Jevon Longdell

The narrowness of the optical transitions of rare-earth-ion dopants makes them highly sensitive probes of their environment. We measured the optical transitions Er³⁺ dopants to determine the previously unknown magnetic ordering of Gd₂SiO₅ – a promising host for quantum applications of rare-earth dopants. By measuring the transitions' magnetic-field dependence we determined an antiferromagnetic ordering with spins oriented along or slightly canted from the crystal's a* axis. The optical transitions are narrower than the coupling to gadolinium spins revealing information about the coupling strengths. We further optically measured a Néel temperature of 1.86 ± 0.01_stat. ± 0.07_syst. K, and assembled a phase diagram in applied field and temperature showcasing a triple point where two gadolinium sites order semi-independently from each other. At high applied field the erbium dopants show long optical coherence times up to 0.4 ms at 3 T; at low fields these are probably limited by three low-frequency magnon modes below 10 GHz, observed directly. This study can be used to benchmark a method of magnetic structure determination.

We report microwave spectroscopy of ¹⁶⁷Er³⁺ doped in CaWO₄ which reveals the hyperfine splitting of the erbium electronic ground state (Z1, Jeff.=15/2) induced by the I=7/2 nuclear spin. From spectra measured below∼50 mK in magnetic fields up to 200 mT, we extract spin-Hamiltonian parameters including the electron g, hyperfine A, and nuclear electric quadrupolar Q tensors. Crucially, our analysis demonstrates 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 CaWO₄ as a promising host for long lifetime quantum memories.

We report microwave spectroscopy of ¹⁶⁷Er³⁺ doped in CaWO₄ which reveals the hyperfine splitting of the erbium electronic ground state (Z₁, J_eff.=15/2) induced by the I=7/2 nuclear spin. From spectra measured below∼50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron g, hyperfine A, and nuclear electric quadrupolar 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 fiields, we uncover that ZEFOZ points lie either along the c axis or within the a–b plane. These results establish CaWO₄ as a promising host for long lifetime quantum memories

Data supporting the manuscript: Optical spectroscopy of single- and two-ion transitions in an antiferromagnetic stoichiometric rare-earth crystal.

Transmission spectra for the ground 4I9/2 state to the lowest 4F3/2 doublet of neodymium in magnetically ordered neodymium gallate.

There are four files given: sigma- and pi-polarisation for magnetic field applied along the b and c axes of the crystal (in Pbnm setting). Files are provided in matlab format as they can be read easily in many programming languages. Each file has three stored arrays. B = applied magnetic field in Tesla, f = optical frequency in GHz relative to 341644 GHz, transmission = normalised transmission through the sample.
 

We characterise optical transitions of neodymium ions (Nd3+) in antiferromagnetic neodymium gallate (NdGaO3) with applied fields up to 3 T. The magnetic phase of this material has not previously been studied with the field along its magnetisation axis. The measured optical spectra indicate three magnetic phases -- antiferromagnetic, intermediate, and paramagnetic -- where the intermediate phase likely forms a different magnetic structure from typical spin-flop phases. The observed absorptions were classified into two distinct families of optical transitions: single-Nd and two-Nd absorptions. We demonstrate that the optical transitions in the antiferromagnetic and paramagnetic phases can be modelled using a standard single-ion crystal-field Hamiltonian that interacts with a mean magnetisation from the rest of the lattice, and we expand that model to encompass pairs of ions, explaining the origins of the two-Nd transitions. This study offers a deeper understanding of the optical transitions in rare-earth antiferromagnetic crystals, which have been recently attracting significant interest for microwave-to-optical quantum transduction, despite being relatively unexplored to date.

The amplitude of resonant oscillations in a non-Hermitian environment can either decay or grow in time, corresponding to a mode with either loss or gain. When two coupled modes have a specific difference between their loss or gain, a feature termed an exceptional point emerges in the excitations' energy manifold, at which both the eigenfrequencies and eigenmodes of the system coalesce. Exceptional points have intriguing effects on the dynamics of systems due to their topological properties. They have been explored in contexts including optical, microwave, optomechanical, electronic and magnonic systems, and have been used to control systems including optical microcavities, the lasing modes of a PT-symmetric waveguide, and terahertz pulse generation. A challenging problem that remains open in all of these scenarios is the fully deterministic and direct manipulation of the systems' loss and gain on timescales relevant to coherent control of excitations. Here we demonstrate the rapid manipulation of the gain and loss balance of excitations of a magnonic hybrid system on durations much shorter than their decay rate, allowing us to exploit non-Hermitian physics for coherent control. By encircling an exceptional point, we demonstrate population transfer between coupled magnon-polariton modes, and confirm the distinctive chiral nature of exceptional point encircling. We then study the effect of driving the system directly through an exceptional point, and demonstrate that this allows the coupled system to be prepared in an equal superposition of eigenmodes. We also show that the dynamics of the system at the exceptional point are dependent on its generalised eigenvectors. These results extend the established toolbox of adiabatic transfer techniques with a new approach for coherent state preparation, and provide a new avenue for exploring the dynamical properties of non-Hermitian systems.

