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Physical Review A

Optically detected magnetic resonance to characterize atomlike microwave-optical transducers

Li Ma, Luke S. Trainor, Gavin G. G. King, Harald G. L. Schwefel, Jevon J. Longdell

Published May 15, 2023• 3 citations
Publisher

Abstract

We introduce a method for optically detected magnetic resonance for atomlike systems in an optical resonator. Driving the spin transitions of these systems with microwaves causes changes to the populations of the ground-state spin levels, which we detect by changes in the optical cavity frequency. The technique is useful for characterizing experiments aimed at quantum microwave-to-optical transduction because it provides a way of only probing the spin transitions of the atomlike systems that are in the optical resonator's mode. We demonstrate the technique using a cryogenic erbium-doped whispering-gallery-mode resonator inside a microwave resonator. We compare our results with more standard electron paramagnetic resonance to show that our optical modes are confined to a region of large microwave magnetic-field amplitude. Our optical modes have a $Q$ factor better than ${10}^{8}$ making them the highest $Q$-factor resonators studied with cryogenic rare-earth-ion dopants, allowing us to report ensemble strong coupling between the erbium dopants and an optical whispering-gallery-mode resonator.

DOI
10.1103/physreva.107.053514

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We introduce a method for optically detected magnetic resonance for atomlike systems in an optical resonator. Driving the spin transitions of these systems with microwaves causes changes to the populations of the ground-state spin levels, which we detect by changes in the optical cavity frequency. The technique is useful for characterizing experiments aimed at quantum microwave-to-optical transduction because it provides a way of only probing the spin transitions of the atomlike systems that are in the optical resonator's mode. We demonstrate the technique using a cryogenic erbium-doped whispering-gallery-mode resonator inside a microwave resonator. We compare our results with more standard electron paramagnetic resonance to show that our optical modes are confined to a region of large microwave magnetic-field amplitude. Our optical modes have a QQQ factor better than 108{10}^{8}108 making them the highest QQQ-factor resonators studied with cryogenic rare-earth-ion dopants, allowing us to report ensemble strong coupling between the erbium dopants and an optical whispering-gallery-mode resonator.
We showcase an erbium-doped whispering-gallery-mode resonator with optical modes that display intrinsic quality factors better than 10810^8108 (linewidths less than 2 MHz), and coupling strengths to collective erbium transitions of up to 2$π\times$1.2 GHz - enough to reach the ensemble strong coupling regime. Our optical cavity sits inside a microwave resonator, allowing us to probe the spin transition which is tuned by an external magnetic field. We show a modified optically detected magnetic resonance measurement that measures population transfer by a change in coupling strength rather than absorption coefficient. This modification was enabled by the strong coupling to our modes, and allows us to optically probe the spin transition detuned by more than the inhomogeneous linewidth. We contrast this measurement with electron paramagnetic resonance to experimentally show that our optical modes are confined in a region of large microwave magnetic field and we explore how such a geometry could be used for coherent microwave-optical transduction.
Efficient and reversible optical to microwave transducers are required for entanglement transfer between superconducting qubits and light in quantum networks. Rare-earth-doped crystals with narrow optical and spin transitions are a promising system for enabling these devices. Current resonant transduction approaches use ground-state electron spin transitions that have coherence lifetimes often limited by spin flip-flop processes and spectral diffusion, even at very low temperatures. We investigate spin coherence in an optically excited state of an Er^{3+}: Y_{2}SiO_{5} crystal at temperatures from 1.6 to 3.5 K for a low 8.7 mT magnetic field compatible with superconducting resonators. Spin coherence and population lifetimes of up to 1.6 μs and 1.2 ms, respectively, are measured by optically detected spin echo experiments. Analysis of decoherence processes suggest that ms coherence can be reached at lower temperatures for the excited-state spins, whereas ground-state spin coherence would be limited to a few μs due to resonant interactions with other Er^{3+} spins in the lattice and greater instantaneous spectral diffusion from the radio-frequency control pulses. We propose a quantum transducer scheme with potential for close to unity efficiency that exploits the advantages offered by spin states of the optically excited electronic energy levels.
