Abstract:
We show that the Hamiltonian describing N nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge Z has a ground state when N

Abstract:
We propose and analyze a scheme for photon trapping in an optical resonator coupled with two-level atoms. We show that when the cavity is excited by two identical light fields from two ends of the cavity respectively, the output light from the cavity is suppressed while the intra-cavity light field is near the maximum due to the excitation of the polariton state of the coupled cavity and atom system. We also present methods for the direct probing of the trapped polariton state. The photon trapping is manifested by the destructive interference of the transmitted light and the incident light. Such photon trapping is quite generic and should be observable experimentally in a variety of cavity quantum electrodynamics systems.

Abstract:
We give a comprehensive account of our proposed experimental method of using atoms or molecules in order to measure parameters of neutrinos still undetermined; the absolute mass scale, the mass hierarchy pattern (normal or inverted), the neutrino mass type (Majorana or Dirac), and the CP violating phases including Majorana phases. There are advantages of atomic targets, due to the closeness of available atomic energies to anticipated neutrino masses, over nuclear target experiments. Disadvantage of using atomic targets, the smallness of rates, is overcome by the macro-coherent amplification mechanism. The atomic or molecular process we use is a cooperative deexcitation of a collective body of atoms in a metastable level |e> emitting a neutrino pair and a photon; |e> -> |g> + gamma + nu_i nu_j where nu_i's are neutrino mass eigenstates. The macro-coherence is developed by trigger laser irradiation. We discuss aspects of the macro-coherence development by setting up the master equation for the target quantum state and propagating electric field. With a choice of heavy target atom or molecule such as Xe or I_2 that has a large M1 x E1 matrix element between |e> and |g>, we show that one can determine three neutrino masses along with the mass hierarchy pattern by measuring the photon spectral shape. If one uses a target of available energy of a fraction of 1 eV, Majorana CP phases may be determined. Our master equation, when applied to E1 x E1 transition such as pH_2 vibrational transition Xv=1 -> 0, can describe explosive PSR events in which most of the energy stored in |e> is released within a few nanoseconds. The present paper is intended to be self-contained explaining some details related theoretical works in the past, and further reports new simulations and our ongoing experimental efforts of the project to realize the neutrino mass spectroscopy using atoms/molecules.

Abstract:
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the boundary-value problem is well-posed for two classes of boundary data and show that the well-posed solution in general has velocity discontinuities, henceforth broken extrema. Along regular segments, broken extrema satisfy the Euler-Lagrange neutral differential delay equations with state-dependent deviating arguments. At points where velocities are discontinuous, broken extrema satisfy the Weierstrass-Erdmann conditions that energies and momenta are continuous. The electromagnetic fields of the variational trajectories are derived quantities that can be extended only to a bounded region B of space-time. For extrema with a finite number of velocity discontinuities, extended fields are defined for all point in B with the exception of sets of zero measure. The extended fields satisfy the integral laws of classical electrodynamics for most surfaces and curves inside B. As an application, we study globally bounded trajectories with vanishing far-fields for the hydrogenoid atomic models of hydrogen, muonium and positronium. Our model uses solutions of the neutral differential delay equations along regular segments and a variational approximation for the collisional segments. Each hydrogenoid model predicts a discrete set of finitely measured neighbourhoods of orbits with vanishing far-fields at the correct atomic magnitude and in quantitative and qualitative agreement with experiment and quantum mechanics, i.e., the spacings between consecutive discrete angular momenta agree with Planck's constant within thirty-percent, while orbital frequencies agree with a corresponding spectroscopic line within a few percent.

Abstract:
Single-photon cooling is a recently introduced method to cool atoms and molecules for which standard methods might not be applicable. We numerically examine this method in a two-dimensional wedge trap as well as in a two-dimensional harmonic trap. An element of the method is an optical dipole box trapping atoms irreversibly. We show that the cooling efficiency of the single-photon method can be improved by optimizing the trajectory of this optical dipole box.

Abstract:
The proposed paradigm of plasmonic atoms and plasmonic molecules allows one to describe and predict the strongly localized plasmonic oscillations in the clusters of nanoparticles and some other nanostructures in uniform way. Strongly localized plasmonic molecules near the contacting surfaces might become the fundamental elements (by analogy with Lego bricks) for a construction of fully integrated opto-electronic nanodevices of any complexity and scale of integration.

Abstract:
The self-consistent equations for the order parameters of Bose-Einstein condensation (BEC) of molecules and Bardeen-Cooper-Schrieffer (BCS) condensation of atoms in a Fermi gas of atoms with an attractive two-body interaction between atoms have been derived within the Hartree-Fock-Bogoliubov approximation from the path integral representation of the grand partition function. We have found that the order parameters for BEC and BCS are proportional to each other, which implies that BEC and BCS onsets simultaneously. We have also found that the common critical temperature of BEC and BCS increases as the average number of molecules increases and that the atom-molecule coupling enhances the common critical temperature.

Abstract:
A Lagrangian for quantum electrodynamics is found which makes it explicit that the photon mass is eventually set to zero in the physical part on observational ground. It remains possible to obtain a counterterm Lagrangian where the only non-gauge-invariant term is proportional to the squared divergence of the potential, while the photon propagator in momentum space falls off like the inverse squared power of k at large k, which indeed agrees with perturbative renormalizability. The resulting radiative corrections to the Coulomb potential in QED are also shown to be gauge-independent. A fundamental role of the space of four-vectors with components given by four-by-four matrices is therefore suggested by our scheme, where such matrices can be used to define a single gauge-fixing function in the functional integral.

Abstract:
This review article discusses fundamentals of dielectric, low-loss, optical micro-resonator sensing, including figures of merit and a variety of microcavity designs, and future perspectives in microcavity-based optical sensing. Resonance frequency and quality (Q) factor are altered as a means of detecting a small system perturbation, resulting in realization of optical sensing of a small amount of sample materials, down to even single molecules. Sensitivity, Q factor, minimum detectable index change, noises (in sensor system components and microcavity system including environments), microcavity size, and mode volume are essential parameters to be considered for optical sensing applications. Whispering gallery mode, photonic crystal, and slot-type microcavities typically provide compact, high-quality optical resonance modes for optical sensing applications. Surface Bloch modes induced on photonic crystals are shown to be a promising candidate thanks to large field overlap with a sample and ultra-high-Q resonances. Quantum optics effects based on microcavity quantum electrodynamics (QED) would provide novel single-photo-level detection of even single atoms and molecules via detection of doublet vacuum Rabi splitting peaks in strong coupling.

Abstract:
Atoms and molecules are important conceptual entities we invented to understand the physical world around us. The key to their usefulness lies in the organization of nuclear and electronic degrees of freedom into a single dynamical variable whose time evolution we can better imagine. The use of such effective variables in place of the true microscopic variables is possible because of the separation between nuclear/electronic and atomic/molecular time scales. Where separation of time scales occurs, identification of analogous objects in financial markets can help advance our understanding of their dynamics. To detect separated time scales and identify their associated effective degrees of freedom in financial markets, we devised a two-stage statistical clustering scheme to analyze the price movements of stocks in several equity markets. Through this two-time-scale clustering analysis, we discovered a hierarchy of levels of self-organization in real financial markets. We call these statistically robust self-organized dynamical structures financial atoms, financial molecules, and financial supermolecules. In general, the detailed compositions of these dynamical structures cannot be deduced based on raw financial intuition alone, and must be explained in terms of the underlying portfolios, and investment strategies of market players. More interestingly, we find that major market events such as the Chinese Correction and the Subprime Crisis leave many tell-tale signs within the correlational structures of financial molecules.