Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

Three component spin echo generation by radiation damping

Matthew P. Augustine, Erwin Louis Hahn

Published Aug 22, 1997• 18 citations
Publisher

Abstract

Exploration of the theory for spin–cavity coupling in inhomogeneously broadened spin ensembles shows that all three components of magnetization can be refocused. The conventional spin echo generated by two components of magnetization is a special case of this three component refocusing in the limit of negligible radiation damping. We demonstrate this effect by an analytical theorem, numerical simulation, and experiment.

DOI
10.1063/1.474683

Related papers

Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

Kamanasish Debnath, Gavin Dold, John J. L. Morton +1 more

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.

arXiv:2004.01116•Physical Review Letters•Sep 22, 2020•17 citations

Radiation Damping Effects in Two Level Maser Oscillators

Avigail Yariv, J. R. Singer, James C. Kemp

Several experiments [1,2] have noted recently that when an inverted two-level spin system was permitted to radiate spontaneously, the resulting oscillation was characterized by an appreciable amplitude modulation. The phenomenon was first believed to be the result of interference of different spin packets in an inhomogeneously broadened spectrum [1]. A theoretical analysis (which will be reported separately) shows that this is not the case. The spins are not independent but are coupled together by means of their radiation field. This explanation has since been by its original authors.

Journal of Applied Physics•Feb 1, 1959•9 citations

Dynamical evolution of an inverted spin ensemble in a cavity: Inhomogeneous broadening as a stabilizing mechanism

Brian Julsgaard, Klaus Mølmer

We study the evolution of an inverted spin ensemble coupled to a cavity. While the inversion itself presents an inherent instability in the system, the inhomogeneous broadening of spin-resonance frequencies provides a stabilizing mechanism. The detailed behavior of mean values and variances of the spin components and the cavity field is accounted for under both stable and unstable conditions.

arXiv:1209.4167•Physical Review A•Dec 7, 2012•30 citations

Superradiant Damping Effects in Photon-Echo Theory

Antonio M. Ponte Goncalves, Andree A. Tallet, R. Lefèbvre

A theoretical model for superradiant damping effect in inhomogeneously broadened media and its application to photon-echo problems are discussed. Only optically thin systems are considered, and all nonradiative relaxation mechanisms are neglected. Numerical calculations are performed for a very wide square inhomogeneous line shape and square applied pulses. It is shown that excitation of the system becomes increasingly difficult as the superradiant lifetime ${\ensuremath{\tau}}_{s}$ becomes comparable with ${T}_{2}^{*}$. The energy reradiated after the end of the exciting pulse is considerable for ${\ensuremath{\tau}}_{s}\ensuremath{\approx}{T}_{2}^{*}$ and for some applied pulse areas. Two-pulse sequences produce multiple echoes as the microscopic polarizations spontaneously rephase. The first-echo amplitude maximum is found to occur for first-applied-pulse areas increasingly above $\frac{1}{2}\ensuremath{\pi}$ as ${\ensuremath{\tau}}_{s}$ decreases. For a given first-pulse area, the echo intensities increase initially as ${\ensuremath{\tau}}_{s}$ decreases (negligible damping) and finally decrease and vanish (important damping). The ratio of the second- to first-echo amplitudes is found to be proportional to $\frac{{T}_{2}^{*}}{{\ensuremath{\tau}}_{s}}$ for small superradiance levels and to decrease when ${\ensuremath{\tau}}_{s}$ approaches ${T}_{2}^{*}$. An approximate estimate of this ratio is derived for the region of linearity in $\frac{{T}_{2}^{*}}{{\ensuremath{\tau}}_{s}}$.

Physical Review A•May 1, 1970•13 citations

Fundamental limitations in spin-ensemble quantum memories for cavity fields

Brian Julsgaard, Klaus Mølmer

Inhomogeneously broadened spin ensembles play an important role in present-day implementation of hybrid quantum processing architectures. When coupled to a cavity, such an ensemble may serve as a multimode quantum memory for the cavity field, and by employing spin-refocusing techniques the quantum-memory time can be extended to the coherence time of individual spins in the ensemble. In this paper, we investigate such a memory protocol capable of storing an unknown cavity-field state, and we examine separately the various constituents of the protocol: the storage and readout part, the memory hold time with the spin ensemble and cavity field decoupled, and the parts employing spin-refocusing techniques. Using both analytical and numerical methods, we derive how the obtainable memory performance scales with various physical parameters.

arXiv:1309.5517•Physical Review A•Dec 20, 2013•21 citations

Quantum beat echoes

T. Hashi, Yukio Fukuda, M Tanigawa

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.

•Aug 27, 1992•0 citations
Exploration of the theory for spin–cavity coupling in inhomogeneously broadened spin ensembles shows that all three components of magnetization can be refocused. The conventional spin echo generated by two components of magnetization is a special case of this three component refocusing in the limit of negligible radiation damping. We demonstrate this effect by an analytical theorem, numerical simulation, and experiment.
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.
Several experiments [1,2] have noted recently that when an inverted two-level spin system was permitted to radiate spontaneously, the resulting oscillation was characterized by an appreciable amplitude modulation. The phenomenon was first believed to be the result of interference of different spin packets in an inhomogeneously broadened spectrum [1]. A theoretical analysis (which will be reported separately) shows that this is not the case. The spins are not independent but are coupled together by means of their radiation field. This explanation has since been by its original authors.
A theoretical model for superradiant damping effect in inhomogeneously broadened media and its application to photon-echo problems are discussed. Only optically thin systems are considered, and all nonradiative relaxation mechanisms are neglected. Numerical calculations are performed for a very wide square inhomogeneous line shape and square applied pulses. It is shown that excitation of the system becomes increasingly difficult as the superradiant lifetime ${\ensuremath{\tau}}_{s}$ becomes comparable with T2∗{T}_{2}^{*}T2∗​. The energy reradiated after the end of the exciting pulse is considerable for ${\ensuremath{\tau}}_{s}\ensuremath{\approx}{T}_{2}^{*}$ and for some applied pulse areas. Two-pulse sequences produce multiple echoes as the microscopic polarizations spontaneously rephase. The first-echo amplitude maximum is found to occur for first-applied-pulse areas increasingly above $\frac{1}{2}\ensuremath{\pi}$ as ${\ensuremath{\tau}}_{s}$ decreases. For a given first-pulse area, the echo intensities increase initially as ${\ensuremath{\tau}}_{s}$ decreases (negligible damping) and finally decrease and vanish (important damping). The ratio of the second- to first-echo amplitudes is found to be proportional to $\frac{{T}_{2}^{*}}{{\ensuremath{\tau}}_{s}}$ for small superradiance levels and to decrease when ${\ensuremath{\tau}}_{s}$ approaches T2∗{T}_{2}^{*}T2∗​. An approximate estimate of this ratio is derived for the region of linearity in $\frac{{T}_{2}^{*}}{{\ensuremath{\tau}}_{s}}$.
Inhomogeneously broadened spin ensembles play an important role in present-day implementation of hybrid quantum processing architectures. When coupled to a cavity, such an ensemble may serve as a multimode quantum memory for the cavity field, and by employing spin-refocusing techniques the quantum-memory time can be extended to the coherence time of individual spins in the ensemble. In this paper, we investigate such a memory protocol capable of storing an unknown cavity-field state, and we examine separately the various constituents of the protocol: the storage and readout part, the memory hold time with the spin ensemble and cavity field decoupled, and the parts employing spin-refocusing techniques. Using both analytical and numerical methods, we derive how the obtainable memory performance scales with various physical parameters.
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.