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arXiv:1504.07733 · Physical Review A

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

Jeremy Bourhill, Maxim Goryachev, Warrick G. Farr, Michael Edmund Tobar

Published Aug 4, 2015• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.92.023805

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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.
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.
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.
A combination of electron spin interactions in a magnetic field allows us to control the resonance frequencies of a high-Q whispering-gallery (WG) cavity mode doublet, resulting in precise measurements of an avoided crossing between the two modes comprising the doublet. We show that the resonant photons effectively behave as spin-12\frac{1}{2}21​ particles and that the physical origins of the doublet phenomenon arise from an energy splitting between the states of photon spin angular momentum. The exclusive role of the photon spin in splitting the mode frequency is emphasized, and we demonstrate that the gyrotropic and anisotropic properties of the crystalline media supporting the WG mode lead to strong coupling between the bosonic and the spin degrees of freedom of cavity photons. Despite the demonstrated similarities to Jaynes-Cummings-type systems, the mode doublet system exhibits a significant difference due to its linearity. Unlike traditional experiments dealing with interactions between fields and matter, here the crystalline medium plays a role of macroscopic symmetry breaking, assisting in the strong coupling between these photon degrees of freedom. Such a regime is demonstrated experimentally with a method to effectively control the photon spin state. Our experiments demonstrate controllable time-reversal symmetry breaking in a high-QQQ cavity.
Interaction of Whispering Gallery Modes (WGMs) with dilute spin ensembles in solids is an interesting paradigm of Hybrid Quantum Systems potentially beneficial for Quantum Signal Processing applications. Unexpected ion transitions are measured in single crystal Y2SiO5 using WGM spectroscopy with large Zero Field Splittings at 14.7 GHz, 18.4 GHz, and 25.4 GHz, which also feature considerable anisotropy of the g-tensors as well as two inequivalent lattice sites, indicating spins from Iron Group Ion (IGI) impurities. The comparison of undoped and Rare-Earth doped crystals reveal that the IGIs are introduced during co-doping of Eu3+ or Er3+ with concentration at much lower levels of order 100 ppb. The strong coupling regime 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 avenues for “spins-in-solids” Quantum Electrodynamics.
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.
The quantum coupling of spatially distant spins via optical photons using cavity quantum electrodynamic (cQED) methods has proved experimentally challenging due to the large spin-photon coupling strengths required. To achieve such coupling strengths using traditional cQED methods requires either individual spins and ultra-small cavities or an ensemble of identical spins coupled to larger cavities. In this work we describe a method to couple distant spins via the collective enhanced coupling to a large ensemble ∼ N, of degenerate optical Whispering Gallery Modes (WGM) in a spherical resonator where the spins are spatially located at the antipodes. The setup can be scaled-up to build 1D, 2D and 3D cQED lattices to enable quantum simulation or computing.