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arXiv:2004.01116 · Physical Review Letters

Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

Kamanasish Debnath, Gavin Dold, John J. L. Morton, Klaus Mølmer

Published Sep 22, 2020• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.125.137702

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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.
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.
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.
Observation of the optical analog of the delayed nutation echo [V. S. Kuz'min et al., Zh. \'Eksp. Teor. Fiz. 99, 215 (1991) [Sov. Phys. JETP 72, 121 (1991)] recently shown in nuclear magnetic resonance is reported. We call this echo a stimulatednnutationnecho (SNE) in analogy to the three-pulse-stimulated echo that is produced from a hole pattern burnt into an inhomogeneous line. In a SNE two-pulse sequence, the first pulse burns a train of holes into the inhomogeneous absorption spectrum and its duration tp{\mathrm{t}}_{\mathrm{p}}tp​ is stored. After a long delay time the second pulse burns its own train of holes. When coincidence of these holes takes place, the SNE occurs at a time t=tp{\mathrm{t}}_{\mathrm{p}}tp​ following the start of the second pulse. Thus the second pulse reads exactly the duration of the first pulse. It is shown that for a Gaussian-shaped beam, the echo becomes sharper and well recognizable. This echo may be used for Rabi frequency measurement and spectral diffusion studies.
Abstract The spin echo [1 ] discovered by Erwin Hahn in 1950 is one of the most sophisticated phenomena in physics. It demonstrates the fact that the decay of coherence due to the inhomogeneous broadening can be recovered by an ingenious ‘effective time reversal’ technique. Since then, the research on coherent transients has been developed in the field of pulsed magnetic resonance [2]. The advent of the laser stimulated the studies in the optical region. Optical analogues of most of the coherent transients in magnetic resonance have been realized [ 3] except for those in solids, whose mechanisms are based on the spin temperature hypothesis [4] . Thus coherent interactions between radiation and atoms have been extensively studied and the techniques developed have been effectively used in a variety of fields. In the studies of so-called two-level problems the coherence is generated by a direct excitation of the relevant transitions by radiofrequency (r.f.), microwave, or laser fields.
We study experimentally the dynamical and decay properties of the stimulated nutation echo (SNE) in a two-level spin system, the signal of which allows the observation timescale of the driven coherence relaxation to be extended. This signal appears in the transient response of the system to the second pulse at time τ 1 from its start and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time τ between the two pulses. Another is caused by the coherence loss during the excitation by the first pulse and the reading time of the second pulse. Experimental results on the decay properties induced by these mechanisms are presented for the first time. We investigate the dependence of these decay rates on the pulse intensity and we examine its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids.