Cavity nonlinear optics with few photons and ultracold quantum particles

The light force on particles trapped in the field of a high-Q cavity mode depends on the quantum state of field and particle. Different photon numbers generate different optical potentials anddifferent motional states induce different field evolution. Even for weak saturation and linear polarizability the induced particle motion leads to nonlinear field dynamics. We derive a corresponding effective field Hamiltonian containing all the powers of the photon number operator, which predicts nonlinear phase shifts and squeezing even at the few-photon level. Wave-function simulations of the full particle-field dynamics confirm this and show significant particle-field entanglement in addition.Comment: 5 pages, 5 figure

The topology of Stein fillable manifolds in high dimensions II

We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 admits a weakly fillable contact structure provided M admits a weak symplectic filling. We also study the connection between Stein fillability and connected sums: we give examples of almost contact manifolds for which the connected sum is Stein fillable, while the components are not. Concerning obstructions to Stein fillings, we show that the (8k-1)-dimensional sphere has an almost contact structure which is not Stein fillable once k > 1. As a consequence we deduce that any highly connected almost contact (8k-1)-manifold (with k > 1) admits an almost contact structure which is not Stein fillable. The proofs rely on a new number-theoretic result about Bernoulli numbers.Comment: We corrected mistakes in the proofs of Lemma 2.9 and Corollary 2.10. This lead to an assumption being removed from the statement of Theorem 1.3. The paper is now published in Geometry and Topology. The appendix was written by Bernd C. Kellne

New results and perspectives on R_{AA} measurements below 20 GeV CM-energy at fixed target machines

Transverse momentum spectra of pi^{+/-} at midrapidity are measured at high p_T in p+p and p+Pb collisions at 158 GeV/nucleon beam energy by the NA49 experiment. This study is complementary to our previous results on the same spectra from Pb+Pb collisions. The nuclear modification factors R_{A+A/p+p}, R_{p+A/p+p} and R_{A+A/p+A} as a function of p_T are extracted and compared to RHIC measurements, thus providing insight into the energy dependence of nuclear modification. The modification factor R_{A+A/p+A} proved to be consistent with our previous results on the central to peripheral modification factor R_{CP}. The limitation of our current p_T range is discussed and planned future upgrades are outlined. Some aspects of the FAIR-CBM experiment are also presented as a natural future continuation of the measurements at very high p_T.Comment: Proceedings of Quark Matter 200

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