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Semiclassical spin damping: Superradiance\nrevisited

P. A. Braun, D. Braun, F. Haake, J. Weber

Published May 15, 1998• 0 citations
OpenAlex

Abstract

\n \nA well known description of superradiance from pointlike collections of many\natoms involves the dissipative motion of a large spin. The pertinent\n"superradiance master equation" allows for a formally exact solution which\nwe subject to a semiclassical evaluation. The clue is a saddle-point\napproximation for an inverse Laplace transform. All previous approximate\ntreatments, disparate as they may appear, are encompassed in our systematic\nformulation. A byproduct is a hitherto unknown rigorous relation between\ncoherences and probabilities. Our results allow for generalizations to spin\ndynamics with chaos in the classical limit. \n\n\n\n

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\n \nA well known description of superradiance from pointlike collections of many\natoms involves the dissipative motion of a large spin. The pertinent\n"superradiance master equation" allows for a formally exact solution which\nwe subject to a semiclassical evaluation. The clue is a saddle-point\napproximation for an inverse Laplace transform. All previous approximate\ntreatments, disparate as they may appear, are encompassed in our systematic\nformulation. A byproduct is a hitherto unknown rigorous relation between\ncoherences and probabilities. Our results allow for generalizations to spin\ndynamics with chaos in the classical limit. \n\n\n\n
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a semiclassical evaluation. The clue is a saddle-point approximation for an inverse Laplace transform. All previous approximate treatments, disparate as they may appear, are encompassed in our systematic formulation. A byproduct is a hitherto unknown rigorous relation between coherences and probabilities. Our results allow for generalizations to spin dynamics with chaos in the classical limit.
Nonlinear evolution of the Landau-Lifshitz type can be exactly linearized. Special cases include the radiation-damped spin system and the superradiant system in the semiclassical regime, in the presence of time-varying driving fields. For these, the resultant linear system is simply that of a spin 1 / 2 particle, with the radiation damping rate, or superradiant characteristic time, manifested as an imaginary addition to the spin's resonance frequency. Consequently, methods from inverse scattering theory can be used to design driving fields. The behavior of these systems under stochastic excitation can be determined exactly.
Quantum scars enable memory and recurrent dynamics, but their fate under dissipation remains poorly understood. Here, we show that distinct quantum scars can respond qualitatively differently to the same dissipative channel. We consider a collective spin model coupled to a lossy cavity and, guided by its classical limit, identify scars associated with two unstable structures: a saddle point on a dissipation-free invariant manifold with vanishing cavity field and an unstable superradiant fixed point with finite photon occupation. The former is immune to photon loss in the classical limit and exhibits persistent quantum revivals, whereas the latter couples directly to the dissipative channel, but exhibits slow dynamics. Remarkably, the superradiant scar also supports chaos-assisted quantum tunneling between two symmetry-related, macroscopically distinct semiclassical configurations, despite the presence of dissipation. Our results identify an experimentally accessible setting for exploring dissipative scarring and chaos-assisted tunneling in cavity QED.
Abstract Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for the same system. Here, we derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. The use of the damping-basis formalism allows us to devise a general procedure to go from one master equation to the other and vice versa, by working with functions of time and their Laplace transforms only. We further analyze the Lindbladian form of the time-local and the integro-differential master equations, where we account for the appearance of different sets of Lindbladian operators. In addition, we investigate a Redfield-like approximation, that transforms the exact integro-differential equation into a time-local one by means of a coarse graining in time. Besides relating the structure of the resulting master equation to those associated with the exact dynamics, we study the effects of the approximation on Markovianity. In particular, we show that, against expectation, the coarse graining in time can possibly introduce memory effects, leading to a violation of a divisibility property of the dynamics.