We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting $\mathit{LC}$ circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations, we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in ``dark states'' can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space.We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting $\mathit{LC}$ circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations, we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in ``dark states'' can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space.

arXiv:1101.5300Physical Review AJun 6, 20117 citations

Exact solution and scaling theory of superradiance

Toshihico Arimitsu, Masuo Suzuki

Physica A Statistical Mechanics and its ApplicationsFeb 1, 197810 citations

Emergence of superradiance in dissipative dipolar-coupled spin systems

Saptarshi Saha, Yeshma Ibrahim, Rangeet Bhattacharyya

Abstract In the superradiance phenomenon, a collection of non-interacting atoms exhibits collective dissipation due to interaction with a common radiation field, resulting in a non-monotonic decay profile. This work shows that the dissipative dipolar-coupled systems exhibit an identical collective dissipation aided by the nonsecular part of the dipolar coupling. We consider a simplified dipolar network where the dipolar interaction between the spin-pairs is assumed to be identical. For a suitable choice of the initial condition, the resulting dynamics requires dealing with a smaller subspace that helps extend the analysis to a larger spin network. To include the nonsecular dipolar relaxation, we use a fluctuation-regulated quantum master equation. Moreover, we find that for an ensemble of N spins, the maximum intensity of the radiation exhibits a nearly quadratic scaling (N 2), and the dipolar relaxation time follows an inverse square proportionality ( 1 / N 2 ); these two observations help characterize the emergence of superradiance. Our results agree well with the standard results of pure spin superradiance observed experimentally in various systems.Abstract In the superradiance phenomenon, a collection of non-interacting atoms exhibits collective dissipation due to interaction with a common radiation field, resulting in a non-monotonic decay profile. This work shows that the dissipative dipolar-coupled systems exhibit an identical collective dissipation aided by the nonsecular part of the dipolar coupling. We consider a simplified dipolar network where the dipolar interaction between the spin-pairs is assumed to be identical. For a suitable choice of the initial condition, the resulting dynamics requires dealing with a smaller subspace that helps extend the analysis to a larger spin network. To include the nonsecular dipolar relaxation, we use a fluctuation-regulated quantum master equation. Moreover, we find that for an ensemble of N spins, the maximum intensity of the radiation exhibits a nearly quadratic scaling (N 2), and the dipolar relaxation time follows an inverse square proportionality ( 1 / N 2 ); these two observations help characterize the emergence of superradiance. Our results agree well with the standard results of pure spin superradiance observed experimentally in various systems.

arXiv:2406.09100Journal of Physics A Mathematical and TheoreticalDec 12, 20242 citations

Fluctuation in superradiance

Masuo Suzuki

Physica A Statistical Mechanics and its ApplicationsJan 1, 19767 citations

Mathematical models of the kinetics of superradiance

А.В. Андреев, Oleg Tikhomirov

Soviet physics. DokladyFeb 1, 19830 citations

Dynamics of Critical Fluctuations. I

Kyozi Kawasaki

The dynamics of critical fluctuations is treated theoretically by extending the usual macroscopic dynamical variables to include all other dynamical variables that could exhibit the critical slowing-down. The equations of motion for these generalized macroscopic dynamical variables are derived with the help of Mori's general theory of Brownian motion, which involve the “first moment frequency matrix” Ωq and the microscopic damping for these new dynamical variables, where q is the wave vector characterizing macroscopic inhomogeneity. The latter involves only the dynamical variables that perform rapid random motions and is disregarded, or is disposed of by means of a dimensional argument. Then the dynamics of critical fluctuations is completely governed by Ωq which is expressed in terms of equaltime correlations of long wave-length fluctuations only and allows the analysis with the help of the Widom-Kadanoff static scaling laws. The theory is applied to the problem of anomalous spin relaxations in ferro and antiferromagnets in the paramagnetic region, and the inverse characteristic times near the transition points are found to behave asymptotically as κ(5-η)/2f(q/κ) and κ3/2f(q/κ), respectively, where κ is the inverse correlation range of spin fluctuations and η the parameter measuring the deviation of spin pair correlation from the Ornstein-Zernike form. Finally a close analogy is pointed out between the present treatment of critical fluctuations are the theory of hydrodynamic turbulence.The dynamics of critical fluctuations is treated theoretically by extending the usual macroscopic dynamical variables to include all other dynamical variables that could exhibit the critical slowing-down. The equations of motion for these generalized macroscopic dynamical variables are derived with the help of Mori's general theory of Brownian motion, which involve the “first moment frequency matrix” Ωq and the microscopic damping for these new dynamical variables, where q is the wave vector characterizing macroscopic inhomogeneity. The latter involves only the dynamical variables that perform rapid random motions and is disregarded, or is disposed of by means of a dimensional argument. Then the dynamics of critical fluctuations is completely governed by Ωq which is expressed in terms of equaltime correlations of long wave-length fluctuations only and allows the analysis with the help of the Widom-Kadanoff static scaling laws. The theory is applied to the problem of anomalous spin relaxations in ferro and antiferromagnets in the paramagnetic region, and the inverse characteristic times near the transition points are found to behave asymptotically as κ(5-η)/2f(q/κ) and κ3/2f(q/κ), respectively, where κ is the inverse correlation range of spin fluctuations and η the parameter measuring the deviation of spin pair correlation from the Ornstein-Zernike form. Finally a close analogy is pointed out between the present treatment of critical fluctuations are the theory of hydrodynamic turbulence.

Progress of Theoretical PhysicsMay 1, 196846 citations

We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting

\mathit{LC}

circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations, we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in ``dark states'' can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space.