavities with paramagnetic ions imposes a tradeoff between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultrapure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid whispering gallery/electron spin resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of high-purity sapphire cooled close to 100 mK reveal the presence of Fe3+{}^{3+}3+, Cr3+{}^{3+}3+, and V2+{}^{2+}2+ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition ($\ensuremath{\Delta}{m}_{s}=2$) for Fe3+{}^{3+}3+, as well as hyperfine transitions of V2+{}^{2+}2+.
The microwave properties of a crystalline sapphire dielectric whispering gallery mode resonator have been measured at very low excitation strength (E/ℏω≈1) and low temperatures (T≈30 mK). The measurements were sensitive enough to observe saturation due to a highly detuned electron spin resonance, which limited the loss tangent of the material to about 2×10−8 measured at 13.868 and 13.259 GHz. Small power dependent frequency shifts were also measured which correspond to an added magnetic susceptibility of order 10−9. This work shows that quantum limited microwave resonators with Q-factors >108 are possible with the implementation of a sapphire whispering gallery mode system.