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Physical Review A

Ruby NMR laser: A phenomenon of spontaneous self-organization of a nuclear spin system

Peter Boesiger, Ernst Brun, D. Meier

Published Aug 1, 1978• 46 citations
Publisher

Abstract

Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$: ${\mathrm{Cr}}^{3+}$ (ruby) with the $^{27}\mathrm{Al}$ 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 $Q$-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 $^{27}\mathrm{Al}$ 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.

DOI
10.1103/physreva.18.671

Related papers

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

Peter Boesiger, Ernst Brun, D. Meier

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.

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Solid-State Nuclear Spin-Flip Maser Pumped by Dynamic Nuclear Polarization

Peter Boesiger, Ernst Brun, D. Meier

We report the observation of a coherent, maser-type rf radiation of the $^{27}\mathrm{Al}$ nuclear-spin system in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$: ${\mathrm{Cr}}^{3+}$ 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 $\mathrm{LC}$ circuit to a selected NMR line of $^{27}\mathrm{Al}$. Experimental results are discussed which demonstrate the interplay between dynamic nuclear polarization, relaxation, and the radiation field.

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Using nuclear spins, radio waves, sodium atoms, and laser light to investigate spatiotemporal nonlinear systems

Reto Holzner, Josef Simonet, L. Flepp +6 more

Within the wide field of nonlinear dynamics we investigate temporal and spatial behavior of electromagnetic systems. A strange type of laser, the nuclear magnetic resonance (NMR) laser, shows truly chaotic behavior and is therefore ideally suited to analyze experimentally and theoretically a variety of temporal nonlinear effects. Of particular interest is the analysis of its strange attractors in terms of unstable periodic orbits. For the extension of our research from the NMR laser (representing a purely temporal system described by the Bloch-Kirchhoff ordinary differential equations) to spatial and spatiotemporal systems, we chose, as a three-dimensional dynamic system, polarized laser beams interacting nonlinearly with sodium atoms. Among other effects, we have observed beam bouncing, beam splitting, and beam switching. This can be well described by partial differential equations for beam propagation derived from the Schrödinger equation and the Maxwell equations. An intuitive explanation is given in terms of intensity and polarization patterns formed by optical-pumping-induced mutual refractive index modifications between polarized resonant laser beams.

Optical Engineering•Aug 1, 1995•1 citation

Raman heterodyne detection of nuclear magnetic resonance

N. C. Wong, Emily S. Kintzer, J. Mlynek +2 more

A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ at 1.6 K utilizing the ${\mathrm{Pr}}^{3+}$ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ hyperfine splittings where the optical heterodyne signals are shot-noise limited. The ${\mathrm{Pr}}^{3+}$ nuclear quadrupole parameters are obtained for the $^{3}H_{4}$ and $^{1}D_{2}$ states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the $^{3}H_{4}$ and $^{1}D_{2}$ hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.

Physical review. B, Condensed matter•Nov 1, 1983•110 citations

Optically Induced Magnetization in Ruby

Jan P. van der Ziel, N. Bloembergen

The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a $Q$-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the $^{4}A_{2}$ ground state to the levels of the $\overline{E}(^{2}E)$ excited state. The change in ${M}_{z}$ is linearly proportional to $H$ except near the anticrossing points of the $^{4}A_{2}$ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the $^{4}A_{2}$ wave functions. When $H$ has a small component perpendicular to the $z$ axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of ${M}_{z}$ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.

Physical Review•May 17, 1965•57 citations

Thermodynamics and dynamics of atomic self-organization in an optical cavity

Stefan Schütz, Simon B. Jäger, Giovanna Morigi

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.

arXiv:1508.06606•Physical Review A•Dec 7, 2015•29 citations
Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in {\mathrm{Al}}_{2}$${\mathrm{O}}_{3}: 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.
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.
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.
Within the wide field of nonlinear dynamics we investigate temporal and spatial behavior of electromagnetic systems. A strange type of laser, the nuclear magnetic resonance (NMR) laser, shows truly chaotic behavior and is therefore ideally suited to analyze experimentally and theoretically a variety of temporal nonlinear effects. Of particular interest is the analysis of its strange attractors in terms of unstable periodic orbits. For the extension of our research from the NMR laser (representing a purely temporal system described by the Bloch-Kirchhoff ordinary differential equations) to spatial and spatiotemporal systems, we chose, as a three-dimensional dynamic system, polarized laser beams interacting nonlinearly with sodium atoms. Among other effects, we have observed beam bouncing, beam splitting, and beam switching. This can be well described by partial differential equations for beam propagation derived from the Schrödinger equation and the Maxwell equations. An intuitive explanation is given in terms of intensity and polarization patterns formed by optical-pumping-induced mutual refractive index modifications between polarized resonant laser beams.
A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid Pr3+{\mathrm{Pr}}^{3+}Pr3+: LaF3{\mathrm{F}}_{3}F3​ at 1.6 K utilizing the Pr3+{\mathrm{Pr}}^{3+}Pr3+ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the Pr3+{\mathrm{Pr}}^{3+}Pr3+: LaF3{\mathrm{F}}_{3}F3​ hyperfine splittings where the optical heterodyne signals are shot-noise limited. The Pr3+{\mathrm{Pr}}^{3+}Pr3+ nuclear quadrupole parameters are obtained for the 3H4^{3}H_{4}3H4​ and 1D2^{1}D_{2}1D2​ states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the 3H4^{3}H_{4}3H4​ and 1D2^{1}D_{2}1D2​ hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.
The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a QQQ-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the 4A2^{4}A_{2}4A2​ ground state to the levels of the E‾(2E)\overline{E}(^{2}E)E(2E) excited state. The change in Mz{M}_{z}Mz​ is linearly proportional to HHH except near the anticrossing points of the 4A2^{4}A_{2}4A2​ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the 4A2^{4}A_{2}4A2​ wave functions. When HHH has a small component perpendicular to the zzz axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of Mz{M}_{z}Mz​ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.
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.