Fundamental limitation of ultrastrong coupling between light and atoms

In a recent work of ours [Phys. Rev. Lett. 112, 073601 (2014)], we generalized the Power-Zineau-Woolley gauge to describe the electrodynamics of atoms in an arbitrary confined geometry. Here we complement the theory by proposing a tractable form of the polarization field to represent atomic material with well-defined intra-atomic potential. The direct electrostatic dipole-dipole interaction between the atoms is canceled. This theory yields a suitable framework to determine limitations on the light-matter coupling in quantum optical models with discernible atoms. We find that the superradiant criticality is at the border of covalent molecule formation and crystallization.Comment: 6 page

Self-organization of atoms in a cavity field: threshold, bistability and scaling laws

We present a detailed study of the spatial self-organization of laser-driven atoms in an optical cavity, an effect predicted on the basis of numerical simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001 (2003)]. Above a threshold in the driving laser intensity, from a uniform distribution the atoms evolve into one of two stable patterns that produce superradiant scattering into the cavity. We derive analytic formulas for the threshold and critical exponent of this phase transition from a mean-field approach. Numerical simulations of the microscopic dynamics reveal that, on laboratory timescale, a hysteresis masks the mean-field behaviour. Simple physical arguments explain this phenomenon and provide analytical expressions for the observable threshold. Above a certain density of the atoms a limited number of ``defects'' appear in the organized phase, and influence the statistical properties of the system. The scaling of the cavity cooling mechanism and the phase space density with the atom number is also studied.Comment: submitted to PR

A quantum homogeneous space of nilpotent matrices

A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known quantum homogeneous spaces are revisited.Comment: 12 page

How river rocks round: resolving the shape-size paradox

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.Comment: 11 pages, 5 figure

Explaining the elongated shape of 'Oumuamua by the Eikonal abrasion model

The photometry of the minor body with extrasolar origin (1I/2017 U1) 'Oumuamua revealed an unprecedented shape: Meech et al. (2017) reported a shape elongation b/a close to 1/10, which calls for theoretical explanation. Here we show that the abrasion of a primordial asteroid by a huge number of tiny particles ultimately leads to such elongated shape. The model (called the Eikonal equation) predicting this outcome was already suggested in Domokos et al. (2009) to play an important role in the evolution of asteroid shapes.Comment: Accepted by the Research Notes of the AA

Adequacy of the Dicke model in cavity QED: a counter-"no-go" statement

The long-standing debate whether the phase transition in the Dicke model can be realized with dipoles in electromagnetic fields is yet an unsettled one. The well-known statement often referred to as the "no-go theorem", asserts that the so-called A-square term, just in the vicinity of the critical point, becomes relevant enough to prevent the system from undergoing a phase transition. At variance with this common belief, in this paper we prove that the Dicke model does give a consistent description of the interaction of light field with the internal excitation of atoms, but in the dipole gauge of quantum electrodynamics. The phase transition cannot be excluded by principle and a spontaneous transverse-electric mean field may appear. We point out that the single-mode approximation is crucial: the proper treatment has to be based on cavity QED, wherefore we present a systematic derivation of the dipole gauge inside a perfect Fabry-P\'erot cavity from first principles. Besides the impact on the debate around the Dicke phase transition, such a cleanup of the theoretical ground of cavity QED is important because currently there are many emerging experimental approaches to reach strong or even ultrastrong coupling between dipoles and photons, which demand a correct treatment of the Dicke model parameters

Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE in non-divergence form with bounded measurable coefficients. The method of proof is through a Bochner technique. The Heisenberg group is seen to be en extremal manifold for our inequality in the class of manifolds whose Ricci curvature is non-negative.Comment: 13 page