Microwave-to-optical quantum transducers are essential for entangling remote superconducting qubits. Among the available transduction platforms, ensembles of Er3+^{3+}3+ and Yb3+^{3+}3+ ions doped into solids have emerged as leading candidates. While external magnetic fields are needed to split the Zeeman levels of erbium ions and enable a microwave--qubit interface, superconducting qubits suffer decoherence in such fields. In contrast, ytterbium ions exhibit zero-first-order Zeeman transitions and large hyperfine splittings at zero magnetic field (when doped into inorganic crystals). Owing to its long optical and spin coherence times, Yb:YSO has been widely used as a quantum memory, yet its potential for quantum transduction remains largely unexplored. Investigating this material could enable the integration of quantum memory and transduction in a single platform. Here, we demonstrate microwave-to-optical transduction in the continuous-wave regime using a 5\,ppm doped Yb:YSO crystal. The internal transduction efficiency is 2×10−82\times10^{-8}2×10−8 with a bandwidth of 200\,kHz, achieved using a 3D loop-gap microwave resonator (LGR) and a single-pass optical configuration. We explore all the ground states that form a V-type three-level system with the first and second optical excited states and assert the use of the ground state, which provides the highest efficiency and isolated optical transition. We further establish strong spin-microwave coupling from avoided crossing measurements. With a strong microwave drive to saturate the spin transition, we estimate the spin population pumped into the excited state, close to the simulated value. Finally, we calculate target parameter values for maximum efficiency with our system and suggest using 50\,ppm doped Yb:YSO crystal. With the calculated target parameters, the internal transduction efficiency is predicted to reach up to 10−410^{-4}10−4 in the current LGR.
This presentation focus on quantum transduction using rare-earth ions in solid state systems. We propose using magnetic materials with rare-earth dopants, harnessing the strong coupling between rare-earth spin transitions and magnons. We analyze this situation using a formalism similar to Ref. [PRL 113, 203601 (2014)]. We find that hosting rare-earth elements within a magnet dramatically speeds up the transduction rate by more than two orders of magnitude, which gives several key benefits: potentially higher efficiency as it is less affected by device internal losses, higher fidelity operations with the superconducting qubits, and reduced device constraints. Finally, we discuss several routes for implementing this type of quantum transducer.
We propose a method for converting single microwave photons to single optical sideband photons based on spinful impurities in magnetic materials. This hybrid system is advantageous over previous proposals because (i) the implementation allows much higher transduction rates ( 10 3 times faster at the same optical pump Rabi frequency) than state-of-the-art devices, (ii) high-efficiency transduction is found to happen in a significantly larger space of device parameters (in particular, over 1 GHz microwave detuning), and (iii) it does not require mode volume matching between optical and microwave resonators. We identify the needed magnetic interactions as well as potential materials systems to enable this speed up using erbium dopants for telecom compatibility. This is an important step towards realizing high-fidelity entangling operations between remote qubits and will provide additional control of the transduction through perturbation of the magnet.
The coupling between microwave fields and atoms (or atomlike systems) is inherently weaker than for optical fields, making microwave signal manipulation for applications like quantum information processing technically challenging. In order to better understand this coupling and to develop tools for measuring it, we explore the microwave coupling to atoms using the ``atomic candle'' technique, and push it beyond the bounds of the small-signal regime in order to deliver a larger signal. In familiar two-level systems, responses beyond the usual Rabi oscillations can arise when a single-tone drive is phase modulated, causing the steady-state populations to oscillate at integer harmonics of the modulation frequency. Resonant behavior of the first two harmonics for frequencies near the Rabi frequency, known as $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ Rabi resonances, is widely used for microwave-field magnetometry and as a power standard known as the atomic candle. Here, we explore Rabi resonances beyond the small-signal approximation and report upon experimental observations of higher-order-harmonic population response for microwave hyperfine transitions in cold 87Rb^{87}\mathrm{Rb}87Rb atoms, which we compare to numerical simulations.