Giant gg-factors of Natural Impurities in Synthetic Quartz

We report the observation of $g$-factors of natural paramagnetic impurities in a pure synthetic quartz crystal at milli-Kelvin temperatures. Measurements are made by performing spectroscopy using multiple high-$Q$ Whispering Gallery Modes sustained in the crystal. Extreme sensitivity of the method at low temperatures allows the determination of natural residual impurities introduced during the crystal growth. We observe $g$-factors that significantly differ from integer multiples of the electron $g$-factor in vacuum, and with values of up to $7.6$, which reveals much stronger coupling between impurities and the crystal lattice than in previous studies. Both substitutional and interstitial ions are proposed as candidates for the observed interactions

Collective Behaviour of Cr3+^{3+} ions in Ruby Revealed by Whispering Gallery Modes

We present evidence for collective action of Cr$^{3+}$ ion impurities in a highly doped ruby crystal at microwave frequencies. The cylindrical geometry of the crystal allows for the creation of a superradiant, or "spin-mode" doublet, with spatial structure similar to that of microwave whispering gallery modes (WGMs). This results in a strict criteria of selection rules regarding the interaction of resonant WGMs and spin-modes; namely that only modes with the same wavenumber and azimuthal phase may interact. What results is an avoided level crossing between the two, in which both WGM doublet constituents are seen to interact with the spin resonance. We demonstrate that a four harmonic oscillator model is necessary to accurately describe this result.Comment: 5 pages, 5 figure

Jump Chaotic Behaviour of Ultra Low Loss Bulk Acoustic Wave Cavities

We demonstrate a previously unobserved nonlinear phenomenon in an ultra-low loss quartz Bulk Acoustic Wave cavity ($Q>3\times10^9$), which only occurs below 20 milli-Kelvin in temperature and under relatively weak pumping. The phenomenon reveals the emergence of several stable equilibria (at least two foci and two nodes) and jumps between these quasi states at random times. The degree of this randomness as well as separations between levels can be controlled by the frequency of the incident carrier signal. It is demonstrated that the nature of the effect lays beyond the standard Duffing model

Controlling a whispering gallery doublet mode avoided frequency crossing: Strong coupling between photon bosonic and spin degrees of freedom

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--$\frac{1}{2}$ 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 spin degrees of freedom of cavity photons. Despite the demonstrated similarities with 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 for the first time, controllable time-reversal symmetry breaking in a high-$Q$ cavity.Comment: Phys. Rev. A, 201

Strong Coupling between Whispering Gallery Modes and Chromium Ions in Ruby

We report the study of interactions between cavity photons and paramagnetic Cr$^{3+}$ spins in a ruby (Cr$^{3+}$:Al$_2$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 behaviour not predicted by the usual Tavis-Cummings model because of interactions within the two-level spin bath, and the existence of numerous photonic modes

Spin-Photon Interaction in a Cavity with Time-Reversal Symmetry Breaking

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 polarised 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 sub-ensemble of two-level systems with different energy splittings. In the experimental example, these sub-ensembles originate from Fe$^{3+}$ impurity ions effectively seen as a two level systems at the interaction frequency. The temperature dependence of the population of each sub-ensemble (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.Comment: Phys. Rev. B, 201

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

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 ($\Delta m_s =2$) for Fe$^{3+}$, as well as hyperfine transitions of V$^{2+}$

Hybrid optical and electronic laser locking using spectral hole burning

We report on a narrow linewidth laser diode system that is stabilized using both optical and electronic feedback to a spectral hole in cryogenic Tm:YAG. The laser system exhibits very low phase noise. The spectrum of the beat signal between two lasers, over millisecond timescales, is either Fourier limited or limited by the -111dBc/Hz noise floor. The resulting laser is well suited to quantum optics and sensing applications involving rare earth ion dopants.Comment: 4 pages, 3 figure

Determination of the Anisotropy of Permittivity of Quantum Paraelectric Strontium Titanate

The dielectric properties of strontium titanate (SrTiO$_3$) have previously been reported from room temperature to low temperatures with conflicting results. In this work, precision measurement of the permittivity is undertaken by simultaneously measuring transverse electric and transverse magnetic resonant modes within a single crystal. It is unequivocally shown that the permittivity is isotropic at room temperature with a permittivity of order $316.3\pm2.2$ by measuring multiple modes of different electric field polarisations. As the crystal is cooled to 5 K and undergoes well known phase transitions, we show the material becomes uniaxial anisotropic with the ratio of the parallel to perpendicular permittivity to the cylinder z-axis of the sample as high as 2.4 below 6 K

Strong Coupling Between P1 Diamond Impurity Centres and 3D Lumped Photonic Microwave Cavity

We report strong coupling between an ensemble of N impurity (P1) centres in diamond and microwave photons using a unique double post re-entrant cavity. The cavity is designed so that the magnetic component of the cavity field is spatially separated from the electric component and focused into the small volume in which the diamond sample is mounted. The novelty of the structure simultaneously allows high magnetic filling factor (38.4\%) and low frequencies necessary to interact, at low magnetic field, with transitions in diamond such as those in NV$^{-}$ and P1 centres. Coupling strength (or normal-mode splitting) of 51.42 MHz, was achieved with P1 centres at 6.18 GHz and 220 mT in a centimetre-scale cavity, with a corresponding cooperativity factor of 4.7. This technique offers an alternative way, with some significant advantages, to couple 3D cavities to transitions in diamond and achieve the strong coupling necessary for applications to quantum information processing