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arXiv:2309.11169 · Applied Physics Letters

Scaling of self-stimulated spin echoes

Sebastian E. de Graaf, Aditya Jayaraman, Sergey Kubatkin, Andrey V. Danilov, V. Ranjan

Published Jan 8, 2024• 5 citations
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Abstract

Self-stimulated echoes have recently been reported in the high cooperativity and inhomogeneous coupling regime of spin ensembles with superconducting resonators. In this work, we study their relative amplitudes using echo-silencing made possible by a fast frequency tunable resonator. The highly anisotropic spin linewidth of Er3+ electron spins in the CaWO4 crystal also allows to study the dependence on spin-resonator ensemble cooperativity. It is demonstrated that self-stimulated echoes primarily result from a combination of two large control pulses and the echo preceding it.

DOI
10.1063/5.0176953

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Self-stimulated echoes have recently been reported in the high cooperativity and inhomogeneous coupling regime of spin ensembles with superconducting resonators. In this work, we study their relative amplitudes using echo-silencing made possible by a fast frequency tunable resonator. The highly anisotropic spin linewidth of Er3+ electron spins in the CaWO4 crystal also allows to study the dependence on spin-resonator ensemble cooperativity. It is demonstrated that self-stimulated echoes primarily result from a combination of two large control pulses and the echo preceding it.
We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.
We show experimentally and describe theoretically how a conventional magnetic resonance Hahn echo sequence can lead to a self-stimulated pulse echo train when an inhomogeneously broadened spin ensemble is coupled to a resonator. Effective strong coupling between the subsystems assures that the first Hahn echo can act as a refocusing pulse on the spins, leading to self-stimulated secondary echoes. Within the framework of mean field theory, we show that this process can continue multiple times leading to a train of echoes. We introduce an analytical model that explains the shape of the first echo and numerical results that account well for the experimentally observed shape and strength of the echo train and provides insights into the collective effects involved.
The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth ions and suppress on demand the echo emission ("echo silencing") by two methods: (1) detuning the resonator during the spin rephasing, and (2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.
Ensembles of bismuth-donor spins in silicon are promising storage elements for microwave quantum memories due to their long coherence times, which exceed seconds. The operation of an efficient quantum memory requires the achievement of critical coupling between the spin ensemble and a suitable high-quality factor resonator---this in turn requires a thorough understanding of the line shapes for the relevant spin-resonance transitions, particularly considering the influence of the resonator itself on line broadening. Here, we present pulsed electron-spin-resonance measurements of ensembles of bismuth donors in natural silicon, above which niobium superconducting resonators have been patterned. By studying spin transitions across a range of frequencies and fields, we identify distinct line-broadening mechanisms and, in particular, those that can be suppressed by operating at magnetic-field-insensitive ``clock transitions.'' Given the donor concentrations and resonator used here, we measure a cooperativity $C\ensuremath{\sim}0.2$ and based on our findings we discuss a route to achieve unit cooperativity, as required for a quantum memory.
Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a $\ensuremath{\pi}/{2}_{X}\ensuremath{-}\ensuremath{\tau}\ensuremath{-}{\ensuremath{\pi}}_{Y}\ensuremath{-}\ensuremath{\tau}\ensuremath{-}\ensuremath{\pi}/{2}_{\mathrm{\ensuremath{\Phi}}}$ sequence, dependent on the relative phase $\mathrm{\ensuremath{\Phi}}$. We demonstrate experimentally this detection method using an ensemble of Er3+{\mathrm{Er}}^{3+}Er3+ ion spins in a scheelite crystal of CaWO4{\mathrm{CaWO}}_{4}CaWO4​. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the 183W^{183}\mathrm{W}183W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.
A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er3+-doped Y2SiO5 crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewidth of down to 75 MHz.