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The Journal of Chemical Physics

Self-sustained Maser oscillations of a large magnetization driven by a radiation damping-based electronic feedback

Daniel Abergel, Alain Louis‐Joseph, Jean‐Yves Lallemand

Published Apr 22, 2002• 25 citations
Publisher

Abstract

In this paper, the dynamics of a magnetization undergoing a radiation-damping based feedback radio-frequency field is investigated both theoretically and experimentally. It is shown that due to the presence of T1 relaxation the evolution equations predict the existence of self-sustained maser pulses. This phenomenon is a consequence of the competition between two different processes, namely, T1 relaxation and a precession about a magnetization-dependent radio-frequency field. Experiments show the existence of periodic revivals of the free induction decay over unusually long periods of time, on the order of tens of seconds.

DOI
10.1063/1.1462583

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In this paper, the dynamics of a magnetization undergoing a radiation-damping based feedback radio-frequency field is investigated both theoretically and experimentally. It is shown that due to the presence of T1 relaxation the evolution equations predict the existence of self-sustained maser pulses. This phenomenon is a consequence of the competition between two different processes, namely, T1 relaxation and a precession about a magnetization-dependent radio-frequency field. Experiments show the existence of periodic revivals of the free induction decay over unusually long periods of time, on the order of tens of seconds.
We present experimental single and multimode sustained ^{1}H NMR masers in solution on thermally polarized spins at room temperature and 9.4 T achieved through the electronic control of radiation feedback (radiation damping). Our observations illustrate the breakdown of the usual three-dimensional Maxwell-Bloch equations for radiation feedback and a simple toy model of few coupled classical moments is used to interpret these experiments. This Letter represents a significant step to bring the spontaneous radiation damping based NMR masers in various contexts to the next stage of feedback-controlled and reproducible experiments.
We describe a simple nonlinear optical device which transforms an ingoing cw light beam into a periodically modulated one. The mechanism of operation is due to a spin precession in the ground state of optically pumped atoms with a J=(1/2)\ensuremath{\rightarrow}J'=(1/2) transition in the presence of a static transverse magnetic field. With optical feedback from a resonator, this magnetically induced spin precession can be self-sustained and then can give rise to a self-pulsing of the transmitted light at roughly the Larmor frequency. A detailed theoretical description of the system is presented and stability criteria are considered. In contrast to earlier work, our calculations take into account the resonator round-trip time, an optical detuning from the atomic resonance, and absorptive losses within the resonator. New signal features are predicted: These include a complicated structure of the initial transient as well as a precipitation to a stationary state. Our theoretical model is confirmed by measurements which are performed by means of a Fabry-Perot resonator containing sodium vapor. The behavior of the device is studied for a wide range of experimental parameters; threshold powers for oscillation (\ensuremath{\gtrsim}5 mW) and the oscillation frequency and its tuning range (140 kHz--13 MHz) are investigated as well as the dynamics of the system following a step input of light.
Spin masers with optical detection and artificial feedback are widely used in fundamental and practical applications. However, a full picture of the maser dynamics is still absent. By solving the feedback-driven Bloch equations, we simulated the dynamics of an ideal spin maser in a broad parameter space. Rich nonlinear dynamics including high-order-harmonic generation, nonperiodic spin oscillations, and frequency comb were revealed when the artificial feedback interaction exceeds the normal spin-field interaction. We also propose a pulse feedback spin maser protocol, which constructs an ultralow field magnetic frequency comb and could be useful in precision atomic magnetometers in searching for spin-dependent exotic interactions.
When a two-state quantum system, capable of making radiative transitions, is driven by a high-frequency field, there occur damping effects due to the reaction of the sample to its own radiated field. This damping, which becomes important for high-Q rf structures and for samples of large dc susceptibilities, is here analyzed classically for a simple prototype system—a magnetic spin system obeying the Bloch equations. These equations are augmented to include the radiation-damping torques and are then solved for the four cases of usual interest. Firstly, for steady-state slow passage, radiation damping broadens and lowers the absorption and dispersion signals. Secondly, for adiabatic fast passage, damping causes the dispersion signal to dip at the line center and causes the otherwise absent absorption signal to become finite. However, if the radiation damping field becomes larger than the rf driving field a complete adiabatic inversion is shown to be no longer possible. Thirdly, the conditions for the occurrence of delayed power peaks of the free-precession signal are discussed. Fourthly, for the case of the driven nonsteady state, the stimulated emission may, for large radiation damping, become quite large if the system is driven from an initially ``negative temperature'' condition.
Equations are given describing the beat-frequency variation and mode competition in a gaseous optical maser operated in a magnetic field parallel to the maser axis. The equations include only lowest order nonlinear terms. Important terms in the amplitude- and frequency-determining equations are shown to arise from an induced atomic precession. These terms have a character similar to those describing the effects of selective depletion of the velocity distribution or "hole burning." It is shown that the induced atomic precession causes parametric conversion of an optical field of one circular polarization into one of the other polarization with a frequency shift equal to the rate of precession. This process tends to make the competition between modes of different polarizations important. An additional feature, not found in the scalar theory, is that, for sufficiently large magnetic fields, competition can be important between modes separated in frequency by several Doppler-broadened linewidths.
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce self-sustained oscillations at the base Larmor frequency due to nonlinearity. These features have driven the development of single-species and multiple-species spin masers. The latter, with multiple discrete Larmor frequencies, provides significant advantages for precision measurement by mitigating uncertainties in precession frequencies due to long-term drifts in experimental conditions. The self-sustained oscillations of single-species and multiple-species spin masers correspond to limit cycles and quasi-periodic orbits of the stable nonlinear dynamics of the systems, respectively; the correspondence is elucidated in a recent study on a related spin system featuring two discrete intrinsic Larmor frequencies under dual bias magnetic fields [T. Wang et al., Commun. Phys. 8, 41 (2025)]. Here, we extend the study to the case where the intrinsic Larmor frequencies of individual spins of the system, given rise to by an inhomogeneous bias magnetic field, form a continuum. We show that generically the stable dynamics of the system includes limit cycles, quasi-periodic orbits, and chaos. We establish the relation between the synchronization frequency of limit cycles and the field inhomogeneity and derive an equation determining the stability of limit cycles. Furthermore, detailed characteristics of different dynamical phases, especially the robustness of limit cycles and quasi-periodic orbits against experimental fluctuations, are discussed. Our findings not only encompass the case of discrete Larmor frequencies, but also provide crucial insights for precision measurement and the exploration of continuous time crystals and quasi-crystals.