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Physical Review A

Collective ordering phenomena and instabilities of the Al27 nuclear spin system in ruby

Peter Boesiger, Ernst Brun, D. Meier

Published Sep 1, 1979• 15 citations
Publisher

Abstract

The dynamic properties of the ruby NMR laser are discussed from the point of view of synergetics. The authors present a theoretical approach together with the experimental verification. The cooperative features of the instabilities and the disorder-order transitions far from thermal equilibrium of the ruby NMR laser are described by means of order parameters and their dynamic equations, which are generalized Bloch equations. The heat-reservoir description of the conventional spin dynamics in ruby is thereby taken into account. The theory is applied to the free-running NMR laser with its threshold, the critical narrowing of cw NMR lines below threshold, and the steady-state output above threshold. The theory is then extended to the driven NMR laser where an external resonant rf field is applied to form, together with the self-induced radiation field, a competitive- or cooperative-field configuration. The authors present data concerning bistability and hysteresis of the driven NMR laser; in particular, its first-order-type phase transitions from a competitive- to a cooperative-field configuration are discussed. Finally, a novel pulsation mode of the ruby NMR laser is described.

DOI
10.1103/physreva.20.1073

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Journal of Physics B Atomic and Molecular Physics•Dec 21, 1977•65 citations
The dynamic properties of the ruby NMR laser are discussed from the point of view of synergetics. The authors present a theoretical approach together with the experimental verification. The cooperative features of the instabilities and the disorder-order transitions far from thermal equilibrium of the ruby NMR laser are described by means of order parameters and their dynamic equations, which are generalized Bloch equations. The heat-reservoir description of the conventional spin dynamics in ruby is thereby taken into account. The theory is applied to the free-running NMR laser with its threshold, the critical narrowing of cw NMR lines below threshold, and the steady-state output above threshold. The theory is then extended to the driven NMR laser where an external resonant rf field is applied to form, together with the self-induced radiation field, a competitive- or cooperative-field configuration. The authors present data concerning bistability and hysteresis of the driven NMR laser; in particular, its first-order-type phase transitions from a competitive- to a cooperative-field configuration are discussed. Finally, a novel pulsation mode of the ruby NMR laser is described.
Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​: Cr3+{\mathrm{Cr}}^{3+}Cr3+ (ruby) with the 27Al^{27}\mathrm{Al}27Al spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after QQQ-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the 27Al^{27}\mathrm{Al}27Al spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.
A master equation of a Laser system is presented from a dynamical point of .It is assumed that the Laser system is coupled with other independent subsystems.They p!ay a role as distinct reservoirs in our Laser system.As an application of this approach, the master equation is obtained for a system that corresponds to a Laser model considered by Scully-Lamb.The equation obtained heye includes the dynamical effect of an atomic system, i. e., atomic coherence. gl. IntroductionRecently various statistical mechanical theories have been developed by many authors in order to explain the properties of Laser systems.Especially, Haken et al.i) presented a model in which the Laser system is in contact with several independent heat reservoirs of different temperatures, undergoing irreversible processes among them.In particular, Weidlich and Haake2) showed the existence of the lasing state which might be considered as a revelation of the phase change in an open system by the method of a master equation similar to the Wangnness-Bloch equation of nuclear spin induction.In this theory the relaxation processes are lntroduced phenomenologica!ly in the master equation, without taking into account its detailed derivation from a microscopic point of view.On the other hand, Scully-Lamb3) independently developed a quantal theory of Laser, which is an extention of the famous semiclassic theory by Lamb, and obtained the statistical properties of radiation field of Laser systems.In g2, one of the purposes of this paper is presented.Here, from a dynamical point of view, a generalized master equation was setforth for a system coupled with several independent subsystems.Thus the discussion in g2 is analogous to Argyres' theory") for the relaxation of spin system, in wh!ch Wangness-Bloch equation was derived from a dynamical point of view.The second purpose of this paper is to present a generalized master equation corresponding to the Laser system considered by Scully-Lamb as described in g3.gZ. Derivation of the master equation Now let us consider the following system.The system with which we are mainly concerned shali be called A and is described by dynamical variables {ai}.
Pattern formation of atoms in high-finesse optical resonators results from the mechanical forces of light associated with superradiant scattering into the cavity mode. It occurs when the laser intensity exceeds a threshold value such that the pumping processes counteract the losses. We consider atoms driven by a laser and coupling with a mode of a standing-wave cavity and describe their dynamics with a Fokker-Planck equation, in which the atomic motion is semiclassical but the cavity field is a full quantum variable. The asymptotic state of the atoms is a thermal state, whose temperature is solely controlled by the detuning between the laser and the cavity frequency and by the cavity loss rate. From this result we derive the free energy and show that in the thermodynamic limit self-organization is a second-order phase transition. The order parameter is the field inside the resonator to which one can associate a magnetization in analogy to ferromagnetism, the control field is the laser intensity, but the steady state is intrinsically out of equilibrium. In the symmetry-broken phase, quantum noise induces jumps of the spatial density between two ordered patterns: We characterize the statistical properties of this temporal behavior at steady state and show that the thermodynamic properties of the system can be extracted by detecting the light at the cavity output. The results of our analysis are in full agreement with previous studies; we extend them by deriving a self-consistent theory which is valid also when the cavity field is in the shot-noise limit and elucidate the nature of the self-organization transition.
We report the observation of a coherent, maser-type rf radiation of the 27Al^{27}\mathrm{Al}27Al nuclear-spin system in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​: Cr3+{\mathrm{Cr}}^{3+}Cr3+ pumped by dynamic nuclear polarization to negative temperature. A theoretical description is presented for the sharp, superradiant bursts which follow the fast tuning of a resonant LC\mathrm{LC}LC circuit to a selected NMR line of 27Al^{27}\mathrm{Al}27Al. Experimental results are discussed which demonstrate the interplay between dynamic nuclear polarization, relaxation, and the radiation field.
Our model, presented earlier, which predicts the circumstances under which intrinsic mirrorless optical bistability (OB) can occur due to atomic pair correlation in a small volume, is outlined and the results presented. These results, which Predict a first-order phase transition in steady state for an externally-driven collection of a large number of atoms far removed from thermodynamic equilibriun, forms the motivation for a detailed microscopic examination of the dynamical behavior of atonic pair correlation in the presence of externally-applied coherent radiation. 4 model is presented and results are discussed for the transient dynamic evolution of two, two-level atoms separated from each other by a distance r in the presence of an externally-applied coherent radiation field. The results predict collective radiation reaction, frequency shifts, relaxation in terms of the atomic seoaration r (assumed much larger than single atom dimensions), the externally-applied field intensity and spacial uniformity of the field with respect to the inter-atomic volume.
Analytic results for the fluorescent spectrum arising in the cooperative interaction of a population of two-level atoms, driven by resonant laser radiation with the electromagnetic field are presented. The bistability and hysteresis characterising single-time atomic averages are evidenced explicitly as this spectrum is viewed throughout a hysteresis cycle. In the region of bistability full support is given to the designation of a cooperative and a non-cooperative branch. Spectral features reveal linewidths associated with cooperative and non-cooperative atomic decay rates respectively. A dominant feature is strong coherent scattering throughout the cooperative region, fully supporting an identification of this problem with super-radiant phenomena. Linewidth narrowing is predicted in the vicinity of both instabilities.