In a non-Hermitian system, the amplitude of resonant oscillations can either grow or decay in time, corresponding to a mode with either gain or loss. When two coupled modes have a specific gain–loss imbalance, an exceptional point emerges at which both eigenfrequencies and eigenmodes of the system coalesce. Exceptional points have qualitative effects on the dynamics of systems due to their topological properties, and have been used to control systems including optical microcavities, the lasing of a parity–time-symmetric waveguide and terahertz pulse generation. A challenging open problem is the fully deterministic and direct manipulation of the systems’ loss and gain on timescales relevant to the coherent control of excitations. Here we demonstrate the rapid manipulation of the complex frequency of magnon–polaritons on durations much shorter than their decay rate, allowing us to exploit non-Hermitian physics for coherent control. By dynamically encircling an exceptional point, we demonstrate population transfer between coupled magnon–polariton modes. We then drive the system directly through an exceptional point, and demonstrate that this allows the coupled system to be prepared in an equal superposition of eigenmodes. These findings establish a highly controllable hybrid platform for exploring the rich dynamical properties of non-Hermitian systems.

The absorption spectra of rare-earth ions have very narrow linewidths. Even in solid-state crystals, exceedingly long coherence times have been observed for the spin and optical transitions of rare-earth-ion dopants. The influence of electronic and nuclear spins in the host crystal is a key factor limiting these coherence times. Here we suppress the effects of electron spins by using erbium dopants in a gadolinium vanadate host that is fully concentrated in electron spins but operated at sufficiently low temperatures that the spins form an antiferromagnetically ordered state. We achieve long optical coherence times and, furthermore, observe avoided crossings in the optical spectra, which are caused by strong coupling between the erbium ions and gadolinium magnons in the host crystal. This indicates the possibility of magnon-mediated microwave-to-optical quantum transduction using rare-earth ions, which would provide a connection between telecommunications technology and solid-state quantum devices operating in the microwave regime.

Rare-earth ions are characterised by transitions with very narrow linewidths even in solid state crystals. Exceedingly long coherence times have been shown on both spin and optical transitions of rare-earth-ion doped crystals. A key factor, and generally the limitation, for such coherence times, is the effects of electronic and nuclear spins in the host crystal. Despite the attractive prospect, a low-strain, spin-free host crystal for rare-earth-ion dopants has not yet been demonstrated. The dopants experience the lowest strain when they substitute for another rare earth (including yttrium). However every stable isotope of the trivalent rare earth ions has either an electron spin, an nuclear spin, or both. The long optical coherence times reported here with erbium dopants in antiferromagnetically ordered gadolinium vanandate suggest an alternative method to achieve the quiet magnetic environment needed for long coherence times: use a magnetic host fully concentrated in electron spins and operate at temperatures low enough for these spins to be ordered. We also observe avoided crossings in the optical spectra, caused by strong coupling between the erbium ions and gadolinium magnons in the host crystal. This suggests the exciting prospect of microwave to optical quantum transduction using the rare-earth ions in these materials mediated by magnons of the host spins.

We report microwave to optical upconversion in isotopically purified erbium-doped yttrium orthosilicate in a Fabry-Pérot resonator at millikelvin temperatures. This follows on from investigations made at higher temperatures and with natural isotopic ratios for the erbium dopants. In these previous investigations the highest efficiency was seen only for moderately strong microwave powers. The removal of the unwanted erbium-167 which has hyperfine structure and provides unwanted background optical absorption, and the lower temperatures has removed this problem. We now see efficiencies still increasing as the microwave power is decreased when we reach the smallest input powers for which we could measure an output. Efficiencies of 2×10−6 were observed and we discuss potential improvements, including better optical cavity frequency stability and better thermalisation of the erbium spins.