Evolution of collective N atom states in single photon superradiance: Effect of virtual Lamb shift processes

We present analytical solutions for the evolution of collective states of N atoms. On the one hand is a (timed) Dicke state prepared by the conditional absorption of a single photon and exhibiting superradiant decay. This is in strong contrast to the evolution of a symmetric Dicke state which is trapped for large atomic clouds. We show that virtual processes yield only a small effect on the evolution of the rapidly decaying timed Dicke state. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important and provide new decay channels resulting in a slow decay of the otherwise trapped state.     

The single photon superradiance from the eigenmode analysis

Using the eigenmode analysis of the scalar photon theory, I compute the probability of the atoms remaining excited and the probability for the atoms remaining in the initial quantum state of a system of two-level atoms cloud in a sphere initially prepared to radiate in the forward direction, i.e., the single photon superradiance problem. The convergence in the results obtained for increasingly larger radii for the sphere suggests that the asymptotic limits for these quantities are obtained for a sphere with a radius equal to six times the resonant wavelength. I predict the maximal value of the probability of secondary excited states from large spheres at 17.1%.     

Proton-polarizability effect in the Lamb shift for the hydrogen atom

The proton-polarizability contribution to the Lamb shift for the ordinary and muonic hydrogen atoms is calculated on the basis of the isobar model and experimental data on structure functions for deep-inelastic lepton-nucleon scattering. The contributions of Born terms, vector mesons, and nucleon resonances are taken into account in constructing cross sections for the absorption of transversely and longitudinally polarized virtual photons, σ _T,L.     

Polarization of the vacuum in a relativistic hydrogenlike atom: The Lamb shift

This paper examines the shift of energy levels in a hydrogenlike atom induced by vacuum polarization effects. The contribution of free polarization is found for the ground state and several excited states in a closed analytical form. For the first time an expression is derived for the radiative correction to the energy in the form of an explicit function of the parameter Zα. The results are valid for states nl _j with the largest values of orbital and total angular momenta (l=n−1 and j=l+1/2). The final expression, found in terms of generalized hypergeometric functions, is a function of three variables, Zα, n, and the ratio of the particle masses on the orbit and in the vacuum loop, i.e., the result is valid for ordinary atoms and for muonic atoms. Several useful asymptotic expressions are also derived. Zh. éksp. Teor. Fiz. 116, 1575–1586 (November 1999)     

Interaction theory: Relativistic hydrogen atom and the Lamb shift

The Dirac relativistic equation for the hydrogen atom as augmented by dual interaction terms is solved exactly and the eigenvalues for the bound states are determined. These areE _n =[1 + ²/ (n + s)²]^–1/2, withs ²=k ²– ²(1±)², where is a constant which is a measure of the strength of the dual interaction relative to the standard interaction ^µ A _µ . It is shown that the ratios of the experimental values for the Lamb shifts of various energy levels in hydrogen and singly ionized helium are correctly given by the theory. The origin of the anomalous magnetic moment and, in fact, the operator for the total magnetic moment is given.     

On the evolution of N-atom state prepared by absorption of a single photon

We study evolution of timed symmetric N-atom state prepared by conditional absorption of a single photon and exhibiting superradiant decay. We find analytical expression for the initial decay rate of the state valid for any size of spherical atomic cloud. We show that the timed symmetric state is only approximately an eigenstate of the system for a large atomic cloud even if virtual processes are neglected.     

The inverse problem for a general N × N spectral equation

The spectral transform ?u/?x = {A(ζ)+B(x,ζ)} · u, where u is an n-element column vector and A(ζ) and B(x,ζ) are nxn matrices, is considered. A set of spectral data is given and the problem of reconcstructing B(x, ζ) from this spectral data is solved for a large class of cases. A special case of this spectral transform is used to solve the Boussinesq equation.     

Non-perturbative effects and infrared renormalons within the 1/N expansion of the O(N) non-linear sigma model

We analyze the structure of the Borel transform of the two-dimensional O(N) non-linear σ model within its $\text{1}\text{N}$ expansion. We check the existence of IR singularities (IR renormalons) and the presence of non-perturbative terms which organize themselves in an operator expansion à la Shifman-Vainshtein-Zakharov. We prove that renormalons cancel between the different terms of the operator expansion, so that there is a well-defined resummation procedure of the perturbative series. We suggest that this mechanism provides a general solution of the IR renormalons problem for massless UV free field theories.     

Gauge independence of the non-relativistic Lamb shift including retardation effects

Summary It is shown that the non-relativistic Lamb shift (including retardation effects), obtained in the second-order perturbation theory, is gauge independent.     

Observation of unique photon statistics of single artificial atom laser

We demonstrate a photonic crystal nanocavity laser essentially driven by a self-assembled InAs/GaAs single quantum dot gain and its unique photon statistics. Gain tuning measurements and photon correlation measurements indicated that a single quantum dot plays a substantial role in the laser oscillation. Photon correlation measurements showed a distinct transition from anti-bunching to Poissonian via photon bunching around the threshold with the increase of the excitation power. Numerical simulations, including contributions of other light sources besides a single quantum dot, indicated that the photon bunching feature around the threshold can be enhanced by the interfusion of incoherent photons into the cavity mode.     

Decoding the dynamics of a single trapped atom from photon correlations

Received: 4 September 1998     

Nonconvergence of the 1/N expansion for SU(N) gauge fields on a lattice

We present specific examples that demonstrate the non-convergence of the 1/N expansion for the lattice theory of SU(N) gauge fields.     

Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

It is shown that the limit as N → ∞ with g²N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

Observation of entanglement of a single photon with a trapped atom

We report the observation of entanglement between a single trapped atom and a single photon at a wavelength suitable for low-loss communication over large distances, thereby achieving a crucial step towards long range quantum networks. To verify the entanglement, we introduce a single atom state analysis. This technique is used for full state tomography of the atom-photon qubit pair. The detection efficiency and the entanglement fidelity are high enough to allow in a next step the generation of entangled atoms at large distances, ready for a final loophole-free Bell experiment.     

Quantum transport of a single photon through a subwavelength hole by a single atom

The localization and transport of a photon through a subwavelength hole with the help of a neutral atom are studied. A method proposed and realized in the study is based on the absorption of a photon by a neutral atom directly in front of a subwavelength hole, the flight of the atom through the hole, and photon emission on the other side of the screen. The influence of the interaction of the excited atom flying through the subwavelength channel with the screen material is estimated. The estimate showed that the atomic excitation can be quenched in holes with diameters smaller than 200 nm, which affects the photon transport efficiency.     

The phase structure of SU(N)/Z(N) lattice gauge theories

The phase structure of pure SU(N)/Z(N) lattice gauge theories in four dimensions is discussed. The presence of ZN monopoles plausibly leads to a phase transition. A Monte Carlo simulation of SO(3) shows the presence of a very strong, may be first order, phase transition.     

Instanton effects in N = 2 supersymmetric quantum mechanics

Supersymmetric quantum mechanics with several bosonic and fermionic dynamic variables is considered. Two different N = 2 supersymmetric models involving instantons are discussed in detail. Instantons fail to break supersymmetry in one of the models considered. The vacuum state is degenerate in this model which generally results in spontaneous breaking of internal left-right symmetry. In another model supersymmetry is destroyed dynamically due to special complex instanton solutions. Possible implications for SUSY field theories are discussed.