Superradiant Laser: First-Order Phase Transition and Non-stationary Regime

We solve the superradiant laser model in two limiting cases. First the stationary low-pumping regime is considered where a first-order phase transition in the semiclassical solution occurs. This discontinuity is smeared out in the quantum regime. Second, we solve the model in the non-stationary regime where we find a temporally periodic solution. For a certain parameter range well separated pulses may occur.Comment: RevTeX, 10 pages, 4 figure

Long-lived Quantum Coherence between Macroscopically Distinct States in Superradiance

The dephasing influence of a dissipative environment reduces linear superpositions of macroscopically distinct quantum states (sometimes also called Schr\"odinger cat states) usually almost immediately to a statistical mixture. This process is called decoherence. Couplings to the environment with a certain symmetry can lead to slow decoherence. In this Letter we show that the collective coupling of a large number of two-level atoms to an electromagnetic field mode in a cavity that leads to the phenomena of superradiance has such a symmetry, at least approximately. We construct superpositions of macroscopically distinct quantum states decohering only on a classical time scale and propose an experiment in which the extraordinarily slow decoherence should be observable.Comment: 4 pages of revte

Sigma models for quantum chaotic dynamics

We review the construction of the supersymmetric sigma model for unitary maps, using the color- flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization

Semiclassical spin damping: Superradiance revisited

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.Comment: 12 pages standard revtex; to be published in EPJ

Level Dynamics and Universality of Spectral Fluctuations

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning by establishing a power law for the $\hbar$ dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas-Yukawa gas.Comment: 5 pages, RevTex, 3 figures, improved style, published versio